Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,11,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, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
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: | \(13.3425023061\) |
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 | 11.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.11 |
Dual form | 21.11.h.a.2.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | 121.500 | − | 210.444i | 0.500000 | − | 0.866025i | ||||
\(4\) | −512.000 | + | 886.810i | −0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5453.50 | − | 15897.6i | 0.324478 | − | 0.945893i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −29524.5 | − | 51137.9i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 124416. | + | 215495.i | 0.500000 | + | 0.866025i | ||||
\(13\) | −560257. | −1.50893 | −0.754467 | − | 0.656337i | \(-0.772105\pi\) | ||||
−0.754467 | + | 0.656337i | \(0.772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −524288. | − | 908093.i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.46313e6 | − | 4.26626e6i | −0.994761 | − | 1.72298i | −0.585916 | − | 0.810372i | \(-0.699265\pi\) |
−0.408844 | − | 0.912604i | \(-0.634068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.68296e6 | − | 3.07922e6i | −0.656929 | − | 0.753953i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88281e6 | + | 8.45728e6i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43489e7 | −1.00000 | ||||||||
\(28\) | 1.13060e7 | + | 1.29758e7i | 0.656929 | + | 0.753953i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.49218e7 | − | 4.31658e7i | 0.870504 | − | 1.50776i | 0.00902749 | − | 0.999959i | \(-0.497126\pi\) |
0.861476 | − | 0.507798i | \(-0.169540\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.04662e7 | 1.00000 | ||||||||
\(37\) | 4.71595e7 | + | 8.16826e7i | 0.680081 | + | 1.17793i | 0.974956 | + | 0.222399i | \(0.0713887\pi\) |
−0.294875 | + | 0.955536i | \(0.595278\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.80712e7 | + | 1.17903e8i | −0.754467 | + | 1.30678i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.11109e8 | 1.43603 | 0.718016 | − | 0.696027i | \(-0.245051\pi\) | ||||
0.718016 | + | 0.696027i | \(0.245051\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −2.54804e8 | −1.00000 | ||||||||
\(49\) | −2.22994e8 | − | 1.73395e8i | −0.789428 | − | 0.613843i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.86852e8 | − | 4.96842e8i | 0.754467 | − | 1.30678i | ||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.19708e9 | −1.98952 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.86124e7 | + | 1.70802e8i | 0.116757 | + | 0.202229i | 0.918481 | − | 0.395466i | \(-0.129417\pi\) |
−0.801724 | + | 0.597695i | \(0.796084\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.73984e8 | + | 1.90489e8i | −0.981407 | + | 0.191941i | ||||
\(64\) | 1.07374e9 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.30441e8 | − | 1.09196e9i | 0.466950 | − | 0.808782i | −0.532337 | − | 0.846533i | \(-0.678686\pi\) |
0.999287 | + | 0.0377510i | \(0.0120194\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.78842e8 | + | 1.69540e9i | −0.472170 | + | 0.817823i | −0.999493 | − | 0.0318424i | \(-0.989863\pi\) |
0.527323 | + | 0.849665i | \(0.323196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.18652e9 | + | 2.05512e9i | 0.500000 | + | 0.866025i | ||||
\(76\) | 5.04448e9 | 1.98952 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.05044e9 | − | 1.81942e9i | −0.341378 | − | 0.591285i | 0.643310 | − | 0.765605i | \(-0.277560\pi\) |
−0.984689 | + | 0.174321i | \(0.944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.74339e9 | + | 3.01964e9i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 4.10436e9 | − | 8.02718e8i | 0.981407 | − | 0.191941i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.05536e9 | + | 8.90676e9i | −0.489616 | + | 1.42729i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.05599e9 | − | 1.04893e10i | −0.870504 | − | 1.50776i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.84916e8 | 0.103049 | 0.0515245 | − | 0.998672i | \(-0.483592\pi\) | ||||
0.0515245 | + | 0.998672i | \(0.483592\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000e9 | − | 8.66025e9i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.07685e10 | − | 1.86516e10i | −0.928902 | − | 1.60891i | −0.785162 | − | 0.619290i | \(-0.787421\pi\) |
−0.143740 | − | 0.989616i | \(-0.545913\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 7.34664e9 | − | 1.27248e10i | 0.500000 | − | 0.866025i | ||||
\(109\) | −1.53268e10 | + | 2.65469e10i | −0.996139 | + | 1.72536i | −0.422043 | + | 0.906576i | \(0.638687\pi\) |
−0.574096 | + | 0.818788i | \(0.694646\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.29195e10 | 1.36016 | ||||||||
\(112\) | −1.72957e10 | + | 3.38265e9i | −0.981407 | + | 0.191941i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.65413e10 | + | 2.86504e10i | 0.754467 | + | 1.30678i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.29687e10 | − | 2.24625e10i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.55199e10 | + | 4.42018e10i | 0.870504 | + | 1.50776i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.44093e10 | 1.64685 | 0.823426 | − | 0.567424i | \(-0.192060\pi\) | ||||
0.823426 | + | 0.567424i | \(0.192060\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.56497e10 | − | 4.44266e10i | 0.718016 | − | 1.24364i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.12560e10 | + | 1.58918e10i | −1.95253 | + | 0.381870i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.02935e11 | 1.98377 | 0.991883 | − | 0.127156i | \(-0.0405849\pi\) | ||||
0.991883 | + | 0.127156i | \(0.0405849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.09587e10 | + | 5.36220e10i | −0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.35838e10 | + | 2.58602e10i | −0.926318 | + | 0.376743i | ||||
\(148\) | −9.65826e10 | −1.36016 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.02493e9 | + | 8.70343e9i | −0.0640096 | + | 0.110868i | −0.896254 | − | 0.443541i | \(-0.853722\pi\) |
0.832245 | + | 0.554409i | \(0.187055\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.97049e10 | − | 1.20732e11i | −0.754467 | − | 1.30678i | ||||
\(157\) | 8.94251e10 | − | 1.54889e11i | 0.937479 | − | 1.62376i | 0.167325 | − | 0.985902i | \(-0.446487\pi\) |
0.770153 | − | 0.637859i | \(-0.220180\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.14947e11 | − | 1.99093e11i | −0.998983 | − | 1.73029i | −0.538546 | − | 0.842596i | \(-0.681026\pi\) |
−0.460437 | − | 0.887692i | \(-0.652307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.76029e11 | 1.27688 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.45445e11 | + | 2.51918e11i | −0.994761 | + | 1.72298i | ||||
\(172\) | −1.08088e11 | + | 1.87213e11i | −0.718016 | + | 1.24364i | ||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.07822e11 | + | 1.23747e11i | 0.656929 | + | 0.753953i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.39127e11 | 1.74570 | 0.872849 | − | 0.487991i | \(-0.162270\pi\) | ||||
0.872849 | + | 0.487991i | \(0.162270\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.79256e10 | 0.233514 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.82518e10 | + | 2.28114e11i | −0.324478 | + | 0.945893i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 1.30460e11 | − | 2.25963e11i | 0.500000 | − | 0.866025i | ||||
\(193\) | 5.23711e10 | − | 9.07094e10i | 0.195571 | − | 0.338740i | −0.751516 | − | 0.659715i | \(-0.770677\pi\) |
0.947088 | + | 0.320975i | \(0.104011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.67942e11 | − | 1.08975e11i | 0.926318 | − | 0.376743i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.04037e11 | + | 1.80197e11i | −0.333366 | + | 0.577408i | −0.983170 | − | 0.182695i | \(-0.941518\pi\) |
0.649803 | + | 0.760102i | \(0.274851\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.53197e11 | − | 2.65345e11i | −0.466950 | − | 0.808782i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.93736e11 | + | 5.08766e11i | 0.754467 | + | 1.30678i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.52947e11 | −1.80033 | −0.900165 | − | 0.435548i | \(-0.856555\pi\) | ||||
−0.900165 | + | 0.435548i | \(0.856555\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.50323e11 | − | 6.31602e11i | −1.14372 | − | 1.31264i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.37859e11 | + | 4.11983e11i | 0.472170 | + | 0.817823i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.01050e12 | −1.83236 | −0.916181 | − | 0.400764i | \(-0.868745\pi\) | ||||
−0.916181 | + | 0.400764i | \(0.868745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.76650e11 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | 6.12904e11 | − | 1.06158e12i | 0.994761 | − | 1.72298i | ||||
\(229\) | −4.35317e11 | − | 7.53991e11i | −0.691239 | − | 1.19726i | −0.971432 | − | 0.237317i | \(-0.923732\pi\) |
0.280193 | − | 0.959944i | \(-0.409601\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.10514e11 | −0.682757 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.80808e10 | + | 4.86373e10i | −0.0345401 | + | 0.0598252i | −0.882779 | − | 0.469789i | \(-0.844330\pi\) |
0.848239 | + | 0.529614i | \(0.177663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.23644e11 | + | 7.33773e11i | 0.500000 | + | 0.866025i | ||||
\(244\) | −2.01958e11 | −0.233514 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.37998e12 | + | 2.39020e12i | 1.50103 | + | 2.59986i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 3.29752e11 | − | 9.61269e11i | 0.324478 | − | 0.945893i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.49756e11 | + | 9.52205e11i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.55574e12 | − | 3.04268e11i | 1.33487 | − | 0.261070i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.45572e11 | + | 1.11816e12i | 0.466950 | + | 0.808782i | ||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.07601e12 | − | 1.86371e12i | −0.736157 | − | 1.27506i | −0.954214 | − | 0.299125i | \(-0.903305\pi\) |
0.218058 | − | 0.975936i | \(-0.430028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.50315e12 | + | 1.72515e12i | 0.991263 | + | 1.13767i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.35818e12 | − | 2.35244e12i | 0.832836 | − | 1.44252i | −0.0629434 | − | 0.998017i | \(-0.520049\pi\) |
0.895780 | − | 0.444498i | \(-0.146618\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.94321e12 | −1.74101 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.09893e11 | + | 1.57598e12i | −0.501254 | + | 0.868198i | 0.498745 | + | 0.866749i | \(0.333795\pi\) |
−0.999999 | + | 0.00144882i | \(0.999539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00800e12 | − | 1.74590e12i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.07517e11 | − | 1.86226e11i | 0.0515245 | − | 0.0892430i | ||||
\(292\) | −1.00233e12 | − | 1.73609e12i | −0.472170 | − | 0.817823i | ||||
\(293\) | 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 | ||||||||
\(300\) | −2.43000e12 | −1.00000 | ||||||||
\(301\) | 1.15128e12 | − | 3.35613e12i | 0.465960 | − | 1.35833i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.58277e12 | + | 4.47350e12i | −0.994761 | + | 1.72298i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.80080e12 | 1.76044 | 0.880221 | − | 0.474564i | \(-0.157394\pi\) | ||||
0.880221 | + | 0.474564i | \(0.157394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.23350e12 | −1.85780 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.90787e11 | − | 5.03657e11i | −0.0967949 | − | 0.167654i | 0.813561 | − | 0.581479i | \(-0.197526\pi\) |
−0.910356 | + | 0.413825i | \(0.864192\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.15130e12 | 0.682757 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.78523e12 | − | 3.09212e12i | −0.500000 | − | 0.866025i | ||||
\(325\) | 2.73563e12 | − | 4.73825e12i | 0.754467 | − | 1.30678i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.72442e12 | + | 6.45089e12i | 0.996139 | + | 1.72536i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.82406e12 | + | 6.62346e12i | 0.962463 | + | 1.66704i | 0.716281 | + | 0.697812i | \(0.245843\pi\) |
0.246182 | + | 0.969224i | \(0.420824\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.78472e12 | − | 4.82328e12i | 0.680081 | − | 1.17793i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.38957e12 | + | 4.05078e12i | −0.324478 | + | 0.945893i | ||||
\(337\) | −1.76722e12 | −0.406575 | −0.203288 | − | 0.979119i | \(-0.565163\pi\) | ||||
−0.203288 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.97267e12 | + | 2.59946e12i | −0.836782 | + | 0.547536i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.92571e12 | 1.53077 | 0.765387 | − | 0.643571i | \(-0.222548\pi\) | ||||
0.765387 | + | 0.643571i | \(0.222548\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.03908e12 | 1.50893 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.06844e12 | + | 1.57070e13i | −1.47910 | + | 2.56187i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.30279e12 | −1.00000 | ||||||||
\(364\) | −6.33426e12 | − | 7.26979e12i | −0.991263 | − | 1.13767i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.32140e12 | − | 5.75283e12i | 0.498874 | − | 0.864074i | −0.501126 | − | 0.865375i | \(-0.667081\pi\) |
0.999999 | + | 0.00130024i | \(0.000413881\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.24027e13 | 1.74101 | ||||||||
\(373\) | −6.91658e12 | − | 1.19799e13i | −0.957960 | − | 1.65923i | −0.727445 | − | 0.686166i | \(-0.759292\pi\) |
−0.230515 | − | 0.973069i | \(-0.574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.56347e13 | −1.99938 | −0.999688 | − | 0.0249920i | \(-0.992044\pi\) | ||||
−0.999688 | + | 0.0249920i | \(0.992044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.61073e12 | − | 1.14501e13i | 0.823426 | − | 1.42622i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.23288e12 | − | 1.07957e13i | −0.718016 | − | 1.24364i | ||||
\(388\) | −4.53077e11 | + | 7.84753e11i | −0.0515245 | + | 0.0892430i | ||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.65541e12 | − | 4.59931e12i | −0.269265 | − | 0.466380i | 0.699407 | − | 0.714723i | \(-0.253447\pi\) |
−0.968672 | + | 0.248343i | \(0.920114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.52827e12 | + | 1.90307e13i | −0.645556 | + | 1.88187i | ||||
\(400\) | 1.02400e13 | 1.00000 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.39626e13 | + | 2.41839e13i | −1.31353 | + | 2.27511i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.92050e12 | + | 3.32640e12i | −0.167802 | + | 0.290642i | −0.937647 | − | 0.347589i | \(-0.887000\pi\) |
0.769845 | + | 0.638231i | \(0.220334\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.20539e13 | 1.85780 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.25066e13 | − | 2.16621e13i | 0.991883 | − | 1.71799i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.67749e12 | −0.202449 | −0.101225 | − | 0.994864i | \(-0.532276\pi\) | ||||
−0.101225 | + | 0.994864i | \(0.532276\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.25312e12 | − | 6.36236e11i | 0.229172 | − | 0.0448207i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 7.52296e12 | + | 1.30301e13i | 0.500000 | + | 0.866025i | ||||
\(433\) | 2.56872e13 | 1.68763 | 0.843815 | − | 0.536634i | \(-0.180304\pi\) | ||||
0.843815 | + | 0.536634i | \(0.180304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.56947e13 | − | 2.71840e13i | −0.996139 | − | 1.72536i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.33172e12 | + | 1.44310e13i | 0.510989 | + | 0.885060i | 0.999919 | + | 0.0127363i | \(0.00405421\pi\) |
−0.488929 | + | 0.872323i | \(0.662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.28330e12 | + | 1.65229e13i | −0.136889 | + | 0.990586i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | −1.17348e13 | + | 2.03253e13i | −0.680081 | + | 1.17793i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.85565e12 | − | 1.70699e13i | 0.324478 | − | 0.945893i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.22106e12 | + | 2.11493e12i | 0.0640096 | + | 0.110868i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.92304e13 | + | 3.33080e13i | 0.964732 | + | 1.67096i | 0.710334 | + | 0.703865i | \(0.248544\pi\) |
0.254398 | + | 0.967100i | \(0.418123\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.40144e13 | −1.59867 | −0.799333 | − | 0.600889i | \(-0.794813\pi\) | ||||
−0.799333 | + | 0.600889i | \(0.794813\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | −3.38766e13 | −1.50893 | ||||||||
\(469\) | −1.39214e13 | − | 1.59775e13i | −0.613506 | − | 0.704117i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.17303e13 | − | 3.76380e13i | −0.937479 | − | 1.62376i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.81079e13 | 1.98952 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.64214e13 | − | 4.57633e13i | −1.02620 | − | 1.77743i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.65599e13 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.64619e13 | − | 4.58333e13i | 0.965997 | − | 1.67316i | 0.259087 | − | 0.965854i | \(-0.416578\pi\) |
0.706911 | − | 0.707303i | \(-0.250088\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.58640e13 | −1.99797 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.22648e13 | −1.74101 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.85763e13 | + | 4.94956e13i | 0.923640 | + | 1.59979i | 0.793733 | + | 0.608266i | \(0.208135\pi\) |
0.129907 | + | 0.991526i | \(0.458532\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | 2.13876e13 | − | 3.70444e13i | 0.638442 | − | 1.10581i | ||||
\(508\) | −2.78576e13 | + | 4.82507e13i | −0.823426 | + | 1.42622i | ||||
\(509\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.16148e13 | + | 2.48072e13i | 0.620364 | + | 0.711988i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.53432e13 | + | 6.12161e13i | 0.994761 | + | 1.72298i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.62653e13 | + | 4.54928e13i | 0.718016 | + | 1.24364i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.96510e13 | − | 5.13571e13i | −0.757760 | − | 1.31248i | −0.943991 | − | 0.329972i | \(-0.892961\pi\) |
0.186231 | − | 0.982506i | \(-0.440373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.91422e13 | − | 7.65532e12i | 0.981407 | − | 0.191941i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.07133e13 | + | 3.58764e13i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.75101e13 | − | 8.01953e13i | 0.645556 | − | 1.88187i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.17759e13 | + | 7.23580e13i | 0.901446 | + | 1.56135i | 0.825618 | + | 0.564230i | \(0.190827\pi\) |
0.0758283 | + | 0.997121i | \(0.475840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.12039e13 | − | 7.13672e13i | 0.872849 | − | 1.51182i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.58525e13 | 1.34473 | 0.672365 | − | 0.740219i | \(-0.265278\pi\) | ||||
0.672365 | + | 0.740219i | \(0.265278\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.82296e12 | − | 1.00857e13i | 0.116757 | − | 0.202229i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.46530e13 | + | 6.77733e12i | −0.670062 | + | 0.131049i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.27029e13 | + | 9.12841e13i | −0.991883 | + | 1.71799i | ||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.18275e14 | −2.16688 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.84976e13 | + | 4.41834e13i | 0.656929 | + | 0.753953i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.33658e13 | − | 7.51117e13i | 0.714441 | − | 1.23745i | −0.248733 | − | 0.968572i | \(-0.580014\pi\) |
0.963175 | − | 0.268877i | \(-0.0866524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.17017e13 | − | 5.49089e13i | −0.500000 | − | 0.866025i | ||||
\(577\) | −1.93774e13 | + | 3.35627e13i | −0.302982 | + | 0.524780i | −0.976810 | − | 0.214108i | \(-0.931316\pi\) |
0.673828 | + | 0.738888i | \(0.264649\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.27262e13 | − | 2.20424e13i | −0.195571 | − | 0.338740i | ||||
\(580\) | 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 | \(\pi\) | |||||||||
\(588\) | 9.62181e12 | − | 6.96272e13i | 0.136889 | − | 0.990586i | ||||
\(589\) | −2.45542e14 | −3.46377 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.94503e13 | − | 8.56505e13i | 0.680081 | − | 1.17793i | ||||
\(593\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.52810e13 | + | 4.37879e13i | 0.333366 | + | 0.577408i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.47133e14 | 1.87645 | 0.938225 | − | 0.346026i | \(-0.112469\pi\) | ||||
0.938225 | + | 0.346026i | \(0.112469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.44539e13 | −0.933900 | ||||||||
\(604\) | −5.14553e12 | − | 8.91231e12i | −0.0640096 | − | 0.110868i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.05366e13 | − | 7.02114e13i | −0.491930 | − | 0.852048i | 0.508027 | − | 0.861341i | \(-0.330375\pi\) |
−0.999957 | + | 0.00929320i | \(0.997042\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.86337e13 | + | 6.69156e13i | −0.446339 | + | 0.773081i | −0.998144 | − | 0.0608915i | \(-0.980606\pi\) |
0.551806 | + | 0.833973i | \(0.313939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.61388e13 | − | 2.79533e13i | 0.177590 | − | 0.307595i | −0.763464 | − | 0.645850i | \(-0.776503\pi\) |
0.941055 | + | 0.338255i | \(0.109837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.42756e14 | 1.50893 | ||||||||
\(625\) | −4.76837e13 | − | 8.25906e13i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.15713e13 | + | 1.58606e14i | 0.937479 | + | 1.62376i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.37959e13 | 0.637743 | 0.318872 | − | 0.947798i | \(-0.396696\pi\) | ||||
0.318872 | + | 0.947798i | \(0.396696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.14831e13 | + | 1.58453e14i | −0.900165 | + | 1.55913i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.24934e14 | + | 9.71460e13i | 1.19120 | + | 0.926249i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.06767e13 | −0.370076 | −0.185038 | − | 0.982731i | \(-0.559241\pi\) | ||||
−0.185038 | + | 0.982731i | \(0.559241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.99781e14 | + | 3.90726e13i | −1.70864 | + | 0.334170i | ||||
\(652\) | 2.35411e14 | 1.99797 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.15599e14 | 0.944340 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.25946e14 | − | 2.18145e14i | 0.998108 | − | 1.72877i | 0.445811 | − | 0.895127i | \(-0.352916\pi\) |
0.552298 | − | 0.833647i | \(-0.313751\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.22776e14 | + | 2.12654e14i | −0.916181 | + | 1.58687i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.35641e13 | 0.170677 | 0.0853386 | − | 0.996352i | \(-0.472803\pi\) | ||||
0.0853386 | + | 0.996352i | \(0.472803\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.00630e13 | − | 1.21353e14i | 0.500000 | − | 0.866025i | ||||
\(676\) | −9.01271e13 | + | 1.56105e14i | −0.638442 | + | 1.10581i | ||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.82589e12 | − | 1.40681e13i | 0.0334371 | − | 0.0974733i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | −1.48936e14 | − | 2.57964e14i | −0.994761 | − | 1.72298i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.11564e14 | −1.38248 | ||||||||
\(688\) | −1.10682e14 | − | 1.91706e14i | −0.718016 | − | 1.24364i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.32905e14 | + | 2.30199e14i | 0.843629 | + | 1.46121i | 0.886806 | + | 0.462142i | \(0.152919\pi\) |
−0.0431768 | + | 0.999067i | \(0.513748\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.64945e14 | + | 3.22594e13i | −0.981407 | + | 0.191941i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.32320e14 | − | 4.02389e14i | 1.35304 | − | 2.34353i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.85204e13 | − | 1.36001e14i | −0.438280 | − | 0.759123i | 0.559277 | − | 0.828981i | \(-0.311079\pi\) |
−0.997557 | + | 0.0698577i | \(0.977745\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.20275e13 | + | 1.07435e14i | −0.341378 | + | 0.591285i | ||||
\(712\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.55243e14 | + | 6.94773e13i | −1.82326 | + | 0.356588i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.82362e12 | + | 1.18189e13i | 0.0345401 | + | 0.0598252i | ||||
\(724\) | −1.73633e14 | + | 3.00741e14i | −0.872849 | + | 1.51182i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.60012e14 | −0.787915 | −0.393958 | − | 0.919129i | \(-0.628894\pi\) | ||||
−0.393958 | + | 0.919129i | \(0.628894\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.05891e14 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.45379e13 | + | 4.25009e13i | −0.116757 | + | 0.202229i | ||||
\(733\) | 5.73405e13 | + | 9.93166e13i | 0.270983 | + | 0.469356i | 0.969114 | − | 0.246614i | \(-0.0793181\pi\) |
−0.698131 | + | 0.715970i | \(0.745985\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.38267e14 | − | 2.39486e14i | 0.627331 | − | 1.08657i | −0.360754 | − | 0.932661i | \(-0.617481\pi\) |
0.988085 | − | 0.153908i | \(-0.0491859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.70672e14 | 3.00206 | ||||||||
\(742\) | 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 | ||||||||
\(751\) | −1.34354e14 | − | 2.32707e14i | −0.562405 | − | 0.974114i | −0.997286 | − | 0.0736263i | \(-0.976543\pi\) |
0.434881 | − | 0.900488i | \(-0.356791\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.62229e14 | − | 1.86189e14i | −0.656929 | − | 0.753953i | ||||
\(757\) | −1.03050e14 | −0.414542 | −0.207271 | − | 0.978284i | \(-0.566458\pi\) | ||||
−0.207271 | + | 0.978284i | \(0.566458\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.38447e14 | + | 3.88434e14i | 1.30878 | + | 1.50208i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.33591e14 | + | 2.31386e14i | 0.500000 | + | 0.866025i | ||||
\(769\) | 8.72349e13 | 0.324383 | 0.162192 | − | 0.986759i | \(-0.448144\pi\) | ||||
0.162192 | + | 0.986759i | \(0.448144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.36280e13 | + | 9.28865e13i | 0.195571 | + | 0.338740i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.43377e14 | + | 4.21541e14i | 0.870504 | + | 1.50776i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.24992e14 | − | 3.64366e14i | 0.441342 | − | 1.28657i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.05462e13 | + | 2.93408e14i | −0.136889 | + | 0.990586i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.46101e14 | + | 4.26259e14i | −0.815153 | + | 1.41189i | 0.0940643 | + | 0.995566i | \(0.470014\pi\) |
−0.909218 | + | 0.416321i | \(0.863319\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.52483e13 | − | 9.56928e13i | −0.176178 | − | 0.305150i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.06534e14 | − | 1.84522e14i | −0.333366 | − | 0.577408i | ||||
\(797\) | 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 | ||||||||
\(804\) | 3.13748e14 | 0.933900 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.83164e14 | −0.522078 | −0.261039 | − | 0.965328i | \(-0.584065\pi\) | ||||
−0.261039 | + | 0.965328i | \(0.584065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.22941e14 | −1.47231 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.19987e14 | − | 9.00644e14i | −1.42851 | − | 2.47425i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.45681e14 | − | 1.06723e14i | 1.48088 | − | 0.289626i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.29097e14 | − | 2.23603e14i | 0.341914 | − | 0.592213i | −0.642874 | − | 0.765972i | \(-0.722258\pi\) |
0.984788 | + | 0.173759i | \(0.0555914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.35059e14 | − | 2.33930e14i | 0.344947 | − | 0.597466i | −0.640397 | − | 0.768044i | \(-0.721230\pi\) |
0.985344 | + | 0.170578i | \(0.0545636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.30039e14 | − | 5.71644e14i | −0.832836 | − | 1.44252i | ||||
\(832\) | −6.01571e14 | −1.50893 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.57600e14 | + | 6.19382e14i | −0.870504 | + | 1.50776i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.20707e14 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.85509e14 | − | 6.67721e14i | 0.900165 | − | 1.55913i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.27825e14 | + | 8.36727e13i | −0.981407 | + | 0.191941i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.21104e14 | + | 3.82963e14i | 0.501254 | + | 0.868198i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.94131e14 | −1.97996 | −0.989979 | − | 0.141213i | \(-0.954900\pi\) | ||||
−0.989979 | + | 0.141213i | \(0.954900\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.62993e14 | + | 8.01927e14i | 0.989939 | + | 1.71462i | 0.617507 | + | 0.786565i | \(0.288143\pi\) |
0.372432 | + | 0.928060i | \(0.378524\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.89887e14 | −1.00000 | ||||||||
\(868\) | 8.41876e14 | − | 1.64652e14i | 1.70864 | − | 0.334170i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.53209e14 | + | 6.11776e14i | −0.704598 | + | 1.22040i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.61267e13 | − | 4.52528e13i | −0.0515245 | − | 0.0892430i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.87135e14 | −0.944340 | ||||||||
\(877\) | 5.11427e14 | + | 8.85818e14i | 0.985794 | + | 1.70744i | 0.638355 | + | 0.769742i | \(0.279615\pi\) |
0.347439 | + | 0.937703i | \(0.387051\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.02467e15 | 1.90889 | 0.954443 | − | 0.298393i | \(-0.0964506\pi\) | ||||
0.954443 | + | 0.298393i | \(0.0964506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.96721e14 | − | 8.64979e14i | 0.534367 | − | 1.55775i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.17375e14 | − | 8.96120e14i | 0.916181 | − | 1.58687i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.95245e14 | + | 5.11379e14i | −0.500000 | + | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.66397e14 | − | 6.50050e14i | −0.943370 | − | 1.08270i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.70279e14 | − | 4.68138e14i | 0.440328 | − | 0.762671i | −0.557386 | − | 0.830254i | \(-0.688195\pi\) |
0.997714 | + | 0.0675832i | \(0.0215288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 6.27614e14 | + | 1.08706e15i | 0.994761 | + | 1.72298i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.91529e14 | 1.38248 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.46611e14 | + | 1.11996e15i | 0.986428 | + | 1.70854i | 0.635411 | + | 0.772174i | \(0.280831\pi\) |
0.351017 | + | 0.936369i | \(0.385836\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.83297e14 | − | 1.01030e15i | 0.880221 | − | 1.52459i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.21084e14 | −1.36016 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.35870e14 | + | 1.10136e15i | −0.928902 | + | 1.60891i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.90488e14 | + | 1.37844e15i | −0.272344 | + | 1.97079i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.41648e15 | −1.96115 | −0.980576 | − | 0.196141i | \(-0.937159\pi\) | ||||
−0.980576 | + | 0.196141i | \(0.937159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.41322e14 | −0.193590 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 2.61383e14 | − | 4.52729e14i | 0.341378 | − | 0.591285i | ||||
\(949\) | 5.48403e14 | − | 9.49862e14i | 0.712474 | − | 1.23404i | ||||
\(950\) | 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 | ||||||||
\(961\) | −8.32377e14 | − | 1.44172e15i | −1.01555 | − | 1.75899i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.87547e13 | − | 4.98046e13i | −0.0345401 | − | 0.0598252i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.44854e14 | −0.762656 | −0.381328 | − | 0.924440i | \(-0.624533\pi\) | ||||
−0.381328 | + | 0.924440i | \(0.624533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | −8.67624e14 | −1.00000 | ||||||||
\(973\) | 5.61358e14 | − | 1.63643e15i | 0.643688 | − | 1.87643i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.64758e14 | − | 1.15139e15i | −0.754467 | − | 1.30678i | ||||
\(976\) | 1.03403e14 | − | 1.79098e14i | 0.116757 | − | 0.202229i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.81007e15 | 1.99228 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.82621e15 | −3.00206 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.77520e14 | + | 1.51991e15i | −0.918097 | + | 1.59019i | −0.115794 | + | 0.993273i | \(0.536941\pi\) |
−0.802303 | + | 0.596918i | \(0.796392\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.85849e15 | 1.92493 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.43391e14 | + | 1.46080e15i | −0.856156 | + | 1.48291i | 0.0194120 | + | 0.999812i | \(0.493821\pi\) |
−0.875568 | + | 0.483095i | \(0.839513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.76687e14 | − | 1.17206e15i | −0.680081 | − | 1.17793i |
(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 | 21.11.h.a.11.1 | yes | 2 | |
3.2 | odd | 2 | CM | 21.11.h.a.11.1 | yes | 2 | |
7.2 | even | 3 | inner | 21.11.h.a.2.1 | ✓ | 2 | |
21.2 | odd | 6 | inner | 21.11.h.a.2.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.11.h.a.2.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
21.11.h.a.2.1 | ✓ | 2 | 21.2 | odd | 6 | inner | |
21.11.h.a.11.1 | yes | 2 | 1.1 | even | 1 | trivial | |
21.11.h.a.11.1 | yes | 2 | 3.2 | odd | 2 | CM |