Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,18,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, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.5");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
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: | \(38.4766383424\) |
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 | 21.18.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 | \(0.666667\pi\) | |||||||
\(3\) | 9841.50 | − | 5681.99i | 0.866025 | − | 0.500000i | ||||
\(4\) | −65536.0 | − | 113512.i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.37909e6 | + | 1.51898e7i | −0.0904189 | + | 0.995904i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.45701e7 | − | 1.11839e8i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −1.28995e9 | − | 7.44750e8i | −0.866025 | − | 0.500000i | ||||
\(13\) | − | 4.89177e9i | − | 1.66321i | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||
0.555366 | − | 0.831606i | \(-0.312578\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.58993e9 | + | 1.48782e10i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.26967e11 | − | 7.33047e10i | −1.71509 | − | 0.990208i | −0.927346 | − | 0.374205i | \(-0.877916\pi\) |
−0.787744 | − | 0.616003i | \(-0.788751\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.27358e10 | + | 1.57326e11i | 0.419647 | + | 0.907687i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.81470e11 | + | 6.60725e11i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.46755e12i | − | 1.00000i | ||||||
\(28\) | 1.81459e12 | − | 8.38933e11i | 0.907687 | − | 0.419647i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.37326e12 | + | 2.52490e12i | −0.920939 | + | 0.531704i | −0.883935 | − | 0.467611i | \(-0.845115\pi\) |
−0.0370045 | + | 0.999315i | \(0.511782\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.69267e13 | −1.00000 | ||||||||
\(37\) | −2.10510e13 | + | 3.64613e13i | −0.985274 | + | 1.70654i | −0.344562 | + | 0.938764i | \(0.611973\pi\) |
−0.640712 | + | 0.767781i | \(0.721361\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.77950e13 | − | 4.81424e13i | −0.831606 | − | 1.44038i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.48977e13 | −0.716263 | −0.358131 | − | 0.933671i | \(-0.616586\pi\) | ||||
−0.358131 | + | 0.933671i | \(0.616586\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 1.95232e14i | 1.00000i | ||||||||
\(49\) | −2.28827e14 | − | 4.18961e13i | −0.983649 | − | 0.180097i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.55273e14 | + | 3.20587e14i | −1.44038 | + | 0.831606i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.66607e15 | −1.98042 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.59110e15 | − | 1.49597e15i | −1.73053 | − | 0.999124i | −0.886191 | − | 0.463320i | \(-0.846658\pi\) |
−0.844343 | − | 0.535804i | \(-0.820009\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.60975e15 | + | 1.13504e15i | 0.817269 | + | 0.576257i | ||||
\(64\) | 2.25180e15 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.34670e14 | + | 2.33255e14i | 0.0405167 | + | 0.0701769i | 0.885573 | − | 0.464501i | \(-0.153766\pi\) |
−0.845056 | + | 0.534678i | \(0.820433\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.49410e15 | − | 4.32672e15i | 1.08762 | − | 0.627935i | 0.154675 | − | 0.987965i | \(-0.450567\pi\) |
0.932941 | + | 0.360030i | \(0.117234\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.50847e15 | + | 4.33502e15i | 0.866025 | + | 0.500000i | ||||
\(76\) | 1.92164e16i | 1.98042i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.32336e16 | − | 2.29213e16i | 0.981405 | − | 1.69984i | 0.324470 | − | 0.945896i | \(-0.394814\pi\) |
0.656935 | − | 0.753948i | \(-0.271853\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.33859e15 | − | 1.44429e16i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 1.30915e16 | − | 1.85669e16i | 0.576257 | − | 0.817269i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.43048e16 | + | 6.74619e15i | 1.65640 | + | 0.150386i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.86930e16 | + | 4.96977e16i | −0.531704 | + | 0.920939i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.91902e16i | 1.28502i | 0.766278 | + | 0.642509i | \(0.222106\pi\) | ||||
−0.766278 | + | 0.642509i | \(0.777894\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000e16 | − | 8.66025e16i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.12892e17 | − | 1.22913e17i | −1.65593 | − | 0.956053i | −0.974563 | − | 0.224112i | \(-0.928052\pi\) |
−0.681369 | − | 0.731940i | \(-0.738615\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −1.66584e17 | + | 9.61772e16i | −0.866025 | + | 0.500000i | ||||
\(109\) | −9.30230e16 | − | 1.61121e17i | −0.447162 | − | 0.774508i | 0.551038 | − | 0.834480i | \(-0.314232\pi\) |
−0.998200 | + | 0.0599724i | \(0.980899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.78445e17i | 1.97055i | ||||||||
\(112\) | −2.14150e17 | − | 1.50997e17i | −0.817269 | − | 0.576257i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.47089e17 | − | 3.15862e17i | −1.44038 | − | 0.831606i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.52724e17 | + | 4.37730e17i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.73212e17 | + | 3.30944e17i | 0.920939 | + | 0.531704i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.48484e18 | 1.94692 | 0.973460 | − | 0.228856i | \(-0.0734984\pi\) | ||||
0.973460 | + | 0.228856i | \(0.0734984\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.40276e17 | + | 3.11928e17i | −0.620302 | + | 0.358131i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.28858e18 | − | 1.82751e18i | 1.14123 | − | 1.61853i | ||||
\(134\) | 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 | ||||||||
\(139\) | − | 1.31451e18i | − | 0.800091i | −0.916495 | − | 0.400046i | \(-0.868994\pi\) | ||
0.916495 | − | 0.400046i | \(-0.131006\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.10931e18 | + | 1.92137e18i | 0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.49005e18 | + | 8.87871e17i | −0.941913 | + | 0.335856i | ||||
\(148\) | 5.51838e18 | 1.97055 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.17729e18 | − | 2.03913e18i | −0.354471 | − | 0.613962i | 0.632556 | − | 0.774514i | \(-0.282006\pi\) |
−0.987027 | + | 0.160553i | \(0.948672\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.64315e18 | + | 6.31012e18i | −0.831606 | + | 1.44038i | ||||
\(157\) | 6.36649e18 | − | 3.67569e18i | 1.37643 | − | 0.794680i | 0.384698 | − | 0.923042i | \(-0.374306\pi\) |
0.991727 | + | 0.128363i | \(0.0409722\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.84535e18 | − | 8.39239e18i | 0.761606 | − | 1.31914i | −0.180416 | − | 0.983590i | \(-0.557744\pi\) |
0.942022 | − | 0.335551i | \(-0.108922\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.52790e19 | −1.76627 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.63966e19 | + | 9.46658e18i | −1.71509 | + | 0.990208i | ||||
\(172\) | 3.59778e18 | + | 6.23153e18i | 0.358131 | + | 0.620302i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.05623e19 | + | 4.88323e18i | −0.907687 | + | 0.419647i | ||||
\(176\) | 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 | ||||||||
\(181\) | − | 7.31707e18i | − | 0.472138i | −0.971736 | − | 0.236069i | \(-0.924141\pi\) | ||
0.971736 | − | 0.236069i | \(-0.0758592\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.40004e19 | −1.99825 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.22917e19 | + | 2.02388e18i | 0.995904 | + | 0.0904189i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 2.21611e19 | − | 1.27947e19i | 0.866025 | − | 0.500000i | ||||
\(193\) | −4.72356e18 | − | 8.18145e18i | −0.176617 | − | 0.305910i | 0.764103 | − | 0.645095i | \(-0.223182\pi\) |
−0.940720 | + | 0.339185i | \(0.889849\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.02407e19 | + | 2.87202e19i | 0.335856 | + | 0.941913i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.20953e19 | − | 3.00772e19i | 1.50158 | − | 0.866936i | 0.501579 | − | 0.865112i | \(-0.332753\pi\) |
0.999998 | − | 0.00182370i | \(-0.000580503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.65070e18 | + | 1.53038e18i | 0.0701769 | + | 0.0405167i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.27808e19 | + | 4.20200e19i | 1.44038 | + | 0.831606i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.37704e19 | −0.942199 | −0.471099 | − | 0.882080i | \(-0.656143\pi\) | ||||
−0.471099 | + | 0.882080i | \(0.656143\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.23215e19 | − | 6.99108e19i | −0.446256 | − | 0.965243i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.91688e19 | − | 8.51629e19i | 0.627935 | − | 1.08762i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.36793e19i | 0.478282i | 0.970985 | + | 0.239141i | \(0.0768659\pi\) | ||||
−0.970985 | + | 0.239141i | \(0.923134\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.85261e19 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 1.09187e20 | + | 1.89118e20i | 0.990208 | + | 1.71509i | ||||
\(229\) | −1.34333e20 | − | 7.75570e19i | −1.17376 | − | 0.677672i | −0.219198 | − | 0.975680i | \(-0.570344\pi\) |
−0.954563 | + | 0.298009i | \(0.903678\pi\) | |||||||
\(230\) | 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 | ||||||||
\(237\) | − | 3.00773e20i | − | 1.96281i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.00454e19 | + | 1.73467e19i | −0.170072 | + | 0.0981913i | −0.582620 | − | 0.812745i | \(-0.697972\pi\) |
0.412548 | + | 0.910936i | \(0.364639\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.64128e20 | − | 9.47596e19i | −0.866025 | − | 0.500000i | ||||
\(244\) | 3.92160e20i | 1.99825i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.58590e20 | + | 6.21096e20i | −1.64693 | + | 2.85256i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 2.33434e19 | − | 2.57112e20i | 0.0904189 | − | 0.995904i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.47574e20 | − | 2.55606e20i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.24807e20 | − | 3.70042e20i | −1.61047 | − | 1.13554i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.76514e19 | − | 3.05731e19i | 0.0405167 | − | 0.0701769i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.95646e18 | + | 3.43897e18i | 0.0124380 | + | 0.00718106i | 0.506206 | − | 0.862413i | \(-0.331048\pi\) |
−0.493768 | + | 0.869594i | \(0.664381\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.69602e20 | − | 3.55807e20i | 1.50968 | − | 0.697962i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.76007e20 | + | 9.97673e20i | 0.998504 | + | 1.72946i | 0.546612 | + | 0.837386i | \(0.315917\pi\) |
0.451891 | + | 0.892073i | \(0.350750\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.52133e20i | 1.06341i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.09395e21 | − | 6.31593e20i | 1.58057 | − | 0.912541i | 0.585791 | − | 0.810462i | \(-0.300784\pi\) |
0.994776 | − | 0.102079i | \(-0.0325493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.13620e20 | − | 7.16411e20i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.63598e20 | + | 9.76180e20i | 0.642509 | + | 1.11286i | ||||
\(292\) | −9.82267e20 | − | 5.67112e20i | −1.08762 | − | 0.627935i | ||||
\(293\) | 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 | ||||||||
\(300\) | − | 1.13640e21i | − | 1.00000i | ||||||
\(301\) | 7.57089e19 | − | 8.33883e20i | 0.0647637 | − | 0.713329i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.18128e21 | − | 1.25937e21i | 1.71509 | − | 0.990208i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.06009e21i | 1.49008i | 0.667019 | + | 0.745041i | \(0.267570\pi\) | ||||
−0.667019 | + | 0.745041i | \(0.732430\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.79357e21 | −1.91211 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.67683e21 | + | 9.68119e20i | 1.02887 | + | 0.594021i | 0.916662 | − | 0.399663i | \(-0.130873\pi\) |
0.112213 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.46911e21 | −1.96281 | ||||||||
\(317\) | 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 | ||||||||
\(324\) | −1.09296e21 | + | 1.89305e21i | −0.500000 | + | 0.866025i | ||||
\(325\) | 3.23211e21 | − | 1.86606e21i | 1.44038 | − | 0.831606i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.83097e21 | − | 1.05711e21i | −0.774508 | − | 0.447162i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.18080e21 | + | 2.04521e21i | −0.450443 | + | 0.780190i | −0.998413 | − | 0.0563079i | \(-0.982067\pi\) |
0.547971 | + | 0.836497i | \(0.315400\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.71852e21 | + | 4.70862e21i | 0.985274 | + | 1.70654i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.96552e21 | − | 2.69242e20i | −0.995904 | − | 0.0904189i | ||||
\(337\) | −4.46257e21 | −1.46127 | −0.730636 | − | 0.682767i | \(-0.760777\pi\) | ||||
−0.730636 | + | 0.682767i | \(0.760777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.51964e20 | − | 3.41804e21i | 0.268300 | − | 0.963335i | ||||
\(344\) | 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 | ||||||||
\(349\) | − | 7.97556e21i | − | 1.93975i | −0.243608 | − | 0.969874i | \(-0.578331\pi\) | ||
0.243608 | − | 0.969874i | \(-0.421669\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.17890e21 | −1.66321 | ||||||||
\(352\) | 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 | ||||||||
\(361\) | 8.00697e21 | + | 1.38685e22i | 1.46102 | + | 2.53057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.74389e21i | 1.00000i | ||||||||
\(364\) | −4.10387e21 | − | 8.87658e21i | −0.697962 | − | 1.50968i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.13126e21 | − | 4.69459e21i | 1.28972 | − | 0.744622i | 0.311118 | − | 0.950371i | \(-0.399296\pi\) |
0.978605 | + | 0.205749i | \(0.0659631\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.52169e21 | 1.06341 | ||||||||
\(373\) | −3.13320e21 | + | 5.42687e21i | −0.432976 | + | 0.749936i | −0.997128 | − | 0.0757347i | \(-0.975870\pi\) |
0.564152 | + | 0.825671i | \(0.309203\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.03036e22 | 1.24324 | 0.621620 | − | 0.783319i | \(-0.286475\pi\) | ||||
0.621620 | + | 0.783319i | \(0.286475\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.46131e22 | − | 8.43685e21i | 1.68608 | − | 0.973460i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.54475e21 | + | 6.13969e21i | −0.358131 | + | 0.620302i | ||||
\(388\) | 1.12592e22 | − | 6.50053e21i | 1.11286 | − | 0.642509i | ||||
\(389\) | 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 | ||||||||
\(397\) | −1.73248e22 | − | 1.00025e22i | −1.40913 | − | 0.813559i | −0.413821 | − | 0.910358i | \(-0.635806\pi\) |
−0.995304 | + | 0.0967994i | \(0.969139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.29766e21 | − | 2.53072e22i | 0.179067 | − | 1.97230i | ||||
\(400\) | −1.31072e22 | −1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.23512e22 | + | 2.13930e22i | 0.884337 | + | 1.53172i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.69628e22 | + | 1.55670e22i | −1.70262 | + | 0.983006i | −0.759522 | + | 0.650481i | \(0.774567\pi\) |
−0.943094 | + | 0.332525i | \(0.892099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.22209e22i | 1.91211i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.46906e21 | − | 1.29368e22i | −0.400046 | − | 0.692899i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.83194e22 | −1.89244 | −0.946218 | − | 0.323529i | \(-0.895131\pi\) | ||||
−0.946218 | + | 0.323529i | \(0.895131\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.62968e22 | − | 3.72950e22i | 1.15150 | − | 1.63311i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 2.18345e22 | + | 1.26061e22i | 0.866025 | + | 0.500000i | ||||
\(433\) | 1.48866e22i | 0.578961i | 0.957184 | + | 0.289480i | \(0.0934825\pi\) | ||||
−0.957184 | + | 0.289480i | \(0.906518\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.21927e22 | + | 2.11184e22i | −0.447162 | + | 0.774508i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.96629e22 | − | 2.86729e22i | −1.71824 | − | 0.992026i | −0.922137 | − | 0.386862i | \(-0.873559\pi\) |
−0.796101 | − | 0.605163i | \(-0.793108\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.94610e22 | + | 2.28864e22i | −0.647793 | + | 0.761816i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 5.43091e22 | − | 3.13554e22i | 1.70654 | − | 0.985274i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.10544e21 | + | 3.42043e22i | −0.0904189 | + | 0.995904i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.31727e22 | − | 1.33787e22i | −0.613962 | − | 0.354471i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.10055e21 | − | 1.22985e22i | 0.174584 | − | 0.302388i | −0.765433 | − | 0.643515i | \(-0.777475\pi\) |
0.940017 | + | 0.341127i | \(0.110809\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.45502e22 | −0.320207 | −0.160104 | − | 0.987100i | \(-0.551183\pi\) | ||||
−0.160104 | + | 0.987100i | \(0.551183\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 8.28013e22i | 1.66321i | ||||||||
\(469\) | −3.72880e21 | + | 1.72392e21i | −0.0735529 | + | 0.0340054i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.17705e22 | − | 7.23486e22i | 0.794680 | − | 1.37643i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.11854e23i | − | 1.98042i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.78360e23 | + | 1.02976e23i | 2.83835 | + | 1.63872i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.62500e22 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.06702e22 | + | 8.77633e22i | 0.725698 | + | 1.25695i | 0.958686 | + | 0.284467i | \(0.0918166\pi\) |
−0.232987 | + | 0.972480i | \(0.574850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.10125e23i | − | 1.52321i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.67550e22i | − | 1.06341i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.46243e21 | − | 5.99710e21i | 0.0403205 | − | 0.0698372i | −0.845161 | − | 0.534512i | \(-0.820495\pi\) |
0.885481 | + | 0.464675i | \(0.153829\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.50368e23 | + | 8.68152e22i | −1.52964 | + | 0.883137i | ||||
\(508\) | −9.73105e22 | − | 1.68547e23i | −0.973460 | − | 1.68608i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.53868e22 | + | 1.19801e23i | 0.527022 | + | 1.13994i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.07578e23 | + | 1.86331e23i | −0.990208 | + | 1.71509i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.08150e22 | + | 4.08851e22i | 0.620302 | + | 0.358131i | ||||
\(517\) | 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 | ||||||||
\(523\) | −1.38798e23 | − | 8.01353e22i | −1.08423 | − | 0.625978i | −0.152193 | − | 0.988351i | \(-0.548634\pi\) |
−0.932033 | + | 0.362372i | \(0.881967\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.62027e22 | + | 1.08073e23i | −0.576257 | + | 0.817269i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.05250e22 | − | 1.22153e23i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.91892e23 | − | 2.65011e22i | −1.97230 | − | 0.179067i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.53914e23 | − | 2.66586e23i | 0.901780 | − | 1.56193i | 0.0765970 | − | 0.997062i | \(-0.475595\pi\) |
0.825183 | − | 0.564866i | \(-0.191072\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.15755e22 | − | 7.20109e22i | −0.236069 | − | 0.408884i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.70109e23 | 1.97441 | 0.987205 | − | 0.159454i | \(-0.0509733\pi\) | ||||
0.987205 | + | 0.159454i | \(0.0509733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.34615e23 | + | 1.93190e23i | −1.73053 | + | 0.999124i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.29919e23 | + | 2.32626e23i | 1.60414 | + | 1.13108i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.49213e23 | + | 8.61480e22i | −0.692899 | + | 0.400046i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.68547e23i | 1.19130i | ||||||||
\(560\) | 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 | ||||||||
\(567\) | 2.30883e23 | − | 1.06743e23i | 0.907687 | − | 0.419647i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.45147e23 | − | 2.51403e23i | −0.537530 | − | 0.931029i | −0.999036 | − | 0.0438919i | \(-0.986024\pi\) |
0.461507 | − | 0.887137i | \(-0.347309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.45399e23 | − | 2.51838e23i | 0.500000 | − | 0.866025i | ||||
\(577\) | −1.32448e23 | + | 7.64688e22i | −0.448797 | + | 0.259113i | −0.707322 | − | 0.706891i | \(-0.750097\pi\) |
0.258525 | + | 0.966005i | \(0.416764\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.29739e22 | − | 5.36785e22i | −0.305910 | − | 0.176617i | ||||
\(580\) | 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 | \(0.5\pi\) | |||||||||
\(588\) | 2.63972e23 | + | 2.24462e23i | 0.761816 | + | 0.647793i | ||||
\(589\) | 7.40349e23 | 2.10599 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.61653e23 | − | 6.26401e23i | −0.985274 | − | 1.70654i | ||||
\(593\) | 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 | ||||||||
\(597\) | 3.41797e23 | − | 5.92010e23i | 0.866936 | − | 1.50158i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.71692e23i | 1.13038i | 0.824960 | + | 0.565192i | \(0.191198\pi\) | ||||
−0.824960 | + | 0.565192i | \(0.808802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.47825e22 | 0.0810333 | ||||||||
\(604\) | −1.54310e23 | + | 2.67273e23i | −0.354471 | + | 0.613962i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.66573e23 | + | 4.42581e23i | 1.68830 | + | 0.974741i | 0.955820 | + | 0.293954i | \(0.0949711\pi\) |
0.732481 | + | 0.680787i | \(0.238362\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.53080e23 | − | 2.65142e23i | −0.310101 | − | 0.537111i | 0.668283 | − | 0.743907i | \(-0.267030\pi\) |
−0.978384 | + | 0.206796i | \(0.933696\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.55058e23 | + | 8.95225e22i | −0.289149 | + | 0.166940i | −0.637558 | − | 0.770402i | \(-0.720055\pi\) |
0.348409 | + | 0.937343i | \(0.386722\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.55029e23 | 1.66321 | ||||||||
\(625\) | −2.91038e23 | + | 5.04093e23i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.34468e23 | − | 4.81780e23i | −1.37643 | − | 0.794680i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.21877e23 | −1.30184 | −0.650920 | − | 0.759146i | \(-0.725617\pi\) | ||||
−0.650920 | + | 0.759146i | \(0.725617\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.29181e23 | + | 3.05523e23i | −0.815968 | + | 0.471099i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.04946e23 | + | 1.11937e24i | −0.299540 | + | 1.63602i | ||||
\(638\) | 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 | ||||||||
\(643\) | − | 1.04553e24i | − | 1.41106i | −0.708681 | − | 0.705529i | \(-0.750709\pi\) | ||
0.708681 | − | 0.705529i | \(-0.249291\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | −7.15325e23 | − | 5.04377e23i | −0.869090 | − | 0.612797i | ||||
\(652\) | −1.27018e24 | −1.52321 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.11751e24i | − | 1.25587i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.40530e24 | + | 8.11351e23i | −1.49988 | + | 0.865957i | −1.00000 | 0.000137079i | \(-0.999956\pi\) | |
−0.499881 | + | 0.866094i | \(0.666623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.48185e23 | + | 4.29870e23i | 0.239141 | + | 0.414205i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.75121e24 | 1.60402 | 0.802009 | − | 0.597312i | \(-0.203765\pi\) | ||||
0.802009 | + | 0.597312i | \(0.203765\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.69645e23 | − | 5.59825e23i | 0.866025 | − | 0.500000i | ||||
\(676\) | 1.00132e24 | + | 1.73435e24i | 0.883137 | + | 1.52964i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.50667e24 | − | 1.36792e23i | −1.27975 | − | 0.116190i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | 2.14914e24 | + | 1.24080e24i | 1.71509 | + | 0.990208i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.76271e24 | −1.35534 | ||||||||
\(688\) | 4.71568e23 | − | 8.16779e23i | 0.358131 | − | 0.620302i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.98451e22 | − | 2.87781e22i | −0.0364804 | − | 0.0210619i | 0.481649 | − | 0.876364i | \(-0.340038\pi\) |
−0.518129 | + | 0.855302i | \(0.673371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.24652e24 | + | 8.78920e23i | 0.817269 | + | 0.576257i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.34557e24 | − | 3.08627e24i | 3.37967 | − | 1.95125i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.38946e24 | + | 2.40661e24i | −0.817244 | + | 1.41551i | 0.0904608 | + | 0.995900i | \(0.471166\pi\) |
−0.907705 | + | 0.419609i | \(0.862167\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.70899e24 | − | 2.96006e24i | −0.981405 | − | 1.69984i | ||||
\(712\) | 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 | ||||||||
\(721\) | 2.16062e24 | − | 3.06427e24i | 1.10186 | − | 1.56270i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.97128e23 | + | 3.41436e23i | −0.0981913 | + | 0.170072i | ||||
\(724\) | −8.30573e23 | + | 4.79531e23i | −0.408884 | + | 0.236069i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.62788e24i | − | 1.72429i | −0.506661 | − | 0.862145i | \(-0.669120\pi\) | ||
0.506661 | − | 0.862145i | \(-0.330880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.15369e24 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.22825e24 | + | 3.85944e24i | 0.999124 | + | 1.73053i | ||||
\(733\) | −2.31196e24 | − | 1.33481e24i | −1.02470 | − | 0.591610i | −0.109237 | − | 0.994016i | \(-0.534841\pi\) |
−0.915461 | + | 0.402406i | \(0.868174\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.87788e24 | + | 3.25258e24i | 0.776587 | + | 1.34509i | 0.933898 | + | 0.357539i | \(0.116384\pi\) |
−0.157312 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.15002e24i | 3.29385i | ||||||||
\(742\) | 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 | ||||||||
\(751\) | 2.69991e24 | − | 4.67639e24i | 0.973667 | − | 1.68644i | 0.289401 | − | 0.957208i | \(-0.406544\pi\) |
0.684266 | − | 0.729233i | \(-0.260123\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.23117e24 | − | 2.66300e24i | −0.419647 | − | 0.907687i | ||||
\(757\) | −5.17299e24 | −1.74352 | −0.871760 | − | 0.489933i | \(-0.837021\pi\) | ||||
−0.871760 | + | 0.489933i | \(0.837021\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 2.57567e24 | − | 1.19080e24i | 0.811767 | − | 0.375301i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.90470e24 | − | 1.67703e24i | −0.866025 | − | 0.500000i | ||||
\(769\) | 6.15382e24i | 1.81456i | 0.420530 | + | 0.907279i | \(0.361844\pi\) | ||||
−0.420530 | + | 0.907279i | \(0.638156\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.19127e23 | + | 1.07236e24i | −0.176617 | + | 0.305910i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.33653e24 | − | 1.92635e24i | −0.920939 | − | 0.531704i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.26747e24 | − | 6.59820e23i | −1.96248 | − | 0.178175i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.58895e24 | − | 3.04465e24i | 0.647793 | − | 0.761816i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.20358e24 | − | 3.58164e24i | 1.50265 | − | 0.867555i | 0.502653 | − | 0.864488i | \(-0.332357\pi\) |
0.999995 | − | 0.00306646i | \(-0.000976087\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.31794e24 | + | 1.26751e25i | −1.66175 | + | 2.87824i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.82824e24 | − | 3.94229e24i | −1.50158 | − | 0.866936i | ||||
\(797\) | 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 | ||||||||
\(804\) | − | 4.01181e23i | − | 0.0810333i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.37365e23i | − | 0.0445389i | −0.999752 | − | 0.0222695i | \(-0.992911\pi\) | ||
0.999752 | − | 0.0222695i | \(-0.00708918\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.81607e22 | 0.0143621 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.97022e24 | + | 4.02426e24i | 1.22845 | + | 0.709249i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.55235e24 | − | 7.87455e24i | 0.958438 | − | 1.35929i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.55075e24 | + | 4.41803e24i | 0.422445 | + | 0.731696i | 0.996178 | − | 0.0873465i | \(-0.0278387\pi\) |
−0.573733 | + | 0.819042i | \(0.694505\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.34156e24 | − | 3.08395e24i | 0.831678 | − | 0.480169i | −0.0227491 | − | 0.999741i | \(-0.507242\pi\) |
0.854427 | + | 0.519572i | \(0.173909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.13375e25 | + | 6.54573e24i | 1.72946 | + | 0.998504i | ||||
\(832\) | − | 1.10153e25i | − | 1.66321i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.70541e24 | + | 6.41796e24i | 0.531704 | + | 0.920939i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.25715e24 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.52390e24 | + | 6.10357e24i | 0.471099 | + | 0.815968i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.30048e24 | − | 4.44248e24i | −0.817269 | − | 0.576257i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.17741e24 | − | 1.24316e25i | 0.912541 | − | 1.58057i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.19884e24i | 0.146452i | 0.997315 | + | 0.0732258i | \(0.0233294\pi\) | ||||
−0.997315 | + | 0.0732258i | \(0.976671\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −1.39361e25 | − | 8.04600e24i | −1.60398 | − | 0.926058i | −0.990680 | − | 0.136206i | \(-0.956509\pi\) |
−0.613298 | − | 0.789851i | \(-0.710158\pi\) | |||||||
\(860\) | 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 | ||||||||
\(867\) | − | 9.40075e24i | − | 1.00000i | ||||||
\(868\) | −5.81747e24 | + | 8.25055e24i | −0.612797 | + | 0.869090i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.14103e24 | − | 6.58773e23i | 0.116719 | − | 0.0673878i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.10933e25 | + | 6.40472e24i | 1.11286 | + | 0.642509i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.28893e25 | −1.25587 | ||||||||
\(877\) | −8.54701e24 | + | 1.48039e25i | −0.824741 | + | 1.42849i | 0.0773755 | + | 0.997002i | \(0.475346\pi\) |
−0.902117 | + | 0.431492i | \(0.857987\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.38397e24 | −0.399210 | −0.199605 | − | 0.979876i | \(-0.563966\pi\) | ||||
−0.199605 | + | 0.979876i | \(0.563966\pi\) | |||||||
\(884\) | 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 | ||||||||
\(889\) | −2.04773e24 | + | 2.25544e25i | −0.176039 | + | 1.93895i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.95811e24 | − | 2.86257e24i | 0.414205 | − | 0.239141i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −6.45701e24 | − | 1.11839e25i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.99303e24 | − | 8.63683e24i | −0.300577 | − | 0.650143i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.31611e25 | − | 2.27956e25i | −0.954177 | − | 1.65268i | −0.736241 | − | 0.676719i | \(-0.763401\pi\) |
−0.217936 | − | 0.975963i | \(-0.569932\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 1.43114e25 | − | 2.47881e25i | 0.990208 | − | 1.71509i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.03311e25i | 1.35534i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.26832e24 | + | 7.39294e24i | −0.276742 | + | 0.479331i | −0.970573 | − | 0.240807i | \(-0.922588\pi\) |
0.693831 | + | 0.720138i | \(0.255921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.17054e25 | + | 2.02744e25i | 0.745041 | + | 1.29045i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.21212e25 | −1.97055 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.74929e25 | + | 1.58730e25i | −1.65593 | + | 0.956053i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.59824e25 | + | 2.20935e25i | 1.50871 | + | 1.28290i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.20078e25i | − | 1.21001i | −0.796220 | − | 0.605007i | \(-0.793170\pi\) | ||
0.796220 | − | 0.605007i | \(-0.206830\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.20034e25 | 1.18804 | ||||||||
\(940\) | 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 | \(0.666667\pi\) | |||||||
\(948\) | −3.41413e25 | + | 1.97115e25i | −1.69984 | + | 0.981405i | ||||
\(949\) | −2.11653e25 | − | 3.66594e25i | −1.04439 | − | 1.80893i | ||||
\(950\) | 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 | ||||||||
\(961\) | 1.47521e24 | − | 2.55513e24i | 0.0654191 | − | 0.113309i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.93812e24 | + | 2.27367e24i | 0.170072 | + | 0.0981913i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.66598e25 | 1.96254 | 0.981269 | − | 0.192645i | \(-0.0617065\pi\) | ||||
0.981269 | + | 0.192645i | \(0.0617065\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | 2.48407e25i | 1.00000i | ||||||||
\(973\) | 1.99671e25 | + | 1.81283e24i | 0.796814 | + | 0.0723434i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.12059e25 | − | 3.67297e25i | 0.831606 | − | 1.44038i | ||||
\(976\) | 4.45147e25 | − | 2.57006e25i | 1.73053 | − | 0.999124i | ||||
\(977\) | 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 | ||||||||
\(981\) | −2.40260e25 | −0.894325 | ||||||||
\(982\) | 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 | ||||||||
\(988\) | 9.40022e25 | 3.29385 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.92228e25 | − | 5.06154e25i | −0.997920 | − | 1.72845i | −0.554785 | − | 0.831994i | \(-0.687200\pi\) |
−0.443135 | − | 0.896455i | \(-0.646134\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.68373e25i | 0.900885i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.37937e25 | + | 2.52843e25i | −1.42070 | + | 0.820243i | −0.996359 | − | 0.0852587i | \(-0.972828\pi\) |
−0.424343 | + | 0.905501i | \(0.639495\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.35087e25 | + | 3.08933e25i | 1.70654 | + | 0.985274i |
(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 | 21.18.g.a.5.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.18.g.a.5.1 | ✓ | 2 | |
7.3 | odd | 6 | inner | 21.18.g.a.17.1 | yes | 2 | |
21.17 | even | 6 | inner | 21.18.g.a.17.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.18.g.a.5.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.18.g.a.5.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.18.g.a.17.1 | yes | 2 | 7.3 | odd | 6 | inner | |
21.18.g.a.17.1 | yes | 2 | 21.17 | even | 6 | inner |