Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,17,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, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
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: | \(34.0881542099\) |
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 | 21.17.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 | \(0.666667\pi\) | |||||||
\(3\) | −3280.50 | − | 5681.99i | −0.500000 | − | 0.866025i | ||||
\(4\) | −32768.0 | − | 56755.8i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.73624e6 | − | 573128.i | −0.995046 | − | 0.0994185i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.15234e7 | + | 3.72796e7i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −2.14991e8 | + | 3.72375e8i | −0.500000 | + | 0.866025i | ||||
\(13\) | −1.20541e9 | −1.47771 | −0.738853 | − | 0.673866i | \(-0.764632\pi\) | ||||
−0.738853 | + | 0.673866i | \(0.764632\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.14748e9 | + | 3.71955e9i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.19275e10 | − | 2.06590e10i | 0.702297 | − | 1.21641i | −0.265361 | − | 0.964149i | \(-0.585491\pi\) |
0.967658 | − | 0.252265i | \(-0.0811755\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.55612e10 | + | 3.44734e10i | 0.411424 | + | 0.911444i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.62939e10 | − | 1.32145e11i | −0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.82430e11 | 1.00000 | ||||||||
\(28\) | 1.55437e11 | + | 3.44345e11i | 0.411424 | + | 0.911444i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.01393e11 | + | 1.75619e11i | 0.118882 | + | 0.205910i | 0.919325 | − | 0.393499i | \(-0.128736\pi\) |
−0.800443 | + | 0.599409i | \(0.795402\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.82111e12 | 1.00000 | ||||||||
\(37\) | −8.83011e11 | + | 1.52942e12i | −0.251393 | + | 0.435425i | −0.963909 | − | 0.266230i | \(-0.914222\pi\) |
0.712517 | + | 0.701655i | \(0.247555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.95435e12 | + | 6.84913e12i | 0.738853 | + | 1.27973i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.33692e13 | 1.99938 | 0.999691 | − | 0.0248759i | \(-0.00791906\pi\) | ||||
0.999691 | + | 0.0248759i | \(0.00791906\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 2.81793e13 | 1.00000 | ||||||||
\(49\) | 3.25760e13 | + | 6.57520e12i | 0.980232 | + | 0.197852i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.94989e13 | + | 6.84141e13i | 0.738853 | + | 1.27973i | ||||
\(53\) | 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 | ||||||||
\(57\) | −1.56513e14 | −1.40459 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.21444e13 | + | 1.59599e14i | −0.480651 | + | 0.832512i | −0.999754 | − | 0.0221997i | \(-0.992933\pi\) |
0.519102 | + | 0.854712i | \(0.326266\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.44829e14 | − | 2.01509e14i | 0.583622 | − | 0.812026i | ||||
\(64\) | 2.81475e14 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.89437e14 | − | 5.01320e14i | −0.712780 | − | 1.23457i | −0.963809 | − | 0.266592i | \(-0.914102\pi\) |
0.251029 | − | 0.967980i | \(-0.419231\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.19074e14 | − | 1.24547e15i | −0.891643 | − | 1.54437i | −0.837905 | − | 0.545816i | \(-0.816220\pi\) |
−0.0537374 | − | 0.998555i | \(-0.517113\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00565e14 | + | 8.67003e14i | −0.500000 | + | 0.866025i | ||||
\(76\) | −1.56336e15 | −1.40459 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.28746e15 | + | 2.22994e15i | −0.848626 | + | 1.46986i | 0.0338077 | + | 0.999428i | \(0.489237\pi\) |
−0.882434 | + | 0.470436i | \(0.844097\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.26510e14 | − | 1.60476e15i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 1.44666e15 | − | 2.01282e15i | 0.583622 | − | 0.812026i | ||||
\(85\) | 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 | ||||||||
\(91\) | 6.91452e15 | + | 6.90854e14i | 1.47039 | + | 0.146911i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.65243e14 | − | 1.15223e15i | 0.118882 | − | 0.205910i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.56216e16 | 1.99320 | 0.996601 | − | 0.0823822i | \(-0.0262528\pi\) | ||||
0.996601 | + | 0.0823822i | \(0.0262528\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000e15 | + | 8.66025e15i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.00871e16 | + | 1.74714e16i | −0.796288 | + | 1.37921i | 0.125729 | + | 0.992065i | \(0.459873\pi\) |
−0.922018 | + | 0.387147i | \(0.873460\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −9.25465e15 | − | 1.60295e16i | −0.500000 | − | 0.866025i | ||||
\(109\) | 1.76028e16 | + | 3.04889e16i | 0.883423 | + | 1.53013i | 0.847510 | + | 0.530779i | \(0.178101\pi\) |
0.0359135 | + | 0.999355i | \(0.488566\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.15869e16 | 0.502785 | ||||||||
\(112\) | 1.44503e16 | − | 2.01055e16i | 0.583622 | − | 0.812026i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.59445e16 | − | 4.49372e16i | 0.738853 | − | 1.27973i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.29749e16 | + | 3.97936e16i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.64492e15 | − | 1.15093e16i | 0.118882 | − | 0.205910i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.27734e17 | −1.88745 | −0.943725 | − | 0.330732i | \(-0.892704\pi\) | ||||
−0.943725 | + | 0.330732i | \(0.892704\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.66626e16 | − | 1.32783e17i | −0.999691 | − | 1.73151i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.02593e16 | + | 1.11669e17i | −0.819752 | + | 1.14057i | ||||
\(134\) | 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 | ||||||||
\(139\) | 3.06396e16 | 0.219870 | 0.109935 | − | 0.993939i | \(-0.464936\pi\) | ||||
0.109935 | + | 0.993939i | \(0.464936\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −9.24421e16 | − | 1.60114e17i | −0.500000 | − | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.95053e16 | − | 2.06666e17i | −0.318771 | − | 0.947832i | ||||
\(148\) | 1.15738e17 | 0.502785 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.33768e17 | + | 4.04898e17i | 0.864906 | + | 1.49806i | 0.867140 | + | 0.498064i | \(0.165955\pi\) |
−0.00223432 | + | 0.999998i | \(0.500711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.59152e17 | − | 4.48865e17i | 0.738853 | − | 1.27973i | ||||
\(157\) | 3.68491e17 | + | 6.38245e17i | 0.998228 | + | 1.72898i | 0.550652 | + | 0.834735i | \(0.314379\pi\) |
0.447576 | + | 0.894246i | \(0.352288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.87763e17 | + | 3.25215e17i | −0.376798 | + | 0.652634i | −0.990594 | − | 0.136831i | \(-0.956308\pi\) |
0.613796 | + | 0.789465i | \(0.289642\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.87598e17 | 1.18362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.13440e17 | + | 8.89304e17i | 0.702297 | + | 1.21641i | ||||
\(172\) | −7.65761e17 | − | 1.32634e18i | −0.999691 | − | 1.73151i | ||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.61904e17 | + | 8.01742e17i | 0.411424 | + | 0.911444i | ||||
\(176\) | 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 | ||||||||
\(181\) | −1.10757e18 | −0.961482 | −0.480741 | − | 0.876863i | \(-0.659632\pi\) | ||||
−0.480741 | + | 0.876863i | \(0.659632\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.20912e18 | 0.961302 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.62008e18 | − | 1.61868e17i | −0.995046 | − | 0.0994185i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | −9.23379e17 | − | 1.59934e18i | −0.500000 | − | 0.866025i | ||||
\(193\) | −1.13278e18 | − | 1.96203e18i | −0.588420 | − | 1.01917i | −0.994440 | − | 0.105309i | \(-0.966417\pi\) |
0.406020 | − | 0.913864i | \(-0.366916\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.94269e17 | − | 2.06433e18i | −0.318771 | − | 0.947832i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.54740e17 | + | 1.65366e18i | 0.388205 | + | 0.672390i | 0.992208 | − | 0.124592i | \(-0.0397620\pi\) |
−0.604003 | + | 0.796982i | \(0.706429\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.89900e18 | + | 3.28916e18i | −0.712780 | + | 1.23457i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.58860e18 | − | 4.48359e18i | 0.738853 | − | 1.27973i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.82385e18 | −1.99141 | −0.995705 | − | 0.0925844i | \(-0.970487\pi\) | ||||
−0.995705 | + | 0.0925844i | \(0.970487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.80966e17 | − | 1.06550e18i | −0.0978219 | − | 0.216709i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.71785e18 | + | 8.17155e18i | −0.891643 | + | 1.54437i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.01164e19 | 1.65419 | 0.827096 | − | 0.562061i | \(-0.189991\pi\) | ||||
0.827096 | + | 0.562061i | \(0.189991\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.56841e18 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 5.12861e18 | + | 8.88301e18i | 0.702297 | + | 1.21641i | ||||
\(229\) | 6.27243e18 | − | 1.08642e19i | 0.829377 | − | 1.43652i | −0.0691508 | − | 0.997606i | \(-0.522029\pi\) |
0.898528 | − | 0.438917i | \(-0.144638\pi\) | |||||||
\(230\) | 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 | ||||||||
\(237\) | 1.68940e19 | 1.69725 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.10913e18 | − | 7.11722e18i | −0.361088 | − | 0.625423i | 0.627052 | − | 0.778977i | \(-0.284261\pi\) |
−0.988140 | + | 0.153554i | \(0.950928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.07883e18 | + | 1.05288e19i | −0.500000 | + | 0.866025i | ||||
\(244\) | 1.20775e19 | 0.961302 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.43775e19 | + | 2.49026e19i | −1.03779 | + | 1.79750i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −1.61826e19 | − | 1.61686e18i | −0.995046 | − | 0.0994185i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.22337e18 | − | 1.59753e19i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.94172e18 | − | 8.26705e18i | 0.293436 | − | 0.408275i | ||||
\(260\) | 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 | ||||||||
\(268\) | −1.89685e19 | + | 3.28545e19i | −0.712780 | + | 1.23457i | ||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.46294e19 | − | 4.26593e19i | 0.846640 | − | 1.46642i | −0.0375498 | − | 0.999295i | \(-0.511955\pi\) |
0.884190 | − | 0.467128i | \(-0.154711\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.87577e19 | − | 4.15546e19i | −0.607964 | − | 1.34685i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.29219e19 | − | 5.70223e19i | −0.949830 | − | 1.64515i | −0.745778 | − | 0.666195i | \(-0.767922\pi\) |
−0.204053 | − | 0.978960i | \(-0.565411\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.72931e18 | −0.237764 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.02236e19 | + | 6.96693e19i | 0.977663 | + | 1.69336i | 0.670851 | + | 0.741592i | \(0.265929\pi\) |
0.306812 | + | 0.951770i | \(0.400738\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.43306e19 | + | 4.21418e19i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.12466e19 | − | 8.87617e19i | −0.996601 | − | 1.72616i | ||||
\(292\) | −4.71253e19 | + | 8.16233e19i | −0.891643 | + | 1.54437i | ||||
\(293\) | 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 | ||||||||
\(300\) | 6.56100e19 | 1.00000 | ||||||||
\(301\) | −1.34051e20 | − | 1.33935e19i | −1.98948 | − | 0.198775i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.12283e19 | + | 8.87299e19i | 0.702297 | + | 1.21641i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.10946e20 | 1.40606 | 0.703028 | − | 0.711162i | \(-0.251831\pi\) | ||||
0.703028 | + | 0.711162i | \(0.251831\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.32364e20 | 1.59258 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.52667e19 | − | 1.13045e20i | 0.708495 | − | 1.22715i | −0.256921 | − | 0.966433i | \(-0.582708\pi\) |
0.965415 | − | 0.260716i | \(-0.0839588\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.68750e20 | 1.69725 | ||||||||
\(317\) | 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 | ||||||||
\(324\) | −6.07198e19 | + | 1.05170e20i | −0.500000 | + | 0.866025i | ||||
\(325\) | 9.19655e19 | + | 1.59289e20i | 0.738853 | + | 1.27973i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.15492e20 | − | 2.00038e20i | 0.883423 | − | 1.53013i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.30376e20 | + | 2.25819e20i | −0.904847 | + | 1.56724i | −0.0837255 | + | 0.996489i | \(0.526682\pi\) |
−0.821122 | + | 0.570753i | \(0.806651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.80107e19 | − | 6.58365e19i | −0.251393 | − | 0.435425i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.61643e20 | − | 1.61503e19i | −0.995046 | − | 0.0994185i | ||||
\(337\) | −1.91944e20 | −1.15381 | −0.576905 | − | 0.816811i | \(-0.695740\pi\) | ||||
−0.576905 | + | 0.816811i | \(0.695740\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.83095e20 | − | 5.63871e19i | −0.955705 | − | 0.294325i | ||||
\(344\) | 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 | ||||||||
\(349\) | 4.35999e20 | 1.98099 | 0.990494 | − | 0.137553i | \(-0.0439236\pi\) | ||||
0.990494 | + | 0.137553i | \(0.0439236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.40444e20 | −1.47771 | ||||||||
\(352\) | 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 | ||||||||
\(361\) | −1.40310e20 | − | 2.43024e20i | −0.486442 | − | 0.842543i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.01476e20 | 1.00000 | ||||||||
\(364\) | −1.87365e20 | − | 4.15078e20i | −0.607964 | − | 1.34685i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.00369e20 | − | 5.20255e20i | −0.912697 | − | 1.58084i | −0.810238 | − | 0.586101i | \(-0.800662\pi\) |
−0.102459 | − | 0.994737i | \(-0.532671\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.71947e19 | −0.237764 | ||||||||
\(373\) | −2.63443e20 | + | 4.56297e20i | −0.703099 | + | 1.21780i | 0.264274 | + | 0.964448i | \(0.414868\pi\) |
−0.967373 | + | 0.253356i | \(0.918466\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.95267e20 | 0.693588 | 0.346794 | − | 0.937941i | \(-0.387270\pi\) | ||||
0.346794 | + | 0.937941i | \(0.387270\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.19030e20 | + | 7.25781e20i | 0.943725 | + | 1.63458i | ||||
\(382\) | 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 | ||||||||
\(387\) | −5.02983e20 | + | 8.71192e20i | −0.999691 | + | 1.73151i | ||||
\(388\) | −5.11888e20 | − | 8.86616e20i | −0.996601 | − | 1.72616i | ||||
\(389\) | 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 | ||||||||
\(397\) | 7.51236e19 | − | 1.30118e20i | 0.121745 | − | 0.210869i | −0.798711 | − | 0.601715i | \(-0.794484\pi\) |
0.920456 | + | 0.390846i | \(0.127818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.97795e20 | + | 8.97018e19i | 1.39764 | + | 0.139643i | ||||
\(400\) | 6.55360e20 | 1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.22221e20 | − | 2.11693e20i | −0.175673 | − | 0.304274i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.33246e20 | + | 1.27002e21i | 0.936404 | + | 1.62190i | 0.772112 | + | 0.635487i | \(0.219201\pi\) |
0.164292 | + | 0.986412i | \(0.447466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.32214e21 | 1.59258 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.00513e20 | − | 1.74094e20i | −0.109935 | − | 0.190413i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.98700e20 | 0.302676 | 0.151338 | − | 0.988482i | \(-0.451642\pi\) | ||||
0.151338 | + | 0.988482i | \(0.451642\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.20033e20 | − | 8.62686e20i | 0.561037 | − | 0.780602i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −6.06513e20 | + | 1.05051e21i | −0.500000 | + | 0.866025i | ||||
\(433\) | −2.37647e21 | −1.92322 | −0.961609 | − | 0.274424i | \(-0.911513\pi\) | ||||
−0.961609 | + | 0.274424i | \(0.911513\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.15361e21 | − | 1.99812e21i | 0.883423 | − | 1.53013i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.01972e20 | + | 1.56226e21i | −0.653848 | + | 1.13250i | 0.328333 | + | 0.944562i | \(0.393513\pi\) |
−0.982181 | + | 0.187937i | \(0.939820\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.46265e20 | + | 1.07290e21i | −0.661461 | + | 0.749980i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | −3.79679e20 | − | 6.57623e20i | −0.251393 | − | 0.435425i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.61461e21 | − | 1.61321e20i | −0.995046 | − | 0.0994185i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.53375e21 | − | 2.65653e21i | 0.864906 | − | 1.49806i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.12710e20 | − | 3.68425e20i | 0.111804 | − | 0.193651i | −0.804693 | − | 0.593691i | \(-0.797670\pi\) |
0.916498 | + | 0.400040i | \(0.131004\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.88510e21 | −1.83973 | −0.919864 | − | 0.392237i | \(-0.871701\pi\) | ||||
−0.919864 | + | 0.392237i | \(0.871701\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | −3.40060e21 | −1.47771 | ||||||||
\(469\) | 1.37296e21 | + | 3.04157e21i | 0.586510 | + | 1.29932i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.41767e21 | − | 4.18753e21i | 0.998228 | − | 1.72898i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.63999e21 | −1.40459 | ||||||||
\(476\) | 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 | ||||||||
\(481\) | 1.06439e21 | − | 1.84358e21i | 0.371485 | − | 0.643430i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.01136e21 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.09453e21 | + | 5.35989e21i | 0.978055 | + | 1.69404i | 0.669460 | + | 0.742848i | \(0.266526\pi\) |
0.308595 | + | 0.951193i | \(0.400141\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.46382e21 | 0.753597 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.70963e20 | −0.237764 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.19157e21 | − | 2.06386e21i | 0.309967 | − | 0.536879i | −0.668388 | − | 0.743813i | \(-0.733015\pi\) |
0.978355 | + | 0.206934i | \(0.0663486\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | −2.58372e21 | − | 4.47513e21i | −0.591808 | − | 1.02504i | ||||
\(508\) | 4.18557e21 | + | 7.24963e21i | 0.943725 | + | 1.63458i | ||||
\(509\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.41097e21 | + | 7.55646e21i | 0.733686 | + | 1.62537i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.36868e21 | − | 5.83473e21i | 0.702297 | − | 1.21641i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.02416e21 | + | 8.70210e21i | −0.999691 | + | 1.73151i | ||||
\(517\) | 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 | ||||||||
\(523\) | −1.08466e21 | + | 1.87868e21i | −0.193766 | + | 0.335613i | −0.946495 | − | 0.322717i | \(-0.895404\pi\) |
0.752729 | + | 0.658331i | \(0.228737\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.36826e21 | − | 4.68645e21i | 0.583622 | − | 0.812026i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.06631e21 | − | 5.31100e21i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.96782e21 | + | 8.96006e20i | 1.39764 | + | 0.139643i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.64546e21 | − | 2.85003e21i | 0.224239 | − | 0.388393i | −0.731852 | − | 0.681463i | \(-0.761344\pi\) |
0.956091 | + | 0.293071i | \(0.0946772\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.63337e21 | + | 6.29318e21i | 0.480741 | + | 0.832667i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.22073e22 | −1.52307 | −0.761536 | − | 0.648122i | \(-0.775555\pi\) | ||||
−0.761536 | + | 0.648122i | \(0.775555\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.96651e21 | − | 6.87020e21i | −0.480651 | − | 0.832512i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.66322e21 | − | 1.20536e22i | 0.990554 | − | 1.37821i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00400e21 | − | 1.73898e21i | −0.109935 | − | 0.190413i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.81694e22 | −2.95450 | ||||||||
\(560\) | 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 | ||||||||
\(567\) | 4.39495e21 | + | 9.73631e21i | 0.411424 | + | 0.911444i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.31220e21 | − | 5.73690e21i | −0.293108 | − | 0.507678i | 0.681435 | − | 0.731879i | \(-0.261356\pi\) |
−0.974543 | + | 0.224201i | \(0.928023\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.05829e21 | + | 1.04933e22i | −0.500000 | + | 0.866025i | ||||
\(577\) | −1.08257e22 | − | 1.87506e22i | −0.881148 | − | 1.52619i | −0.850066 | − | 0.526676i | \(-0.823438\pi\) |
−0.0310817 | − | 0.999517i | \(-0.509895\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.43217e21 | + | 1.28729e22i | −0.588420 | + | 1.01917i | ||||
\(580\) | 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 | \(\pi\) | |||||||||
\(588\) | −9.45198e21 | + | 1.07169e22i | −0.661461 | + | 0.749980i | ||||
\(589\) | 4.83749e21 | 0.333962 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.79251e21 | − | 6.56881e21i | −0.251393 | − | 0.435425i | ||||
\(593\) | 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 | ||||||||
\(597\) | 6.26405e21 | − | 1.08497e22i | 0.388205 | − | 0.672390i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.87461e22 | 1.68882 | 0.844411 | − | 0.535696i | \(-0.179951\pi\) | ||||
0.844411 | + | 0.535696i | \(0.179951\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.49186e22 | 1.42556 | ||||||||
\(604\) | 1.53202e22 | − | 2.65354e22i | 0.864906 | − | 1.49806i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.19870e21 | − | 3.80826e21i | 0.119304 | − | 0.206641i | −0.800188 | − | 0.599749i | \(-0.795267\pi\) |
0.919492 | + | 0.393108i | \(0.128600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.98133e22 | + | 3.43176e22i | 0.993740 | + | 1.72121i | 0.593622 | + | 0.804744i | \(0.297698\pi\) |
0.400118 | + | 0.916464i | \(0.368969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.03008e22 | + | 3.51621e22i | 0.941865 | + | 1.63136i | 0.761911 | + | 0.647682i | \(0.224262\pi\) |
0.179954 | + | 0.983675i | \(0.442405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.39676e22 | −1.47771 | ||||||||
\(625\) | −1.16415e22 | + | 2.01637e22i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.41494e22 | − | 4.18280e22i | 0.998228 | − | 1.72898i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.02373e22 | −0.407336 | −0.203668 | − | 0.979040i | \(-0.565286\pi\) | ||||
−0.203668 | + | 0.979040i | \(0.565286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.56661e22 | + | 4.44550e22i | 0.995705 | + | 1.72461i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.92674e22 | − | 7.92581e21i | −1.44850 | − | 0.292367i | ||||
\(638\) | 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 | ||||||||
\(643\) | −3.51207e22 | −1.20192 | −0.600960 | − | 0.799279i | \(-0.705215\pi\) | ||||
−0.600960 | + | 0.799279i | \(0.705215\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | −4.47637e21 | + | 6.22822e21i | −0.138764 | + | 0.193071i | ||||
\(652\) | 2.46105e22 | 0.753597 | ||||||||
\(653\) | 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 | ||||||||
\(657\) | 6.19076e22 | 1.78329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.80091e21 | − | 1.35116e22i | −0.214059 | − | 0.370761i | 0.738922 | − | 0.673791i | \(-0.235335\pi\) |
−0.952981 | + | 0.303030i | \(0.902002\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.31867e22 | − | 5.74811e22i | −0.827096 | − | 1.43257i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.33834e22 | 1.98134 | 0.990670 | − | 0.136283i | \(-0.0435155\pi\) | ||||
0.990670 | + | 0.136283i | \(0.0435155\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.15477e22 | − | 3.73216e22i | −0.500000 | − | 0.866025i | ||||
\(676\) | −2.58080e22 | − | 4.47008e22i | −0.591808 | − | 1.02504i | ||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.96092e22 | − | 8.95317e21i | −1.98333 | − | 0.198161i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | 3.36488e22 | − | 5.82814e22i | 0.702297 | − | 1.21641i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.23068e22 | −1.65875 | ||||||||
\(688\) | −5.01849e22 | + | 8.69228e22i | −0.999691 | + | 1.73151i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.88313e22 | + | 8.45782e22i | −0.939450 | + | 1.62718i | −0.172950 | + | 0.984931i | \(0.555330\pi\) |
−0.766500 | + | 0.642244i | \(0.778003\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.36446e22 | − | 4.68117e22i | 0.583622 | − | 0.812026i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.10643e22 | + | 3.64844e22i | 0.353105 | + | 0.611595i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.50674e22 | + | 9.53795e22i | −0.862431 | + | 1.49378i | 0.00714362 | + | 0.999974i | \(0.497726\pi\) |
−0.869575 | + | 0.493801i | \(0.835607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.54209e22 | − | 9.59918e22i | −0.848626 | − | 1.46986i | ||||
\(712\) | 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 | ||||||||
\(721\) | 6.78757e22 | − | 9.44392e22i | 0.929463 | − | 1.29321i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.69600e22 | + | 4.66961e22i | −0.361088 | + | 0.625423i | ||||
\(724\) | 3.62927e22 | + | 6.28608e22i | 0.480741 | + | 0.832667i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.28031e23 | 1.64073 | 0.820367 | − | 0.571837i | \(-0.193769\pi\) | ||||
0.820367 | + | 0.571837i | \(0.193769\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.97664e22 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.96204e22 | − | 6.86245e22i | −0.480651 | − | 0.832512i | ||||
\(733\) | 4.02029e22 | − | 6.96335e22i | 0.482420 | − | 0.835577i | −0.517376 | − | 0.855758i | \(-0.673091\pi\) |
0.999796 | + | 0.0201815i | \(0.00642441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.98365e22 | + | 1.38281e23i | 0.897524 | + | 1.55456i | 0.830650 | + | 0.556795i | \(0.187969\pi\) |
0.0668739 | + | 0.997761i | \(0.478697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.88662e23 | 2.07558 | ||||||||
\(742\) | 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 | ||||||||
\(751\) | −5.83907e22 | + | 1.01136e23i | −0.577064 | + | 0.999505i | 0.418750 | + | 0.908102i | \(0.362468\pi\) |
−0.995814 | + | 0.0914030i | \(0.970865\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.38999e22 | + | 9.72533e22i | 0.411424 | + | 0.911444i | ||||
\(757\) | −4.29074e21 | −0.0397892 | −0.0198946 | − | 0.999802i | \(-0.506333\pi\) | ||||
−0.0198946 | + | 0.999802i | \(0.506333\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −8.34997e22 | − | 1.84980e23i | −0.726923 | − | 1.61038i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −6.05145e22 | + | 1.04814e23i | −0.500000 | + | 0.866025i | ||||
\(769\) | 1.30797e22 | 0.106951 | 0.0534756 | − | 0.998569i | \(-0.482970\pi\) | ||||
0.0534756 | + | 0.998569i | \(0.482970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.42379e22 | + | 1.28584e23i | −0.588420 | + | 1.01917i | ||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.54714e22 | − | 2.67973e22i | 0.118882 | − | 0.205910i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.64651e22 | − | 6.64076e21i | −0.500294 | − | 0.0499862i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.44132e22 | + | 1.07048e23i | −0.661461 | + | 0.749980i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.09332e22 | − | 1.40180e23i | −0.549957 | − | 0.952553i | −0.998277 | − | 0.0586800i | \(-0.981311\pi\) |
0.448320 | − | 0.893873i | \(-0.352023\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.11072e23 | − | 1.92382e23i | 0.710261 | − | 1.23021i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.25699e22 | − | 1.08374e23i | 0.388205 | − | 0.672390i | ||||
\(797\) | 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 | ||||||||
\(804\) | 2.48905e23 | 1.42556 | ||||||||
\(805\) | 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 | ||||||||
\(811\) | −3.66385e23 | −1.95781 | −0.978906 | − | 0.204312i | \(-0.934504\pi\) | ||||
−0.978906 | + | 0.204312i | \(0.934504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.23186e23 | −1.69328 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.78736e23 | − | 4.82785e23i | 1.40416 | − | 2.43208i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.74579e23 | + | 2.42901e23i | −0.862422 | + | 1.19994i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.61208e23 | − | 2.79221e23i | −0.765929 | − | 1.32663i | −0.939754 | − | 0.341851i | \(-0.888946\pi\) |
0.173826 | − | 0.984776i | \(-0.444387\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.25302e22 | + | 1.42947e23i | 0.369979 | + | 0.640822i | 0.989562 | − | 0.144109i | \(-0.0460316\pi\) |
−0.619583 | + | 0.784931i | \(0.712698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.16000e23 | + | 3.74123e23i | −0.949830 | + | 1.64515i | ||||
\(832\) | −3.39293e23 | −1.47771 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.86365e22 | + | 4.95999e22i | 0.118882 | + | 0.205910i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.50246e23 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.56372e23 | + | 4.44049e23i | 0.995705 | + | 1.72461i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.54596e23 | − | 2.15098e23i | 0.583622 | − | 0.812026i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.63907e23 | − | 4.57100e23i | 0.977663 | − | 1.69336i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.67842e23 | −1.31241 | −0.656205 | − | 0.754583i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −2.57599e22 | + | 4.46175e22i | −0.0868958 | + | 0.150508i | −0.906197 | − | 0.422855i | \(-0.861028\pi\) |
0.819302 | + | 0.573363i | \(0.194361\pi\) | |||||||
\(860\) | 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 | ||||||||
\(867\) | 3.19266e23 | 1.00000 | ||||||||
\(868\) | −4.47132e22 | + | 6.22120e22i | −0.138764 | + | 0.193071i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.48890e23 | + | 6.04296e23i | 1.05328 | + | 1.82433i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.36229e23 | + | 5.82366e23i | −0.996601 | + | 1.72616i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.18378e23 | 1.78329 | ||||||||
\(877\) | 3.27719e23 | − | 5.67626e23i | 0.936494 | − | 1.62205i | 0.164545 | − | 0.986370i | \(-0.447384\pi\) |
0.771949 | − | 0.635685i | \(-0.219282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.26584e23 | −0.883708 | −0.441854 | − | 0.897087i | \(-0.645679\pi\) | ||||
−0.441854 | + | 0.897087i | \(0.645679\pi\) | |||||||
\(884\) | 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 | ||||||||
\(889\) | 7.32711e23 | + | 7.32077e22i | 1.87810 | + | 0.187647i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.31493e23 | − | 5.74163e23i | −0.827096 | − | 1.43257i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.15234e23 | − | 3.72796e23i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.63653e23 | + | 8.05615e23i | 0.822593 | + | 1.82232i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.55648e23 | + | 7.89206e23i | 0.994881 | + | 1.72318i | 0.584953 | + | 0.811067i | \(0.301113\pi\) |
0.409928 | + | 0.912118i | \(0.365554\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 3.36109e23 | − | 5.82157e23i | 0.702297 | − | 1.21641i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.22140e23 | −1.65875 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.91158e23 | + | 8.50711e23i | −0.965378 | + | 1.67208i | −0.256782 | + | 0.966469i | \(0.582662\pi\) |
−0.708596 | + | 0.705614i | \(0.750671\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.63957e23 | − | 6.30392e23i | −0.703028 | − | 1.21768i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.69474e23 | 0.502785 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.34218e23 | − | 7.52088e23i | −0.796288 | − | 1.37921i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.24388e23 | − | 5.94563e23i | 0.929084 | − | 1.05342i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.13082e24 | −1.90317 | −0.951585 | − | 0.307387i | \(-0.900546\pi\) | ||||
−0.951585 | + | 0.307387i | \(0.900546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.56429e23 | −1.41699 | ||||||||
\(940\) | 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 | \(0.666667\pi\) | |||||||
\(948\) | −5.53584e23 | − | 9.58835e23i | −0.848626 | − | 1.46986i | ||||
\(949\) | 8.66780e23 | + | 1.50131e24i | 1.31759 | + | 2.28213i | ||||
\(950\) | 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 | ||||||||
\(961\) | 3.43150e23 | − | 5.94354e23i | 0.471734 | − | 0.817067i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.69296e23 | + | 4.66434e23i | −0.361088 | + | 0.625423i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.52912e24 | −1.99999 | −0.999997 | − | 0.00234625i | \(-0.999253\pi\) | ||||
−0.999997 | + | 0.00234625i | \(0.999253\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 7.96765e23 | 1.00000 | ||||||||
\(973\) | −1.75756e23 | − | 1.75604e22i | −0.218780 | − | 0.0218591i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.03386e23 | − | 1.04509e24i | 0.738853 | − | 1.27973i | ||||
\(976\) | −3.95757e23 | − | 6.85471e23i | −0.480651 | − | 0.832512i | ||||
\(977\) | 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 | ||||||||
\(981\) | −1.51548e24 | −1.76685 | ||||||||
\(982\) | 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 | ||||||||
\(988\) | 1.88449e24 | 2.07558 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.08386e23 | + | 5.34141e23i | 0.331517 | + | 0.574204i | 0.982810 | − | 0.184622i | \(-0.0591062\pi\) |
−0.651293 | + | 0.758827i | \(0.725773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.71080e24 | 1.80969 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.18443e22 | + | 1.24438e23i | 0.0735920 | + | 0.127465i | 0.900473 | − | 0.434912i | \(-0.143220\pi\) |
−0.826881 | + | 0.562377i | \(0.809887\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.49389e23 | + | 4.31954e23i | −0.251393 | + | 0.435425i |
(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 | 21.17.h.a.2.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.17.h.a.2.1 | ✓ | 2 | |
7.4 | even | 3 | inner | 21.17.h.a.11.1 | yes | 2 | |
21.11 | odd | 6 | inner | 21.17.h.a.11.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.17.h.a.2.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.17.h.a.2.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.17.h.a.11.1 | yes | 2 | 7.4 | even | 3 | inner | |
21.17.h.a.11.1 | yes | 2 | 21.11 | odd | 6 | inner |