Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,29,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, 29, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 29);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 29 \) |
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: | \(104.303795921\) |
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 | 21.29.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 | \(0.333333\pi\) | |||||||
\(3\) | −2.39148e6 | + | 4.14217e6i | −0.500000 | + | 0.866025i | ||||
\(4\) | −1.34218e8 | + | 2.32472e8i | −0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.89159e11 | − | 5.55466e11i | 0.573792 | − | 0.819001i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.14384e13 | − | 1.98119e13i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | −6.41959e14 | − | 1.11191e15i | −0.500000 | − | 0.866025i | ||||
\(13\) | 6.87801e15 | 1.74685 | 0.873426 | − | 0.486958i | \(-0.161893\pi\) | ||||
0.873426 | + | 0.486958i | \(0.161893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.60288e16 | − | 6.24037e16i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.51754e17 | − | 7.82461e17i | −0.565395 | − | 0.979293i | −0.997013 | − | 0.0772361i | \(-0.975390\pi\) |
0.431618 | − | 0.902056i | \(-0.357943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.37017e18 | + | 2.94035e18i | 0.422380 | + | 0.906419i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.86265e19 | + | 3.22620e19i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.09419e20 | 1.00000 | ||||||||
\(28\) | 7.68982e19 | + | 1.65022e20i | 0.422380 | + | 0.906419i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.44144e20 | + | 1.28890e21i | −0.983090 | + | 1.70276i | −0.332956 | + | 0.942942i | \(0.608046\pi\) |
−0.650134 | + | 0.759819i | \(0.725287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.14094e21 | 1.00000 | ||||||||
\(37\) | 6.03260e21 | + | 1.04488e22i | 0.669391 | + | 1.15942i | 0.978075 | + | 0.208255i | \(0.0667784\pi\) |
−0.308683 | + | 0.951165i | \(0.599888\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.64487e22 | + | 2.84899e22i | −0.873426 | + | 1.51282i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.43151e21 | −0.0870471 | −0.0435236 | − | 0.999052i | \(-0.513858\pi\) | ||||
−0.0435236 | + | 0.999052i | \(0.513858\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 3.44649e23 | 1.00000 | ||||||||
\(49\) | −1.57098e23 | − | 4.32329e23i | −0.341526 | − | 0.939872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.23151e23 | + | 1.59894e24i | −0.873426 | + | 1.51282i | ||||
\(53\) | 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 | ||||||||
\(57\) | 4.32145e24 | 1.13079 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.43379e24 | − | 1.63398e25i | −0.955144 | − | 1.65436i | −0.734039 | − | 0.679107i | \(-0.762367\pi\) |
−0.221104 | − | 0.975250i | \(-0.570966\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.54562e25 | − | 1.35633e24i | −0.996172 | − | 0.0874174i | ||||
\(64\) | 1.93428e25 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.67328e24 | − | 1.32905e25i | 0.208898 | − | 0.361822i | −0.742470 | − | 0.669880i | \(-0.766346\pi\) |
0.951368 | + | 0.308058i | \(0.0996791\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.94167e25 | + | 1.54874e26i | −0.732653 | + | 1.26899i | 0.223092 | + | 0.974797i | \(0.428385\pi\) |
−0.955745 | + | 0.294195i | \(0.904948\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.90897e25 | − | 1.54308e26i | −0.500000 | − | 0.866025i | ||||
\(76\) | 2.42534e26 | 1.13079 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.06809e26 | + | 3.58204e26i | 0.560777 | + | 0.971294i | 0.997429 | + | 0.0716634i | \(0.0228307\pi\) |
−0.436652 | + | 0.899630i | \(0.643836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.61674e26 | + | 4.53232e26i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −8.67450e26 | − | 7.61216e25i | −0.996172 | − | 0.0874174i | ||||
\(85\) | 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 | ||||||||
\(91\) | 2.67664e27 | − | 3.82050e27i | 1.00233 | − | 1.43067i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.55922e27 | − | 6.16475e27i | −0.983090 | − | 1.70276i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.29210e28 | −1.97920 | −0.989602 | − | 0.143832i | \(-0.954058\pi\) | ||||
−0.989602 | + | 0.143832i | \(0.954058\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000e27 | − | 8.66025e27i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.37243e28 | + | 2.37712e28i | 0.907338 | + | 1.57156i | 0.817748 | + | 0.575577i | \(0.195222\pi\) |
0.0895902 | + | 0.995979i | \(0.471444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | −1.46860e28 | + | 2.54368e28i | −0.500000 | + | 0.866025i | ||||
\(109\) | −2.27187e27 | + | 3.93500e27i | −0.0679850 | + | 0.117754i | −0.898014 | − | 0.439966i | \(-0.854990\pi\) |
0.830029 | + | 0.557720i | \(0.188324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.77074e28 | −1.33878 | ||||||||
\(112\) | −4.86840e28 | − | 4.27219e27i | −0.996172 | − | 0.0874174i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.86734e28 | − | 1.36266e29i | −0.873426 | − | 1.51282i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.21050e28 | − | 1.24889e29i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.99755e29 | − | 3.45985e29i | −0.983090 | − | 1.70276i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.57094e29 | −1.96190 | −0.980949 | − | 0.194266i | \(-0.937767\pi\) | ||||
−0.980949 | + | 0.194266i | \(0.937767\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.53809e28 | − | 2.66404e28i | 0.0435236 | − | 0.0753850i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.10434e29 | − | 5.35677e28i | −1.12646 | − | 0.0988507i | ||||
\(134\) | 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 | ||||||||
\(139\) | −1.11082e30 | −1.10519 | −0.552595 | − | 0.833450i | \(-0.686362\pi\) | ||||
−0.552595 | + | 0.833450i | \(0.686362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −8.24223e29 | + | 1.42760e30i | −0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.16648e30 | + | 3.83182e29i | 0.984716 | + | 0.174166i | ||||
\(148\) | −3.23873e30 | −1.33878 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.30608e29 | − | 7.45835e29i | 0.134402 | − | 0.232791i | −0.790967 | − | 0.611859i | \(-0.790422\pi\) |
0.925369 | + | 0.379068i | \(0.123755\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.41540e30 | − | 7.64770e30i | −0.873426 | − | 1.51282i | ||||
\(157\) | 3.48131e30 | − | 6.02980e30i | 0.629719 | − | 1.09071i | −0.357889 | − | 0.933764i | \(-0.616503\pi\) |
0.987608 | − | 0.156942i | \(-0.0501634\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.19289e30 | + | 1.41905e31i | 0.876619 | + | 1.51835i | 0.855028 | + | 0.518581i | \(0.173540\pi\) |
0.0215904 | + | 0.999767i | \(0.493127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.18041e31 | 2.05149 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.03347e31 | + | 1.79002e31i | −0.565395 | + | 0.979293i | ||||
\(172\) | 8.63223e29 | − | 1.49515e30i | 0.0435236 | − | 0.0753850i | ||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.06718e31 | + | 2.29014e31i | 0.422380 | + | 0.906419i | ||||
\(176\) | 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 | ||||||||
\(181\) | 3.77614e31 | 0.932283 | 0.466142 | − | 0.884710i | \(-0.345644\pi\) | ||||
0.466142 | + | 0.884710i | \(0.345644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.02431e31 | 1.91029 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.25814e31 | − | 6.07785e31i | 0.573792 | − | 0.819001i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −4.62580e31 | + | 8.01213e31i | −0.500000 | + | 0.866025i | ||||
\(193\) | −9.91992e31 | + | 1.71818e32i | −0.997024 | + | 1.72690i | −0.431750 | + | 0.901993i | \(0.642104\pi\) |
−0.565274 | + | 0.824903i | \(0.691230\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.21590e32 | + | 2.15054e31i | 0.984716 | + | 0.174166i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.45688e32 | − | 2.52338e32i | 0.953848 | − | 1.65211i | 0.216866 | − | 0.976201i | \(-0.430416\pi\) |
0.736982 | − | 0.675912i | \(-0.236250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.67011e31 | + | 6.35681e31i | 0.208898 | + | 0.361822i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.47806e32 | − | 4.29213e32i | −0.873426 | − | 1.51282i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.63075e32 | −1.62410 | −0.812048 | − | 0.583590i | \(-0.801647\pi\) | ||||
−0.812048 | + | 0.583590i | \(0.801647\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.26347e32 | + | 9.14931e32i | 0.830475 | + | 1.78218i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.27677e32 | − | 7.40759e32i | −0.732653 | − | 1.26899i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.30064e33 | −1.72938 | −0.864690 | − | 0.502306i | \(-0.832485\pi\) | ||||
−0.864690 | + | 0.502306i | \(0.832485\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.52227e32 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | −5.80016e32 | + | 1.00462e33i | −0.565395 | + | 0.979293i | ||||
\(229\) | −1.05623e33 | − | 1.82944e33i | −0.968413 | − | 1.67734i | −0.700151 | − | 0.713995i | \(-0.746884\pi\) |
−0.268262 | − | 0.963346i | \(-0.586449\pi\) | |||||||
\(230\) | 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 | ||||||||
\(237\) | −1.97832e33 | −1.12155 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.92197e33 | + | 3.32896e33i | −0.862004 | + | 1.49303i | 0.00798813 | + | 0.999968i | \(0.497457\pi\) |
−0.869992 | + | 0.493066i | \(0.835876\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.25158e33 | − | 2.16780e33i | −0.500000 | − | 0.866025i | ||||
\(244\) | 5.06473e33 | 1.91029 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.10717e33 | − | 5.38178e33i | −0.987661 | − | 1.71068i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 2.38980e33 | − | 3.41108e33i | 0.573792 | − | 0.819001i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.59615e33 | + | 4.49666e33i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.15157e33 | + | 7.15327e32i | 1.33366 | + | 0.117033i | ||||
\(260\) | 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 | ||||||||
\(268\) | 2.05978e33 | + | 3.56764e33i | 0.208898 | + | 0.361822i | ||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.13011e34 | + | 1.95740e34i | 0.980731 | + | 1.69868i | 0.659555 | + | 0.751657i | \(0.270745\pi\) |
0.321176 | + | 0.947019i | \(0.395922\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.42403e33 | + | 2.02238e34i | 0.737835 | + | 1.58338i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.27285e33 | − | 1.43290e34i | 0.528370 | − | 0.915165i | −0.471082 | − | 0.882089i | \(-0.656137\pi\) |
0.999453 | − | 0.0330753i | \(-0.0105301\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.40473e34 | 1.96618 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.93428e34 | + | 3.35028e34i | −0.915188 | + | 1.58515i | −0.108562 | + | 0.994090i | \(0.534625\pi\) |
−0.806626 | + | 0.591062i | \(0.798709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41755e34 | − | 2.45528e34i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.09003e34 | − | 5.35209e34i | 0.989602 | − | 1.71404i | ||||
\(292\) | −2.40026e34 | − | 4.15737e34i | −0.732653 | − | 1.26899i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.78297e34 | 1.00000 | ||||||||
\(301\) | −2.50288e33 | + | 3.57248e33i | −0.0499469 | + | 0.0712917i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.25523e34 | + | 5.63823e34i | −0.565395 | + | 0.979293i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.44698e34 | 0.370419 | 0.185210 | − | 0.982699i | \(-0.440704\pi\) | ||||
0.185210 | + | 0.982699i | \(0.440704\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.31286e35 | −1.81468 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.78758e34 | + | 8.29234e34i | 0.552708 | + | 0.957318i | 0.998078 | + | 0.0619715i | \(0.0197388\pi\) |
−0.445370 | + | 0.895347i | \(0.646928\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.11030e35 | −1.12155 | ||||||||
\(317\) | 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 | ||||||||
\(324\) | −7.02425e34 | − | 1.21664e35i | −0.500000 | − | 0.866025i | ||||
\(325\) | −1.28113e35 | + | 2.21898e35i | −0.873426 | + | 1.51282i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.08663e34 | − | 1.88210e34i | −0.0679850 | − | 0.117754i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.36091e35 | − | 2.35716e35i | −0.718185 | − | 1.24393i | −0.961718 | − | 0.274040i | \(-0.911640\pi\) |
0.243534 | − | 0.969892i | \(-0.421693\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.38006e35 | − | 2.39034e35i | 0.669391 | − | 1.15942i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.34123e35 | − | 1.91441e35i | 0.573792 | − | 0.819001i | ||||
\(337\) | −3.77901e35 | −1.55081 | −0.775407 | − | 0.631461i | \(-0.782455\pi\) | ||||
−0.775407 | + | 0.631461i | \(0.782455\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.01280e35 | − | 8.09821e34i | −0.965722 | − | 0.259580i | ||||
\(344\) | 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 | ||||||||
\(349\) | −1.90214e35 | −0.478285 | −0.239143 | − | 0.970984i | \(-0.576866\pi\) | ||||
−0.239143 | + | 0.970984i | \(0.576866\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.52585e35 | 1.74685 | ||||||||
\(352\) | 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 | ||||||||
\(361\) | −8.89580e34 | + | 1.54080e35i | −0.139343 | + | 0.241349i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.89752e35 | 1.00000 | ||||||||
\(364\) | 5.28906e35 | + | 1.13502e36i | 0.737835 | + | 1.58338i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.40238e35 | + | 9.35720e35i | −0.671832 | + | 1.16365i | 0.305552 | + | 0.952175i | \(0.401159\pi\) |
−0.977384 | + | 0.211471i | \(0.932174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.91084e36 | 1.96618 | ||||||||
\(373\) | 9.91585e35 | + | 1.71748e36i | 0.982667 | + | 1.70203i | 0.651877 | + | 0.758324i | \(0.273982\pi\) |
0.330789 | + | 0.943705i | \(0.392685\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.14016e36 | −1.69628 | −0.848139 | − | 0.529774i | \(-0.822277\pi\) | ||||
−0.848139 | + | 0.529774i | \(0.822277\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.33228e36 | − | 2.30758e36i | 0.980949 | − | 1.69905i | ||||
\(382\) | 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 | ||||||||
\(387\) | 7.35662e34 | + | 1.27420e35i | 0.0435236 | + | 0.0753850i | ||||
\(388\) | 1.73422e36 | − | 3.00376e36i | 0.989602 | − | 1.71404i | ||||
\(389\) | 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 | ||||||||
\(397\) | −4.30402e35 | − | 7.45478e35i | −0.178159 | − | 0.308580i | 0.763091 | − | 0.646291i | \(-0.223681\pi\) |
−0.941250 | + | 0.337711i | \(0.890347\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.68173e36 | − | 2.40042e36i | 0.648838 | − | 0.926118i | ||||
\(400\) | 2.68435e36 | 1.00000 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.11823e36 | + | 8.86503e36i | −1.71731 | + | 2.97447i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.76446e35 | + | 9.98433e35i | −0.157265 | + | 0.272391i | −0.933881 | − | 0.357583i | \(-0.883601\pi\) |
0.776616 | + | 0.629974i | \(0.216934\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.36818e36 | −1.81468 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.65651e36 | − | 4.60121e36i | 0.552595 | − | 0.957123i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.72538e36 | 1.22396 | 0.611980 | − | 0.790873i | \(-0.290373\pi\) | ||||
0.611980 | + | 0.790873i | \(0.290373\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.27474e37 | − | 1.11863e36i | −1.90297 | − | 0.166992i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | −3.94223e36 | − | 6.82815e36i | −0.500000 | − | 0.866025i | ||||
\(433\) | −1.55655e37 | −1.91131 | −0.955657 | − | 0.294484i | \(-0.904852\pi\) | ||||
−0.955657 | + | 0.294484i | \(0.904852\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.09852e35 | − | 1.05629e36i | −0.0679850 | − | 0.117754i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.81343e35 | + | 1.18012e36i | 0.0690022 | + | 0.119515i | 0.898462 | − | 0.439051i | \(-0.144685\pi\) |
−0.829460 | + | 0.558566i | \(0.811352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.76830e36 | + | 8.05754e36i | −0.643190 | + | 0.765707i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 7.74536e36 | − | 1.34154e37i | 0.669391 | − | 1.15942i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.52742e36 | − | 1.07443e37i | 0.573792 | − | 0.819001i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.05959e36 | + | 3.56731e36i | 0.134402 | + | 0.232791i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.38593e36 | + | 5.86459e36i | 0.195367 | + | 0.338385i | 0.947021 | − | 0.321173i | \(-0.104077\pi\) |
−0.751654 | + | 0.659558i | \(0.770744\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.14736e37 | −1.99360 | −0.996799 | − | 0.0799547i | \(-0.974522\pi\) | ||||
−0.996799 | + | 0.0799547i | \(0.974522\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 4.22375e37 | 1.74685 | ||||||||
\(469\) | −4.39630e36 | − | 9.43436e36i | −0.176469 | − | 0.378698i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.66510e37 | + | 2.88403e37i | 0.629719 | + | 1.09071i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.36583e37 | 1.13079 | ||||||||
\(476\) | 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 | ||||||||
\(481\) | 4.14923e37 | + | 7.18667e37i | 1.16933 | + | 2.02533i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.87111e37 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.71380e37 | − | 2.96840e37i | 0.406028 | − | 0.703261i | −0.588413 | − | 0.808561i | \(-0.700247\pi\) |
0.994441 | + | 0.105300i | \(0.0335802\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.83727e37 | −1.75324 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.07242e38 | 1.96618 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.38658e36 | − | 1.62580e37i | −0.158161 | − | 0.273943i | 0.776044 | − | 0.630678i | \(-0.217223\pi\) |
−0.934206 | + | 0.356735i | \(0.883890\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | −7.60590e37 | + | 1.31738e38i | −1.02574 | + | 1.77664i | ||||
\(508\) | 7.47719e37 | − | 1.29509e38i | 0.980949 | − | 1.69905i | ||||
\(509\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.12300e37 | + | 1.09939e38i | 0.618916 | + | 1.32818i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.94305e37 | − | 8.56161e37i | −0.565395 | − | 0.979293i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.12877e36 | + | 7.15123e36i | 0.0435236 | + | 0.0753850i | ||||
\(517\) | 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 | ||||||||
\(523\) | −8.50630e37 | − | 1.47333e38i | −0.742535 | − | 1.28611i | −0.951338 | − | 0.308151i | \(-0.900290\pi\) |
0.208802 | − | 0.977958i | \(-0.433043\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.20383e38 | − | 1.05640e37i | −0.996172 | − | 0.0874174i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.71969e37 | + | 1.16388e38i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.43841e37 | − | 1.34719e38i | 0.648838 | − | 0.926118i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.83975e38 | − | 3.18655e38i | −0.999995 | − | 1.73204i | −0.502668 | − | 0.864479i | \(-0.667648\pi\) |
−0.497327 | − | 0.867563i | \(-0.665685\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.03058e37 | + | 1.56414e38i | −0.466142 | + | 0.807381i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.86913e38 | −1.80215 | −0.901075 | − | 0.433664i | \(-0.857220\pi\) | ||||
−0.901075 | + | 0.433664i | \(0.857220\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.15815e38 | + | 3.73802e38i | −0.955144 | + | 1.65436i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.79451e38 | + | 2.45228e37i | 1.11726 | + | 0.0980433i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.49092e38 | − | 2.58235e38i | 0.552595 | − | 0.957123i | ||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.42360e37 | −0.152058 | ||||||||
\(560\) | 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 | ||||||||
\(567\) | 1.49922e38 | + | 3.21730e38i | 0.422380 | + | 0.906419i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.39362e38 | + | 4.14586e38i | −0.611151 | + | 1.05855i | 0.379895 | + | 0.925029i | \(0.375960\pi\) |
−0.991047 | + | 0.133516i | \(0.957373\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.21251e38 | − | 3.83218e38i | −0.500000 | − | 0.866025i | ||||
\(577\) | 2.95149e38 | − | 5.11214e38i | 0.650999 | − | 1.12756i | −0.331881 | − | 0.943321i | \(-0.607683\pi\) |
0.982881 | − | 0.184243i | \(-0.0589833\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.74467e38 | − | 8.21800e38i | −0.997024 | − | 1.72690i | ||||
\(580\) | 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 | \(\pi\) | |||||||||
\(588\) | −3.79858e38 | + | 4.52215e38i | −0.643190 | + | 0.765707i | ||||
\(589\) | 1.34468e39 | 2.22334 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.34694e38 | − | 7.52913e38i | 0.669391 | − | 1.15942i | ||||
\(593\) | 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 | ||||||||
\(597\) | 6.96819e38 | + | 1.20693e39i | 0.953848 | + | 1.65211i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.81133e38 | 1.09850 | 0.549249 | − | 0.835659i | \(-0.314914\pi\) | ||||
0.549249 | + | 0.835659i | \(0.314914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.51080e38 | −0.417796 | ||||||||
\(604\) | 1.15591e38 | + | 2.00209e38i | 0.134402 | + | 0.232791i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.06348e38 | + | 1.56984e39i | 0.983226 | + | 1.70300i | 0.649569 | + | 0.760303i | \(0.274950\pi\) |
0.333657 | + | 0.942694i | \(0.391717\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.79362e38 | + | 1.52310e39i | −0.831230 | + | 1.43973i | 0.0658342 | + | 0.997831i | \(0.479029\pi\) |
−0.897064 | + | 0.441901i | \(0.854304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.23916e38 | + | 3.87834e38i | −0.184678 | + | 0.319872i | −0.943468 | − | 0.331463i | \(-0.892458\pi\) |
0.758790 | + | 0.651336i | \(0.225791\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.37050e39 | 1.74685 | ||||||||
\(625\) | −6.93889e38 | − | 1.20185e39i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.34506e38 | + | 1.61861e39i | 0.629719 | + | 1.09071i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.07122e38 | 0.0675256 | 0.0337628 | − | 0.999430i | \(-0.489251\pi\) | ||||
0.0337628 | + | 0.999430i | \(0.489251\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.34658e39 | − | 2.33235e39i | 0.812048 | − | 1.40651i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.08052e39 | − | 2.97356e39i | −0.596596 | − | 1.64182i | ||||
\(638\) | 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 | ||||||||
\(643\) | −3.06254e39 | −1.48295 | −0.741477 | − | 0.670979i | \(-0.765874\pi\) | ||||
−0.741477 | + | 0.670979i | \(0.765874\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | −4.80941e39 | − | 4.22041e38i | −1.95865 | − | 0.171878i | ||||
\(652\) | −4.39853e39 | −1.75324 | ||||||||
\(653\) | 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 | ||||||||
\(657\) | 4.09113e39 | 1.46531 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.11648e39 | − | 3.66585e39i | 0.696296 | − | 1.20602i | −0.273446 | − | 0.961887i | \(-0.588163\pi\) |
0.969742 | − | 0.244133i | \(-0.0785032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.11047e39 | − | 5.38749e39i | 0.864690 | − | 1.49769i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.59787e39 | −1.94304 | −0.971519 | − | 0.236963i | \(-0.923848\pi\) | ||||
−0.971519 | + | 0.236963i | \(0.923848\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.03809e39 | + | 3.53007e39i | −0.500000 | + | 0.866025i | ||||
\(676\) | −4.26867e39 | + | 7.39356e39i | −1.02574 | + | 1.77664i | ||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.02831e39 | + | 7.17715e39i | −1.13565 | + | 1.62097i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | −2.77420e39 | − | 4.80505e39i | −0.565395 | − | 0.979293i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.01038e40 | 1.93683 | ||||||||
\(688\) | 2.31720e38 | + | 4.01350e38i | 0.0435236 | + | 0.0753850i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.25126e39 | + | 5.63136e39i | 0.574592 | + | 0.995223i | 0.996086 | + | 0.0883914i | \(0.0281726\pi\) |
−0.421494 | + | 0.906831i | \(0.638494\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.75627e39 | − | 5.92885e38i | −0.996172 | − | 0.0874174i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.45050e39 | − | 9.44055e39i | 0.756941 | − | 1.31106i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.49571e39 | − | 1.12509e40i | −0.800902 | − | 1.38720i | −0.919023 | − | 0.394203i | \(-0.871021\pi\) |
0.118122 | − | 0.992999i | \(-0.462313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.73113e39 | − | 8.19455e39i | 0.560777 | − | 0.971294i | ||||
\(712\) | 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 | ||||||||
\(721\) | 1.85450e40 | + | 1.62739e39i | 1.80773 | + | 0.158634i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.19275e39 | − | 1.59223e40i | −0.862004 | − | 1.49303i | ||||
\(724\) | −5.06825e39 | + | 8.77846e39i | −0.466142 | + | 0.807381i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.01599e40 | 1.74987 | 0.874935 | − | 0.484241i | \(-0.160904\pi\) | ||||
0.874935 | + | 0.484241i | \(0.160904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.19725e40 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.21122e40 | + | 2.09790e40i | −0.955144 | + | 1.65436i | ||||
\(733\) | 1.14153e40 | + | 1.97718e40i | 0.883142 | + | 1.52965i | 0.847829 | + | 0.530270i | \(0.177909\pi\) |
0.0353127 | + | 0.999376i | \(0.488757\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.44871e40 | + | 2.50924e40i | −0.999905 | + | 1.73189i | −0.488016 | + | 0.872834i | \(0.662279\pi\) |
−0.511889 | + | 0.859052i | \(0.671054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.97230e40 | 1.97532 | ||||||||
\(742\) | 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 | ||||||||
\(751\) | −1.84159e39 | − | 3.18973e39i | −0.101446 | − | 0.175709i | 0.810835 | − | 0.585275i | \(-0.199013\pi\) |
−0.912281 | + | 0.409566i | \(0.865680\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.41412e39 | + | 1.80565e40i | 0.422380 | + | 0.906419i | ||||
\(757\) | 1.42168e40 | 0.700581 | 0.350290 | − | 0.936641i | \(-0.386083\pi\) | ||||
0.350290 | + | 0.936641i | \(0.386083\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 1.30164e39 | + | 2.79329e39i | 0.0574311 | + | 0.123246i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.24173e40 | − | 2.15074e40i | −0.500000 | − | 0.866025i | ||||
\(769\) | 2.36412e40 | 0.934762 | 0.467381 | − | 0.884056i | \(-0.345198\pi\) | ||||
0.467381 | + | 0.884056i | \(0.345198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.66286e40 | − | 4.61220e40i | −0.997024 | − | 1.72690i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.77215e40 | − | 4.80151e40i | −0.983090 | − | 1.70276i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.24574e40 | + | 3.20545e40i | −0.768182 | + | 1.09646i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.13189e40 | + | 2.53797e40i | −0.643190 | + | 0.765707i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.53794e39 | − | 9.59199e39i | 0.158381 | − | 0.274323i | −0.775904 | − | 0.630851i | \(-0.782706\pi\) |
0.934285 | + | 0.356527i | \(0.116039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.48857e40 | − | 1.12385e41i | −1.66849 | − | 2.88992i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.91077e40 | + | 6.77365e40i | 0.953848 | + | 1.65211i | ||||
\(797\) | 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 | ||||||||
\(804\) | −1.97037e40 | −0.417796 | ||||||||
\(805\) | 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 | ||||||||
\(811\) | 4.39401e40 | 0.825219 | 0.412609 | − | 0.910908i | \(-0.364617\pi\) | ||||
0.412609 | + | 0.910908i | \(0.364617\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.08105e41 | −1.96146 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.90546e39 | + | 5.03241e39i | 0.0492160 | + | 0.0852446i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.06308e41 | − | 9.32886e39i | −1.74016 | − | 0.152705i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.14658e40 | + | 1.06462e41i | −0.939800 | + | 1.62778i | −0.173959 | + | 0.984753i | \(0.555656\pi\) |
−0.765842 | + | 0.643029i | \(0.777677\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.97708e40 | − | 1.20847e41i | 0.963630 | − | 1.66906i | 0.250379 | − | 0.968148i | \(-0.419445\pi\) |
0.713251 | − | 0.700909i | \(-0.247222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.95688e40 | + | 6.85352e40i | 0.528370 | + | 0.915165i | ||||
\(832\) | 1.33040e41 | 1.74685 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.14235e40 | + | 1.41030e41i | −0.983090 | + | 1.70276i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.85409e40 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.55746e40 | − | 1.30899e41i | 0.812048 | − | 1.40651i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.74321e40 | − | 8.54999e39i | −0.996172 | − | 0.0874174i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.25162e40 | − | 1.60243e41i | −0.915188 | − | 1.58515i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.40896e41 | 1.30501 | 0.652503 | − | 0.757786i | \(-0.273719\pi\) | ||||
0.652503 | + | 0.757786i | \(0.273719\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | 6.17383e40 | + | 1.06934e41i | 0.518383 | + | 0.897865i | 0.999772 | + | 0.0213584i | \(0.00679910\pi\) |
−0.481389 | + | 0.876507i | \(0.659868\pi\) | |||||||
\(860\) | 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 | ||||||||
\(867\) | 1.35602e41 | 1.00000 | ||||||||
\(868\) | −2.69919e41 | − | 2.36863e40i | −1.95865 | − | 0.171878i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.27769e40 | − | 9.14123e40i | 0.364913 | − | 0.632048i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.47795e41 | + | 2.55989e41i | 0.989602 | + | 1.71404i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.29607e41 | 1.46531 | ||||||||
\(877\) | 2.51101e40 | + | 4.34920e40i | 0.157708 | + | 0.273159i | 0.934042 | − | 0.357164i | \(-0.116256\pi\) |
−0.776334 | + | 0.630322i | \(0.782923\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.21546e41 | 1.83566 | 0.917831 | − | 0.396970i | \(-0.129938\pi\) | ||||
0.917831 | + | 0.396970i | \(0.129938\pi\) | |||||||
\(884\) | 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 | ||||||||
\(889\) | −2.16798e41 | + | 3.09447e41i | −1.12572 | + | 1.60680i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.74569e41 | − | 3.02363e41i | 0.864690 | − | 1.49769i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.14384e41 | + | 1.98119e41i | −0.500000 | + | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.81225e39 | − | 1.89109e40i | −0.0367670 | − | 0.0789012i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.09246e41 | + | 3.62425e41i | −0.820646 | + | 1.42140i | 0.0845564 | + | 0.996419i | \(0.473053\pi\) |
−0.905202 | + | 0.424981i | \(0.860281\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −1.55697e41 | − | 2.69675e41i | −0.565395 | − | 0.979293i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.67058e41 | 1.93683 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.74381e41 | − | 4.75242e41i | −0.895235 | − | 1.55059i | −0.833514 | − | 0.552499i | \(-0.813674\pi\) |
−0.0617212 | − | 0.998093i | \(-0.519659\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.85192e40 | + | 1.01358e41i | −0.185210 | + | 0.320792i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.49463e41 | −1.33878 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.13968e41 | − | 5.43809e41i | 0.907338 | − | 1.57156i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.67311e41 | + | 3.18229e41i | −0.727313 | + | 0.865853i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.90090e41 | −0.472721 | −0.236361 | − | 0.971665i | \(-0.575955\pi\) | ||||
−0.236361 | + | 0.971665i | \(0.575955\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.57977e41 | −1.10542 | ||||||||
\(940\) | 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 | \(0.333333\pi\) | |||||||
\(948\) | 2.65526e41 | − | 4.59904e41i | 0.560777 | − | 0.971294i | ||||
\(949\) | −6.15009e41 | + | 1.06523e42i | −1.27984 | + | 2.21674i | ||||
\(950\) | 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 | ||||||||
\(961\) | −8.21019e41 | − | 1.42205e42i | −1.43293 | − | 2.48191i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.15926e41 | − | 8.93610e41i | −0.862004 | − | 1.49303i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.80431e41 | 1.40839 | 0.704197 | − | 0.710004i | \(-0.251307\pi\) | ||||
0.704197 | + | 0.710004i | \(0.251307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | 6.71936e41 | 1.00000 | ||||||||
\(973\) | −4.32286e41 | + | 6.17023e41i | −0.634149 | + | 0.905152i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.12760e41 | − | 1.06133e42i | −0.873426 | − | 1.51282i | ||||
\(976\) | −6.79776e41 | + | 1.17741e42i | −0.955144 | + | 1.65436i | ||||
\(977\) | 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 | ||||||||
\(981\) | 1.03946e41 | 0.135970 | ||||||||
\(982\) | 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 | ||||||||
\(988\) | 1.66815e42 | 1.97532 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.73880e41 | + | 3.01169e41i | −0.197341 | + | 0.341805i | −0.947666 | − | 0.319265i | \(-0.896564\pi\) |
0.750324 | + | 0.661070i | \(0.229897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.30183e42 | 1.43637 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.25641e41 | + | 1.60326e42i | −0.965407 | + | 1.67213i | −0.256889 | + | 0.966441i | \(0.582698\pi\) |
−0.708518 | + | 0.705693i | \(0.750636\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.60081e41 | + | 1.14329e42i | 0.669391 | + | 1.15942i |
(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 | 21.29.h.a.11.1 | yes | 2 | |
3.2 | odd | 2 | CM | 21.29.h.a.11.1 | yes | 2 | |
7.2 | even | 3 | inner | 21.29.h.a.2.1 | ✓ | 2 | |
21.2 | odd | 6 | inner | 21.29.h.a.2.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.29.h.a.2.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
21.29.h.a.2.1 | ✓ | 2 | 21.2 | odd | 6 | inner | |
21.29.h.a.11.1 | yes | 2 | 1.1 | even | 1 | trivial | |
21.29.h.a.11.1 | yes | 2 | 3.2 | odd | 2 | CM |