Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,38,Mod(5,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.5");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.g (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(182.099480062\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.5 |
Dual form | 21.38.g.a.17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −5.81131e8 | + | 3.35516e8i | −0.866025 | + | 0.500000i | ||||
\(4\) | −6.87195e10 | − | 1.19026e11i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.94136e15 | + | 3.14809e15i | 0.682708 | + | 0.730692i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.25142e17 | − | 3.89957e17i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 7.98700e19 | + | 4.61130e19i | 0.866025 | + | 0.500000i | ||||
\(13\) | − | 3.52663e20i | − | 0.869777i | −0.900484 | − | 0.434889i | \(-0.856788\pi\) | ||
0.900484 | − | 0.434889i | \(-0.143212\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −9.44473e21 | + | 1.63588e22i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.84496e23 | + | 4.52929e23i | 1.72842 | + | 0.997904i | 0.896569 | + | 0.442904i | \(0.146052\pi\) |
0.831851 | + | 0.555000i | \(0.187282\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.76555e24 | − | 8.42580e23i | −0.956588 | − | 0.291444i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.63798e25 | + | 6.30116e25i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.02155e26i | 1.00000i | ||||||||
\(28\) | 1.72575e26 | − | 5.66433e26i | 0.291444 | − | 0.956588i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.74022e27 | − | 3.89147e27i | 1.73174 | − | 0.999820i | 0.856392 | − | 0.516327i | \(-0.172701\pi\) |
0.875348 | − | 0.483493i | \(-0.160632\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.18865e28 | −1.00000 | ||||||||
\(37\) | −9.92707e27 | + | 1.71942e28i | −0.0966250 | + | 0.167359i | −0.910286 | − | 0.413981i | \(-0.864138\pi\) |
0.813661 | + | 0.581340i | \(0.197471\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.18324e29 | + | 2.04943e29i | 0.434889 | + | 0.753249i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12847e30 | −1.88871 | −0.944355 | − | 0.328927i | \(-0.893313\pi\) | ||||
−0.944355 | + | 0.328927i | \(0.893313\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | − | 1.26754e31i | − | 1.00000i | ||||||
\(49\) | −1.25889e30 | + | 1.85194e31i | −0.0678202 | + | 0.997698i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.19760e31 | + | 2.42348e31i | −0.753249 | + | 0.434889i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.07860e32 | −1.99581 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.77999e33 | − | 1.02768e33i | −1.66654 | − | 0.962178i | −0.969481 | − | 0.245166i | \(-0.921158\pi\) |
−0.697060 | − | 0.717012i | \(-0.745509\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.88985e33 | − | 4.38238e32i | 0.974151 | − | 0.225897i | ||||
\(64\) | 2.59615e33 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.13785e33 | − | 8.89901e33i | −0.848003 | − | 1.46878i | −0.882988 | − | 0.469396i | \(-0.844472\pi\) |
0.0349851 | − | 0.999388i | \(-0.488862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.10751e34 | − | 2.94882e34i | 1.72479 | − | 0.995807i | 0.816657 | − | 0.577123i | \(-0.195825\pi\) |
0.908132 | − | 0.418684i | \(-0.137509\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.22828e34 | − | 2.44120e34i | −0.866025 | − | 0.500000i | ||||
\(76\) | − | 1.24500e35i | − | 1.99581i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.11822e35 | + | 1.93681e35i | −0.875842 | + | 1.51700i | −0.0199782 | + | 0.999800i | \(0.506360\pi\) |
−0.855863 | + | 0.517202i | \(0.826974\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.01378e35 | − | 1.75591e35i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 8.97587e34 | + | 3.87073e35i | 0.225897 | + | 0.974151i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.11022e36 | − | 1.03731e36i | 0.635539 | − | 0.593804i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.61130e36 | + | 4.52290e36i | −0.999820 | + | 1.73174i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.37793e36i | 1.12048i | 0.828332 | + | 0.560238i | \(0.189290\pi\) | ||||
−0.828332 | + | 0.560238i | \(0.810710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000e36 | − | 8.66025e36i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.68000e37 | + | 1.54730e37i | 1.55112 | + | 0.895540i | 0.998051 | + | 0.0624056i | \(0.0198772\pi\) |
0.553070 | + | 0.833135i | \(0.313456\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 3.59642e37 | − | 2.07639e37i | 0.866025 | − | 0.500000i | ||||
\(109\) | −2.93868e37 | − | 5.08993e37i | −0.596707 | − | 1.03353i | −0.993304 | − | 0.115534i | \(-0.963142\pi\) |
0.396596 | − | 0.917993i | \(-0.370191\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.33228e37i | − | 0.193250i | ||||||
\(112\) | −7.92793e37 | + | 1.83841e37i | −0.974151 | + | 0.225897i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.37524e38 | − | 7.93993e37i | −0.753249 | − | 0.434889i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.70020e38 | + | 2.94483e38i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.26368e38 | − | 5.34839e38i | −1.73174 | − | 0.999820i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.33146e38 | 1.12094 | 0.560468 | − | 0.828176i | \(-0.310621\pi\) | ||||
0.560468 | + | 0.828176i | \(0.310621\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.81805e39 | − | 1.04965e39i | 1.63567 | − | 0.944355i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.81624e38 | + | 3.80190e39i | 0.450846 | + | 1.94422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.37950e39i | 0.311851i | 0.987769 | + | 0.155925i | \(0.0498360\pi\) | ||||
−0.987769 | + | 0.155925i | \(0.950164\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.25281e39 | + | 7.36609e39i | 0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.48197e39 | − | 1.11846e40i | −0.440115 | − | 0.897942i | ||||
\(148\) | 2.72873e39 | 0.193250 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.75071e39 | + | 8.22847e39i | 0.232105 | + | 0.402018i | 0.958427 | − | 0.285336i | \(-0.0921053\pi\) |
−0.726322 | + | 0.687354i | \(0.758772\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.62623e40 | − | 2.81672e40i | 0.434889 | − | 0.753249i | ||||
\(157\) | −7.27708e40 | + | 4.20142e40i | −1.72907 | + | 0.998281i | −0.835229 | + | 0.549902i | \(0.814665\pi\) |
−0.893844 | + | 0.448378i | \(0.852002\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.89716e40 | − | 1.02142e41i | 0.700120 | − | 1.21264i | −0.268304 | − | 0.963334i | \(-0.586463\pi\) |
0.968424 | − | 0.249309i | \(-0.0802036\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00295e40 | 0.243487 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.53246e41 | − | 2.03947e41i | 1.72842 | − | 0.997904i | ||||
\(172\) | 2.14987e41 | + | 3.72368e41i | 0.944355 | + | 1.63567i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.13605e40 | + | 2.99867e41i | −0.291444 | + | 0.956588i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.11293e42i | 1.90289i | 0.307823 | + | 0.951444i | \(0.400399\pi\) | ||||
−0.307823 | + | 0.951444i | \(0.599601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.37921e42 | 1.92436 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.51212e41 | + | 8.88747e41i | −0.730692 | + | 0.682708i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | −1.50870e42 | + | 8.71049e41i | −0.866025 | + | 0.500000i | ||||
\(193\) | 1.03691e42 | + | 1.79597e42i | 0.540666 | + | 0.936461i | 0.998866 | + | 0.0476117i | \(0.0151610\pi\) |
−0.458200 | + | 0.888849i | \(0.651506\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.29079e42 | − | 1.12280e42i | 0.897942 | − | 0.440115i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.77964e42 | − | 3.33688e42i | 1.71048 | − | 0.987549i | 0.776586 | − | 0.630011i | \(-0.216950\pi\) |
0.933899 | − | 0.357538i | \(-0.116384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.97152e42 | + | 3.44766e42i | 1.46878 | + | 0.848003i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.76913e42 | + | 3.33081e42i | 0.753249 | + | 0.434889i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.97186e42 | 0.798609 | 0.399304 | − | 0.916818i | \(-0.369252\pi\) | ||||
0.399304 | + | 0.916818i | \(0.369252\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.20761e43 | + | 9.77263e42i | 1.91283 | + | 0.582782i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.97875e43 | + | 3.42730e43i | −0.995807 | + | 1.72479i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.05912e43i | 1.10143i | 0.834693 | + | 0.550715i | \(0.185645\pi\) | ||||
−0.834693 | + | 0.550715i | \(0.814355\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.27625e43 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 4.17718e43 | + | 7.23509e43i | 0.997904 | + | 1.72842i | ||||
\(229\) | 5.53910e43 | + | 3.19800e43i | 1.22035 | + | 0.704567i | 0.964992 | − | 0.262281i | \(-0.0844747\pi\) |
0.255354 | + | 0.966848i | \(0.417808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.50072e44i | − | 1.75168i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.91597e42 | + | 3.41559e42i | −0.0506653 | + | 0.0292516i | −0.525119 | − | 0.851029i | \(-0.675979\pi\) |
0.474453 | + | 0.880281i | \(0.342646\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.17828e44 | + | 6.80277e43i | 0.866025 | + | 0.500000i | ||||
\(244\) | 2.82486e44i | 1.92436i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.59731e44 | − | 2.76663e44i | 0.867954 | − | 1.50334i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −1.82031e44 | − | 1.94825e44i | −0.682708 | − | 0.730692i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.78406e44 | − | 3.09008e44i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.33281e43 | + | 1.93230e43i | −0.188255 | + | 0.0436545i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.06140e44 | + | 1.22307e45i | −0.848003 | + | 1.46878i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.76690e45 | − | 1.02012e45i | −1.72695 | − | 0.997055i | −0.901822 | − | 0.432108i | \(-0.857770\pi\) |
−0.825127 | − | 0.564947i | \(-0.808897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.97147e44 | + | 9.75308e44i | −0.253491 | + | 0.832019i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.15841e44 | + | 8.93463e44i | 0.336233 | + | 0.582372i | 0.983721 | − | 0.179703i | \(-0.0575138\pi\) |
−0.647488 | + | 0.762076i | \(0.724180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.50453e45i | − | 1.99964i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.91834e44 | − | 2.26226e44i | 0.171812 | − | 0.0991957i | −0.411628 | − | 0.911352i | \(-0.635040\pi\) |
0.583440 | + | 0.812156i | \(0.301706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.68105e45 | − | 2.91166e45i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.13990e45 | − | 3.70641e45i | −0.560238 | − | 0.970361i | ||||
\(292\) | −7.01970e45 | − | 4.05283e45i | −1.72479 | − | 0.995807i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 6.71032e45i | 1.00000i | ||||||||
\(301\) | −9.20196e45 | − | 9.84872e45i | −1.28944 | − | 1.38006i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.48187e46 | + | 8.55559e45i | −1.72842 | + | 0.997904i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.98787e46i | − | 1.93343i | −0.255859 | − | 0.966714i | \(-0.582358\pi\) | ||
0.255859 | − | 0.966714i | \(-0.417642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.07657e46 | −1.79108 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.87985e46 | + | 1.08533e46i | 1.27807 | + | 0.737892i | 0.976493 | − | 0.215551i | \(-0.0691547\pi\) |
0.301574 | + | 0.953443i | \(0.402488\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.07374e46 | 1.75168 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.39333e46 | + | 2.41331e46i | −0.500000 | + | 0.866025i | ||||
\(325\) | 2.22219e46 | − | 1.28298e46i | 0.753249 | − | 0.434889i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.41551e46 | + | 1.97194e46i | 1.03353 | + | 0.596707i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.51969e46 | + | 6.09628e46i | −0.850524 | + | 1.47315i | 0.0302129 | + | 0.999543i | \(0.490381\pi\) |
−0.880737 | + | 0.473607i | \(0.842952\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.47000e45 | + | 7.74227e45i | 0.0966250 | + | 0.167359i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.99035e46 | − | 3.72831e46i | 0.730692 | − | 0.682708i | ||||
\(337\) | 1.08707e47 | 1.88410 | 0.942048 | − | 0.335479i | \(-0.108898\pi\) | ||||
0.942048 | + | 0.335479i | \(0.108898\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.20036e46 | + | 5.05091e46i | −0.775311 | + | 0.631580i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.62094e46i | − | 0.147061i | −0.997293 | − | 0.0735305i | \(-0.976573\pi\) | ||
0.997293 | − | 0.0735305i | \(-0.0234266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.06559e47 | 0.869777 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.07286e47 | + | 5.32234e47i | 1.49162 | + | 2.58357i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.28177e47i | − | 1.00000i | ||||||
\(364\) | −1.99760e47 | − | 6.08609e46i | −0.832019 | − | 0.253491i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.83590e46 | + | 5.67876e46i | −0.351959 | + | 0.203204i | −0.665548 | − | 0.746355i | \(-0.731802\pi\) |
0.313589 | + | 0.949559i | \(0.398469\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.17788e47 | 1.99964 | ||||||||
\(373\) | 5.04704e46 | − | 8.74173e46i | 0.133790 | − | 0.231731i | −0.791345 | − | 0.611370i | \(-0.790619\pi\) |
0.925135 | + | 0.379639i | \(0.123952\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.68943e47 | 1.31997 | 0.659985 | − | 0.751279i | \(-0.270563\pi\) | ||||
0.659985 | + | 0.751279i | \(0.270563\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.42280e47 | + | 3.13086e47i | −0.970759 | + | 0.560468i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.04350e47 | + | 1.21997e48i | −0.944355 | + | 1.63567i | ||||
\(388\) | 7.59137e47 | − | 4.38288e47i | 0.970361 | − | 0.560238i | ||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.15997e47 | − | 4.71116e47i | −0.682440 | − | 0.394007i | 0.118334 | − | 0.992974i | \(-0.462245\pi\) |
−0.800774 | + | 0.598967i | \(0.795578\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.78794e48 | − | 1.91360e48i | −1.36255 | − | 1.45832i | ||||
\(400\) | −1.37439e48 | −1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.37238e48 | − | 2.37703e48i | −0.869621 | − | 1.50623i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.55113e48 | + | 2.05025e48i | −1.71193 | + | 0.988382i | −0.779969 | + | 0.625818i | \(0.784765\pi\) |
−0.931959 | + | 0.362564i | \(0.881901\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 4.25318e48i | − | 1.79108i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.62843e47 | − | 8.01668e47i | −0.155925 | − | 0.270071i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.10362e48 | 1.72333 | 0.861666 | − | 0.507477i | \(-0.169422\pi\) | ||||
0.861666 | + | 0.507477i | \(0.169422\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00037e48 | − | 8.62636e48i | −0.434705 | − | 1.87461i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −4.94288e48 | − | 2.85377e48i | −0.866025 | − | 0.500000i | ||||
\(433\) | 8.86530e48i | 1.48822i | 0.668057 | + | 0.744110i | \(0.267126\pi\) | ||||
−0.668057 | + | 0.744110i | \(0.732874\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.03888e48 | + | 6.99555e48i | −0.596707 | + | 1.03353i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.83459e48 | − | 2.79125e48i | −0.629167 | − | 0.363250i | 0.151263 | − | 0.988494i | \(-0.451666\pi\) |
−0.780429 | + | 0.625244i | \(0.784999\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.93834e48 | + | 4.66040e48i | 0.830121 | + | 0.557583i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | −1.58575e48 | + | 9.15534e47i | −0.167359 | + | 0.0966250i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.63621e48 | + | 8.17292e48i | 0.682708 | + | 0.730692i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.52156e48 | − | 3.18788e48i | −0.402018 | − | 0.232105i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.65146e48 | + | 9.78862e48i | −0.349713 | + | 0.605720i | −0.986198 | − | 0.165569i | \(-0.947054\pi\) |
0.636486 | + | 0.771288i | \(0.280387\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.71811e49 | 1.80748 | 0.903741 | − | 0.428079i | \(-0.140810\pi\) | ||||
0.903741 | + | 0.428079i | \(0.140810\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 2.18251e49i | 0.869777i | ||||||||
\(469\) | 1.29027e49 | − | 4.23496e49i | 0.494290 | − | 1.62238i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.81929e49 | − | 4.88315e49i | 0.998281 | − | 1.72907i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.59099e49i | 1.99581i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.06376e48 | + | 3.50091e48i | 0.145565 | + | 0.0840422i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.67347e49 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.49323e49 | + | 2.58636e49i | 0.284998 | + | 0.493631i | 0.972609 | − | 0.232449i | \(-0.0746737\pi\) |
−0.687611 | + | 0.726080i | \(0.741340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.91437e49i | 1.40024i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.47015e50i | 1.99964i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.04884e49 | − | 1.04769e50i | 0.735889 | − | 1.27460i | −0.218443 | − | 0.975850i | \(-0.570098\pi\) |
0.954332 | − | 0.298747i | \(-0.0965688\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.32624e49 | + | 1.34306e49i | −0.210866 | + | 0.121744i | ||||
\(508\) | −6.41253e49 | − | 1.11068e50i | −0.560468 | − | 0.970759i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.43062e50 | + | 7.40536e49i | 1.90515 | + | 0.580443i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.36855e50 | + | 2.37039e50i | −0.997904 | + | 1.72842i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.49871e50 | − | 1.44263e50i | −1.63567 | − | 0.944355i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.30288e50 | − | 1.32957e50i | −1.17487 | − | 0.678311i | −0.220047 | − | 0.975489i | \(-0.570621\pi\) |
−0.954822 | + | 0.297178i | \(0.903954\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.75178e49 | − | 2.04915e50i | −0.225897 | − | 0.974151i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.21032e50 | − | 2.09633e50i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.91938e50 | − | 3.66200e50i | 1.45832 | − | 1.36255i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.30237e49 | − | 1.43801e50i | 0.226492 | − | 0.392295i | −0.730274 | − | 0.683154i | \(-0.760608\pi\) |
0.956766 | + | 0.290859i | \(0.0939410\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.73405e50 | − | 6.46756e50i | −0.951444 | − | 1.64795i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.27774e50 | −0.506686 | −0.253343 | − | 0.967377i | \(-0.581530\pi\) | ||||
−0.253343 | + | 0.967377i | \(0.581530\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.01502e50 | + | 4.62747e50i | −1.66654 | + | 0.962178i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.38635e50 | + | 2.17661e50i | −1.70640 | + | 0.395699i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.64195e50 | − | 9.47983e49i | 0.270071 | − | 0.155925i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.10330e51i | 1.64276i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.54590e50 | − | 8.35625e50i | 0.291444 | − | 0.956588i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.27588e50 | + | 1.43343e51i | 0.831853 | + | 1.44081i | 0.896568 | + | 0.442907i | \(0.146053\pi\) |
−0.0647150 | + | 0.997904i | \(0.520614\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.84502e50 | − | 1.01239e51i | 0.500000 | − | 0.866025i | ||||
\(577\) | 7.23872e50 | − | 4.17928e50i | 0.599666 | − | 0.346217i | −0.169244 | − | 0.985574i | \(-0.554133\pi\) |
0.768910 | + | 0.639357i | \(0.220799\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.20516e51 | − | 6.95797e50i | −0.936461 | − | 0.540666i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −9.54531e50 | + | 1.42109e51i | −0.557583 | + | 0.830121i | ||||
\(589\) | 7.05023e51 | 3.99090 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.87517e50 | − | 3.24789e50i | −0.0966250 | − | 0.167359i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.23915e51 | + | 3.87833e51i | −0.987549 | + | 1.71048i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.95401e51i | − | 1.93099i | −0.260428 | − | 0.965493i | \(-0.583864\pi\) | ||
0.260428 | − | 0.965493i | \(-0.416136\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.62698e51 | −1.69601 | ||||||||
\(604\) | 6.52932e50 | − | 1.13091e51i | 0.232105 | − | 0.402018i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.70756e51 | + | 2.14056e51i | 1.20253 | + | 0.694283i | 0.961118 | − | 0.276138i | \(-0.0890548\pi\) |
0.241416 | + | 0.970422i | \(0.422388\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.49869e51 | + | 6.05991e51i | 0.945991 | + | 1.63850i | 0.753754 | + | 0.657156i | \(0.228241\pi\) |
0.192237 | + | 0.981349i | \(0.438426\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.44378e51 | − | 8.33567e50i | 0.326005 | − | 0.188219i | −0.328061 | − | 0.944657i | \(-0.606395\pi\) |
0.654066 | + | 0.756437i | \(0.273062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.47016e51 | −0.869777 | ||||||||
\(625\) | −2.64698e51 | + | 4.58470e51i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.00015e52 | + | 5.77439e51i | 1.72907 | + | 0.998281i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.23496e52 | 1.95483 | 0.977417 | − | 0.211318i | \(-0.0677756\pi\) | ||||
0.977417 | + | 0.211318i | \(0.0677756\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.63269e51 | + | 2.67469e51i | −0.691615 | + | 0.399304i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.53110e51 | + | 4.43963e50i | 0.867775 | + | 0.0589885i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.15200e51i | − | 0.798959i | −0.916742 | − | 0.399479i | \(-0.869191\pi\) | ||
0.916742 | − | 0.399479i | \(-0.130809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.19193e52 | + | 5.08288e51i | −1.94795 | + | 0.451712i | ||||
\(652\) | −1.62100e52 | −1.40024 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.65561e52i | − | 1.99161i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.37929e52 | − | 1.37369e52i | 1.59485 | − | 0.920789i | 0.602397 | − | 0.798197i | \(-0.294213\pi\) |
0.992457 | − | 0.122592i | \(-0.0391207\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.02638e52 | − | 1.77775e52i | −0.550715 | − | 0.953866i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.71216e52 | −1.78381 | −0.891903 | − | 0.452227i | \(-0.850630\pi\) | ||||
−0.891903 | + | 0.452227i | \(0.850630\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.90393e52 | + | 1.09923e52i | −0.866025 | + | 0.500000i | ||||
\(676\) | −2.75081e51 | − | 4.76454e51i | −0.121744 | − | 0.210866i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00783e52 | + | 1.87598e52i | −0.818722 | + | 0.764958i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | −4.85498e52 | − | 2.80302e52i | −1.72842 | − | 0.997904i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.29192e52 | −1.40913 | ||||||||
\(688\) | 2.95476e52 | − | 5.11779e52i | 0.944355 | − | 1.63567i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.37229e52 | + | 3.10169e52i | 1.58422 | + | 0.914650i | 0.994233 | + | 0.107237i | \(0.0342005\pi\) |
0.589987 | + | 0.807413i | \(0.299133\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.19701e52 | − | 9.73247e51i | 0.974151 | − | 0.225897i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.55755e52 | + | 8.99252e51i | −0.334017 | + | 0.192845i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.68621e51 | − | 4.65264e51i | 0.0492248 | − | 0.0852598i | −0.840363 | − | 0.542024i | \(-0.817658\pi\) |
0.889588 | + | 0.456764i | \(0.150992\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.03516e52 | + | 8.72115e52i | 0.875842 | + | 1.51700i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.01181e52 | + | 1.29880e53i | 0.404599 | + | 1.74478i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.29197e51 | − | 3.96981e51i | 0.0292516 | − | 0.0506653i | ||||
\(724\) | 1.32467e53 | − | 7.64798e52i | 1.64795 | − | 0.951444i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.95008e52i | − | 0.455218i | −0.973753 | − | 0.227609i | \(-0.926909\pi\) | ||
0.973753 | − | 0.227609i | \(-0.0730909\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.12976e52 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −9.47786e52 | − | 1.64161e53i | −0.962178 | − | 1.66654i | ||||
\(733\) | −1.47204e52 | − | 8.49885e51i | −0.145713 | − | 0.0841272i | 0.425371 | − | 0.905019i | \(-0.360144\pi\) |
−0.571084 | + | 0.820892i | \(0.693477\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.28868e52 | + | 9.16026e52i | 0.450220 | + | 0.779805i | 0.998399 | − | 0.0565563i | \(-0.0180121\pi\) |
−0.548179 | + | 0.836361i | \(0.684679\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.14370e53i | 1.73591i | ||||||||
\(742\) | 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 | ||||||||
\(751\) | −2.30559e52 | + | 3.99340e52i | −0.145695 | + | 0.252350i | −0.929632 | − | 0.368490i | \(-0.879875\pi\) |
0.783937 | + | 0.620840i | \(0.213208\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.71150e53 | + | 5.21444e52i | 0.956588 | + | 0.291444i | ||||
\(757\) | 2.19345e53 | 1.19634 | 0.598169 | − | 0.801370i | \(-0.295895\pi\) | ||||
0.598169 | + | 0.801370i | \(0.295895\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.37989e52 | − | 2.42226e53i | 0.347813 | − | 1.14161i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.07354e53 | + | 1.19716e53i | 0.866025 | + | 0.500000i | ||||
\(769\) | 3.55605e53i | 1.44988i | 0.688814 | + | 0.724938i | \(0.258132\pi\) | ||||
−0.688814 | + | 0.724938i | \(0.741868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.42511e53 | − | 2.46837e53i | 0.540666 | − | 0.936461i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.90415e53 | + | 2.83141e53i | 1.73174 | + | 0.999820i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.19413e52 | − | 3.91871e52i | 0.141206 | − | 0.131933i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.91064e53 | − | 1.95504e53i | −0.830121 | − | 0.557583i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.92115e53 | + | 2.84123e53i | −1.30778 | + | 0.755046i | −0.981725 | − | 0.190306i | \(-0.939052\pi\) |
−0.326053 | + | 0.945352i | \(0.605719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.62425e53 | + | 6.27738e53i | −0.836881 | + | 1.44952i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.94348e53 | − | 4.58617e53i | −1.71048 | − | 0.987549i | ||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 9.47685e53i | − | 1.69601i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.35792e53i | 0.969235i | 0.874726 | + | 0.484618i | \(0.161041\pi\) | ||||
−0.874726 | + | 0.484618i | \(0.838959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.36906e54 | 1.99411 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.45427e54 | − | 1.41697e54i | −3.26448 | − | 1.88475i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.54550e53 | − | 6.66479e53i | −0.196480 | − | 0.847295i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.79989e53 | − | 1.35098e54i | −0.906132 | − | 1.56947i | −0.819391 | − | 0.573235i | \(-0.805688\pi\) |
−0.0867406 | − | 0.996231i | \(-0.527645\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.44681e53 | + | 1.99002e53i | −0.350073 | + | 0.202115i | −0.664717 | − | 0.747095i | \(-0.731448\pi\) |
0.314644 | + | 0.949210i | \(0.398115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.99542e53 | − | 3.46146e53i | −0.582372 | − | 0.336233i | ||||
\(832\) | − | 9.15566e53i | − | 0.869777i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.17583e54 | + | 2.03659e54i | 0.999820 | + | 1.73174i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.28448e54 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.47822e53 | − | 9.48855e53i | −0.399304 | − | 0.691615i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.42715e54 | + | 3.30943e53i | −0.974151 | + | 0.225897i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.51805e53 | + | 2.62933e53i | −0.0991957 | + | 0.171812i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.96270e53i | 0.417081i | 0.978014 | + | 0.208541i | \(0.0668714\pi\) | ||||
−0.978014 | + | 0.208541i | \(0.933129\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.27435e54 | + | 1.89045e54i | 1.72287 | + | 0.994698i | 0.912855 | + | 0.408284i | \(0.133873\pi\) |
0.810012 | + | 0.586414i | \(0.199461\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.25607e54i | 1.00000i | ||||||||
\(868\) | −1.04106e54 | − | 4.48945e54i | −0.451712 | − | 1.94795i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.13835e54 | + | 1.81193e54i | −1.27751 | + | 0.737574i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.48712e54 | + | 1.43594e54i | 0.970361 | + | 0.560238i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.43915e54 | 1.99161 | ||||||||
\(877\) | −1.64830e54 | + | 2.85494e54i | −0.590940 | + | 1.02354i | 0.403166 | + | 0.915127i | \(0.367910\pi\) |
−0.994106 | + | 0.108412i | \(0.965423\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.57044e54 | −1.44439 | −0.722196 | − | 0.691689i | \(-0.756867\pi\) | ||||
−0.722196 | + | 0.691689i | \(0.756867\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.74472e54 | + | 2.93763e54i | 0.765272 | + | 0.819059i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.64114e54 | − | 2.10221e54i | 0.953866 | − | 0.550715i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.25142e54 | − | 3.89957e54i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.65194e54 | + | 2.63599e54i | 1.80672 | + | 0.550452i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.80620e54 | + | 3.12843e54i | 0.347561 | + | 0.601993i | 0.985816 | − | 0.167832i | \(-0.0536768\pi\) |
−0.638255 | + | 0.769825i | \(0.720343\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 5.74107e54 | − | 9.94383e54i | 0.997904 | − | 1.72842i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 8.79060e54i | − | 1.40913i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.79812e54 | + | 6.57854e54i | −0.573102 | + | 0.992642i | 0.423143 | + | 0.906063i | \(0.360927\pi\) |
−0.996245 | + | 0.0865791i | \(0.972406\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.66962e54 | + | 1.15521e55i | 0.966714 | + | 1.67440i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.44458e54 | −0.193250 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.20676e55 | − | 6.96723e54i | 1.55112 | − | 0.895540i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.37556e54 | + | 1.39582e55i | −1.11283 | + | 1.65676i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.64094e55i | 1.72946i | 0.502234 | + | 0.864732i | \(0.332512\pi\) | ||||
−0.502234 | + | 0.864732i | \(0.667488\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.45659e55 | −1.47578 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | −1.78624e55 | + | 1.03129e55i | −1.51700 | + | 0.875842i | ||||
\(949\) | −1.03994e55 | − | 1.80123e55i | −0.866131 | − | 1.50018i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.27125e55 | − | 3.93393e55i | 1.49928 | − | 2.59683i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.13085e53 | + | 4.69435e53i | 0.0506653 | + | 0.0292516i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.90399e55 | −1.12015 | −0.560073 | − | 0.828443i | \(-0.689227\pi\) | ||||
−0.560073 | + | 0.828443i | \(0.689227\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | − | 1.86993e55i | − | 1.00000i | ||||||
\(973\) | −4.34279e54 | + | 4.05760e54i | −0.227867 | + | 0.212903i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.60921e54 | + | 1.49116e55i | −0.434889 | + | 0.753249i | ||||
\(976\) | 3.36231e55 | − | 1.94123e55i | 1.66654 | − | 0.962178i | ||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.64648e55 | −1.19341 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.39066e55 | −1.73591 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.70537e55 | − | 2.95378e55i | −0.637464 | − | 1.10412i | −0.985987 | − | 0.166820i | \(-0.946650\pi\) |
0.348523 | − | 0.937300i | \(-0.386683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 4.72365e55i | − | 1.70105i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.41780e54 | + | 3.70532e54i | −0.214549 | + | 0.123870i | −0.603424 | − | 0.797421i | \(-0.706197\pi\) |
0.388875 | + | 0.921291i | \(0.372864\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.19531e54 | − | 2.99951e54i | −0.167359 | − | 0.0966250i |
(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 | 21.38.g.a.5.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.38.g.a.5.1 | ✓ | 2 | |
7.3 | odd | 6 | inner | 21.38.g.a.17.1 | yes | 2 | |
21.17 | even | 6 | inner | 21.38.g.a.17.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.38.g.a.5.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.38.g.a.5.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.38.g.a.17.1 | yes | 2 | 7.3 | odd | 6 | inner | |
21.38.g.a.17.1 | yes | 2 | 21.17 | even | 6 | inner |