Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,9,Mod(53,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.2198032451\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 53.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.53 |
Dual form | 84.9.p.a.65.1 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −40.5000 | + | 70.1481i | −0.500000 | + | 0.866025i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2136.50 | − | 1095.52i | −0.889838 | − | 0.456277i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3280.50 | − | 5681.99i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 56447.0 | 1.97637 | 0.988183 | − | 0.153277i | \(-0.0489828\pi\) | ||||
0.988183 | + | 0.153277i | \(0.0489828\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −78983.5 | − | 136803.i | −0.606069 | − | 1.04974i | −0.991882 | − | 0.127165i | \(-0.959412\pi\) |
0.385813 | − | 0.922577i | \(-0.373921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 163377. | − | 105503.i | 0.840067 | − | 0.542483i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −195312. | + | 338291.i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441. | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −291720. | + | 505273.i | −0.315877 | + | 0.547116i | −0.979624 | − | 0.200842i | \(-0.935632\pi\) |
0.663746 | + | 0.747958i | \(0.268966\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.73424e6 | + | 3.00379e6i | 0.925342 | + | 1.60274i | 0.791010 | + | 0.611804i | \(0.209556\pi\) |
0.134333 | + | 0.990936i | \(0.457111\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.28610e6 | + | 3.95965e6i | −0.988183 | + | 1.71158i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.34488e6 | 0.978378 | 0.489189 | − | 0.872178i | \(-0.337293\pi\) | ||||
0.489189 | + | 0.872178i | \(0.337293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.36446e6 | + | 4.68117e6i | 0.583622 | + | 0.812026i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.27953e7 | 1.21214 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.19133e7 | + | 2.06344e7i | 0.860422 | + | 1.49029i | 0.871522 | + | 0.490356i | \(0.163133\pi\) |
−0.0111006 | + | 0.999938i | \(0.503533\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 784040. | + | 1.57334e7i | 0.0497709 | + | 0.998761i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.59374e7 | − | 2.76044e7i | 0.790895 | − | 1.36987i | −0.134519 | − | 0.990911i | \(-0.542949\pi\) |
0.925414 | − | 0.378959i | \(-0.123718\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.95336e7 | + | 3.38332e7i | −0.687845 | + | 1.19138i | 0.284688 | + | 0.958620i | \(0.408110\pi\) |
−0.972533 | + | 0.232763i | \(0.925223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.58203e7 | − | 2.74016e7i | −0.500000 | − | 0.866025i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.80036e7 | + | 4.85036e7i | 0.718960 | + | 1.24528i | 0.961412 | + | 0.275112i | \(0.0887150\pi\) |
−0.242452 | + | 0.970163i | \(0.577952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.15234e7 | + | 3.72796e7i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.20599e8 | − | 6.18389e7i | −1.75865 | − | 0.901771i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.36293e7 | − | 4.09271e7i | −0.315877 | − | 0.547116i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.76908e8 | 1.99830 | 0.999150 | − | 0.0412262i | \(-0.0131264\pi\) | ||||
0.999150 | + | 0.0412262i | \(0.0131264\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.44405e7 | − | 1.46255e8i | −0.750243 | − | 1.29946i | −0.947705 | − | 0.319149i | \(-0.896603\pi\) |
0.197462 | − | 0.980311i | \(-0.436730\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35670e8 | − | 2.34988e8i | 0.961122 | − | 1.66471i | 0.241430 | − | 0.970418i | \(-0.422384\pi\) |
0.719692 | − | 0.694293i | \(-0.244283\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.80947e8 | −1.85068 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.85174e8 | − | 3.20731e8i | −0.988183 | − | 1.71158i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.07179e8 | − | 1.85640e8i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.87837e8 | 1.87525 | 0.937626 | − | 0.347646i | \(-0.113019\pi\) | ||||
0.937626 | + | 0.347646i | \(0.113019\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.35468e8 | + | 2.34637e8i | −0.489189 | + | 0.847300i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.88771e7 | + | 3.78809e8i | 0.0603292 | + | 1.21064i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.53241e8 | −0.410503 | −0.205252 | − | 0.978709i | \(-0.565801\pi\) | ||||
−0.205252 | + | 0.978709i | \(0.565801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.64635e8 | + | 4.64234e7i | −0.995046 | + | 0.0994185i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.35117e8 | + | 2.34030e8i | −0.259898 | + | 0.450157i | −0.966214 | − | 0.257740i | \(-0.917022\pi\) |
0.706316 | + | 0.707896i | \(0.250356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.80867e7 | + | 3.13271e7i | −0.0297688 | + | 0.0515611i | −0.880526 | − | 0.473998i | \(-0.842810\pi\) |
0.850757 | + | 0.525559i | \(0.176144\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.85694e8 | + | 1.01445e9i | 0.829698 | + | 1.43708i | 0.898275 | + | 0.439434i | \(0.144821\pi\) |
−0.0685768 | + | 0.997646i | \(0.521846\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.37053e9 | 2.90602 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.18211e8 | + | 8.97567e8i | −0.606069 | + | 1.04974i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.87891e8 | − | 5.08790e8i | 0.840067 | − | 0.542483i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.14644e9 | 1.99988 | 0.999939 | − | 0.0110495i | \(-0.00351724\pi\) | ||||
0.999939 | + | 0.0110495i | \(0.00351724\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.92995e9 | −1.72084 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.13542e9 | − | 5.82205e8i | −0.889838 | − | 0.456277i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.31592e7 | + | 1.26715e8i | −0.0527278 | + | 0.0913272i | −0.891185 | − | 0.453641i | \(-0.850125\pi\) |
0.838457 | + | 0.544968i | \(0.183458\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.67362e8 | + | 1.50232e9i | −0.553080 | + | 0.957963i | 0.444970 | + | 0.895546i | \(0.353214\pi\) |
−0.998050 | + | 0.0624175i | \(0.980119\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.29093e9 | + | 2.23596e9i | 0.790895 | + | 1.36987i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.83711e8 | −0.0926840 | −0.0463420 | − | 0.998926i | \(-0.514756\pi\) | ||||
−0.0463420 | + | 0.998926i | \(0.514756\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.17680e9 | − | 7.59931e8i | 0.530716 | − | 0.342716i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.58222e9 | − | 2.74049e9i | −0.687845 | − | 1.19138i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.72732e9 | −1.91159 | −0.955797 | − | 0.294027i | \(-0.905004\pi\) | ||||
−0.955797 | + | 0.294027i | \(0.905004\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.56289e9 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.87615e9 | + | 3.24958e9i | 0.682220 | + | 1.18164i | 0.974302 | + | 0.225247i | \(0.0723189\pi\) |
−0.292081 | + | 0.956393i | \(0.594348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.53658e9 | −1.43792 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.78289e9 | − | 4.82011e9i | 0.824951 | − | 1.42886i | −0.0770059 | − | 0.997031i | \(-0.524536\pi\) |
0.901957 | − | 0.431826i | \(-0.142131\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.74339e9 | − | 3.01964e9i | −0.500000 | − | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.45838e9 | − | 7.72214e9i | −1.19781 | − | 2.07467i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.14483e8 | − | 8.31750e9i | −0.0921103 | − | 1.84839i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.49355e9 | + | 2.58690e9i | 0.276912 | + | 0.479625i | 0.970616 | − | 0.240635i | \(-0.0773557\pi\) |
−0.693704 | + | 0.720260i | \(0.744022\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.22214e9 | − | 5.95531e9i | 1.66028 | − | 1.07215i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.09899e9 | + | 3.63556e9i | −0.356526 | + | 0.617522i | −0.987378 | − | 0.158382i | \(-0.949372\pi\) |
0.630852 | + | 0.775904i | \(0.282706\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.82794e9 | 0.631755 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.86273e9 | + | 1.01545e10i | −0.914016 | + | 1.58312i | −0.105681 | + | 0.994400i | \(0.533702\pi\) |
−0.808335 | + | 0.588723i | \(0.799631\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.48788e9 | − | 6.04118e9i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.16478e9 | + | 1.24098e10i | −0.999150 | + | 1.73058i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.14633e9 | − | 3.66439e9i | −0.870597 | − | 0.446412i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.26824e9 | −0.255349 | −0.127675 | − | 0.991816i | \(-0.540751\pi\) | ||||
−0.127675 | + | 0.991816i | \(0.540751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.36794e10 | 1.50049 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.51458e9 | + | 1.64797e10i | 0.991316 | + | 1.71701i | 0.609541 | + | 0.792755i | \(0.291354\pi\) |
0.381776 | + | 0.924255i | \(0.375313\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.10248e10 | + | 1.90955e10i | −0.988183 | + | 1.71158i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.09893e10 | + | 1.90340e10i | 0.961122 | + | 1.66471i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.58984e9 | + | 6.21779e9i | 0.299064 | + | 0.517993i | 0.975922 | − | 0.218120i | \(-0.0699924\pi\) |
−0.676858 | + | 0.736113i | \(0.736659\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.13784e10 | − | 1.97079e10i | 0.925342 | − | 1.60274i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.39043e10 | 1.07803 | 0.539014 | − | 0.842297i | \(-0.318797\pi\) | ||||
0.539014 | + | 0.842297i | \(0.318797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.05986e9 | − | 1.36872e10i | −0.148820 | − | 0.988864i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.96004e10 | −1.99524 | −0.997621 | − | 0.0689403i | \(-0.978038\pi\) | ||||
−0.997621 | + | 0.0689403i | \(0.978038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.99983e10 | 1.97637 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.98501e9 | + | 6.90223e9i | −0.234639 | + | 0.406407i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.73631e10 | 1.00000 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.58797e9 | + | 9.67864e9i | −0.308028 | + | 0.533519i | −0.977931 | − | 0.208929i | \(-0.933002\pi\) |
0.669903 | + | 0.742448i | \(0.266336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.53901e10 | − | 2.66564e10i | −0.795070 | − | 1.37710i | −0.922794 | − | 0.385293i | \(-0.874100\pi\) |
0.127724 | − | 0.991810i | \(-0.459233\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.73548e10 | 1.81046 | 0.905230 | − | 0.424921i | \(-0.139698\pi\) | ||||
0.905230 | + | 0.424921i | \(0.139698\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.97574e10 | + | 3.42208e10i | −0.937626 | + | 1.62402i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.09729e10 | − | 1.90056e10i | −0.489189 | − | 0.847300i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.43416e10 | − | 4.21609e10i | −0.979912 | − | 1.69726i | −0.662667 | − | 0.748914i | \(-0.730575\pi\) |
−0.317245 | − | 0.948343i | \(-0.602758\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.73372e10 | − | 1.40176e10i | −1.07861 | − | 0.553071i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.64667e10 | + | 2.85211e10i | −0.624290 | + | 1.08130i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.13506e10 | + | 3.69802e10i | −0.762985 | + | 1.32153i | 0.178320 | + | 0.983972i | \(0.442934\pi\) |
−0.941305 | + | 0.337556i | \(0.890400\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.20627e9 | − | 1.07496e10i | 0.205252 | − | 0.355506i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.92789e10 | 1.88700 | 0.943499 | − | 0.331375i | \(-0.107512\pi\) | ||||
0.943499 | + | 0.331375i | \(0.107512\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.84727e9 | − | 5.71366e10i | −0.0856480 | − | 1.71871i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.54278e10 | −1.57680 | −0.788399 | − | 0.615164i | \(-0.789090\pi\) | ||||
−0.788399 | + | 0.615164i | \(0.789090\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.37747e10 | − | 5.84994e10i | −0.909354 | − | 1.57505i | −0.814964 | − | 0.579512i | \(-0.803243\pi\) |
−0.0943897 | − | 0.995535i | \(-0.530090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.55612e10 | − | 3.44734e10i | 0.411424 | − | 0.911444i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.09445e10 | − | 1.89564e10i | −0.259898 | − | 0.450157i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.26976e10 | − | 7.39545e10i | −0.978902 | − | 1.69551i | −0.666407 | − | 0.745589i | \(-0.732168\pi\) |
−0.312495 | − | 0.949919i | \(-0.601165\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.71825e10 | 1.89717 | 0.948583 | − | 0.316529i | \(-0.102517\pi\) | ||||
0.948583 | + | 0.316529i | \(0.102517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.42915e10 | + | 4.15170e10i | −1.32881 | + | 0.858094i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.46503e9 | − | 2.53750e9i | −0.0297688 | − | 0.0515611i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.17059e10 | 1.21214 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.78927e10 | + | 1.69555e11i | 1.82882 | + | 3.16760i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.13912e10 | − | 8.90122e10i | 0.913636 | − | 1.58246i | 0.104749 | − | 0.994499i | \(-0.466596\pi\) |
0.808887 | − | 0.587965i | \(-0.200071\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.48824e10 | −1.65940 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.52466e10 | + | 4.37283e10i | 0.407193 | + | 0.705279i | 0.994574 | − | 0.104032i | \(-0.0331743\pi\) |
−0.587381 | + | 0.809311i | \(0.699841\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.60066e10 | + | 1.66288e11i | −1.45301 | + | 2.51669i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.87985e10 | − | 5.08851e10i | 1.15567 | − | 0.746289i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.19751e10 | − | 7.27030e10i | −0.606069 | − | 1.04974i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.00405e10 | + | 1.21314e11i | 0.936143 | + | 1.62145i | 0.772582 | + | 0.634915i | \(0.218965\pi\) |
0.163561 | + | 0.986533i | \(0.447702\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.78105e9 | + | 7.58750e10i | 0.0497709 | + | 0.998761i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.91555e10 | + | 6.78193e10i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.47166e10 | + | 1.46733e11i | 0.988962 | + | 1.71293i | 0.622801 | + | 0.782381i | \(0.285995\pi\) |
0.366161 | + | 0.930551i | \(0.380672\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.69306e10 | + | 1.50568e11i | −0.999939 | + | 1.73195i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.18266e10 | −0.690599 | −0.345300 | − | 0.938492i | \(-0.612223\pi\) | ||||
−0.345300 | + | 0.938492i | \(0.612223\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.81629e10 | − | 1.35382e11i | 0.860422 | − | 1.49029i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.69285e9 | − | 1.34306e11i | −0.0715666 | − | 1.43614i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.88808e11 | 1.93363 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.68252e10 | − | 5.60684e10i | 0.840067 | − | 0.542483i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.19932e10 | + | 2.07727e10i | −0.112821 | + | 0.195411i | −0.916907 | − | 0.399102i | \(-0.869322\pi\) |
0.804086 | + | 0.594513i | \(0.202655\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.03486e10 | − | 5.25653e10i | 0.273801 | − | 0.474237i | −0.696031 | − | 0.718012i | \(-0.745052\pi\) |
0.969832 | + | 0.243775i | \(0.0783857\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.92590e9 | − | 1.02640e10i | −0.0527278 | − | 0.0913272i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.21641e10 | 0.765774 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.02563e10 | − | 1.21688e11i | −0.553080 | − | 0.957963i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.88317e11 | −1.44341 | −0.721707 | − | 0.692199i | \(-0.756642\pi\) | ||||
−0.721707 | + | 0.692199i | \(0.756642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.09131e11 | −1.58179 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.29092e10 | − | 7.43210e10i | −0.316079 | − | 0.547465i | 0.663587 | − | 0.748099i | \(-0.269033\pi\) |
−0.979666 | + | 0.200634i | \(0.935700\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.89988e9 | − | 1.36830e10i | 0.0559472 | − | 0.0969034i | −0.836695 | − | 0.547669i | \(-0.815515\pi\) |
0.892643 | + | 0.450765i | \(0.148849\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.37797e11 | − | 2.38671e11i | 0.938592 | − | 1.62569i | 0.170493 | − | 0.985359i | \(-0.445464\pi\) |
0.768100 | − | 0.640330i | \(-0.221203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.62939e10 | − | 1.32145e11i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00069e11 | −1.26201 | −0.631004 | − | 0.775780i | \(-0.717357\pi\) | ||||
−0.631004 | + | 0.775780i | \(0.717357\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.44028e9 | − | 1.28869e10i | 0.0463420 | − | 0.0802667i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.89914e11 | + | 2.64238e11i | 1.15345 | + | 1.60486i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.41254e11 | −1.99633 | −0.998167 | − | 0.0605142i | \(-0.980726\pi\) | ||||
−0.998167 | + | 0.0605142i | \(0.980726\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.64740e9 | + | 1.13327e11i | 0.0314430 | + | 0.630972i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.56320e11 | 1.37569 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.92703e10 | − | 5.06976e10i | 0.153328 | − | 0.265572i | −0.779121 | − | 0.626874i | \(-0.784334\pi\) |
0.932449 | + | 0.361302i | \(0.117668\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.91457e11 | − | 3.31612e11i | 0.955797 | − | 1.65549i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.80397e11 | −0.879364 | −0.439682 | − | 0.898153i | \(-0.644909\pi\) | ||||
−0.439682 | + | 0.898153i | \(0.644909\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.03797e11 | + | 1.79782e11i | −0.500000 | + | 0.866025i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.77964e11 | − | 1.93807e11i | −1.77816 | − | 0.911779i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.03936e11 | −1.36444 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.46610e11 | − | 2.53936e11i | −0.643059 | − | 1.11381i | −0.984746 | − | 0.173997i | \(-0.944332\pi\) |
0.341687 | − | 0.939814i | \(-0.389002\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.73953e11 | − | 4.74500e11i | 1.12164 | − | 1.94274i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.43843e11 | + | 4.22348e11i | 0.964995 | + | 1.67142i | 0.709628 | + | 0.704577i | \(0.248863\pi\) |
0.255367 | + | 0.966844i | \(0.417804\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.83731e11 | − | 3.18232e11i | 0.718960 | − | 1.24528i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.01813e10 | + | 4.04981e11i | 0.0746806 | + | 1.49863i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.25414e11 | + | 3.90429e11i | 0.824951 | + | 1.42886i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.11506e11 | 1.47312 | 0.736560 | − | 0.676372i | \(-0.236449\pi\) | ||||
0.736560 | + | 0.676372i | \(0.236449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.41810e11 | − | 2.45621e11i | −0.491235 | − | 0.850844i | 0.508714 | − | 0.860936i | \(-0.330121\pi\) |
−0.999949 | + | 0.0100913i | \(0.996788\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.85342e11 | + | 4.94226e11i | −0.956726 | + | 1.65710i | −0.226358 | + | 0.974044i | \(0.572682\pi\) |
−0.730368 | + | 0.683054i | \(0.760651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.22258e11 | 2.39563 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.45528e10 | + | 2.52061e10i | 0.0457494 | + | 0.0792403i | 0.887993 | − | 0.459856i | \(-0.152099\pi\) |
−0.842244 | + | 0.539097i | \(0.818766\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.59764e11 | −1.40008 | −0.700038 | − | 0.714106i | \(-0.746833\pi\) | ||||
−0.700038 | + | 0.714106i | \(0.746833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.47293e11 | + | 3.53421e11i | −1.61481 | + | 1.04278i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.62887e11 | −0.465781 | −0.232890 | − | 0.972503i | \(-0.574818\pi\) | ||||
−0.232890 | + | 0.972503i | \(0.574818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.13953e11 | − | 1.97372e11i | −0.315877 | − | 0.547116i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.00243e11 | + | 3.07784e11i | 1.64681 | + | 0.844426i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.37710e11 | + | 5.84931e11i | −0.880329 | + | 1.52477i | −0.0293527 | + | 0.999569i | \(0.509345\pi\) |
−0.850976 | + | 0.525205i | \(0.823989\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.72468e11 | + | 1.16475e12i | 1.70051 | + | 2.94537i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.88545e10 | 0.205398 | 0.102699 | − | 0.994712i | \(-0.467252\pi\) | ||||
0.102699 | + | 0.994712i | \(0.467252\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.41954e11 | −0.553824 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.64190e11 | − | 4.57591e11i | −0.592964 | − | 1.02704i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.42567e10 | + | 8.88105e11i | 0.0983656 | + | 1.97392i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.31093e11 | − | 7.46675e11i | 0.939662 | − | 1.62754i | 0.173559 | − | 0.984823i | \(-0.444473\pi\) |
0.766102 | − | 0.642719i | \(-0.222194\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.71066e11 | − | 8.15910e11i | 0.997387 | − | 1.72753i | 0.436129 | − | 0.899884i | \(-0.356349\pi\) |
0.561258 | − | 0.827641i | \(-0.310318\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.70018e11 | − | 2.94480e11i | −0.356526 | − | 0.617522i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.55032e11 | + | 2.68523e11i | −0.315877 | + | 0.547116i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.00246e11 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.56159e10 | + | 5.14038e11i | 0.0497709 | + | 0.998761i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.74881e11 | − | 8.22518e11i | −0.914016 | − | 1.58312i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.05395e12 | −1.99077 | −0.995387 | − | 0.0959421i | \(-0.969414\pi\) | ||||
−0.995387 | + | 0.0959421i | \(0.969414\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.01376e11 | + | 6.95204e11i | 0.737189 | + | 1.27685i | 0.953756 | + | 0.300581i | \(0.0971807\pi\) |
−0.216567 | + | 0.976268i | \(0.569486\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.65036e11 | 1.00000 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.99619e11 | − | 1.55819e12i | 1.56310 | − | 2.70736i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.80347e11 | − | 1.00519e12i | −0.999150 | − | 1.73058i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.05413e11 | − | 1.82580e11i | −0.178194 | − | 0.308642i | 0.763068 | − | 0.646318i | \(-0.223692\pi\) |
−0.941262 | + | 0.337677i | \(0.890359\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.21517e12 | −1.99891 | −0.999457 | − | 0.0329612i | \(-0.989506\pi\) | ||||
−0.999457 | + | 0.0329612i | \(0.989506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.04226e12 | − | 5.34436e11i | −1.66867 | − | 0.855635i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.46476e11 | − | 3.52894e11i | 0.821903 | − | 0.530754i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.68215e11 | − | 9.84177e11i | 0.839621 | − | 1.45427i | −0.0505904 | − | 0.998719i | \(-0.516110\pi\) |
0.890212 | − | 0.455547i | \(-0.150556\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.34816e11 | + | 7.53123e11i | 0.609597 | + | 1.05585i | 0.991307 | + | 0.131571i | \(0.0420022\pi\) |
−0.381709 | + | 0.924282i | \(0.624664\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.18636e10 | − | 1.59112e11i | 0.127675 | − | 0.221139i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.35488e12 | −1.85068 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.54014e11 | + | 9.59581e11i | −0.750243 | + | 1.29946i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.74662e11 | − | 8.30005e11i | 0.498702 | − | 1.10480i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.19893e12 | 1.55537 | 0.777685 | − | 0.628654i | \(-0.216394\pi\) | ||||
0.777685 | + | 0.628654i | \(0.216394\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.54136e12 | −1.98263 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.10261e12 | + | 1.90978e12i | −1.35943 | + | 2.35461i | ||||
\(950\) | 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 | ||||||||
\(961\) | 2.56245e11 | + | 4.43829e11i | 0.300443 | + | 0.520382i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.51346e12 | 1.73088 | 0.865438 | − | 0.501016i | \(-0.167040\pi\) | ||||
0.865438 | + | 0.501016i | \(0.167040\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.27400e11 | + | 1.67879e11i | 0.365281 | + | 0.187303i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.93009e11 | − | 1.54674e12i | −0.988183 | − | 1.71158i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.78026e12 | −1.92224 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.02727e11 | − | 6.97543e11i | 0.417557 | − | 0.723230i | −0.578136 | − | 0.815940i | \(-0.696220\pi\) |
0.995693 | + | 0.0927105i | \(0.0295531\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.81555e11 | −0.598127 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.63156e11 | − | 1.66823e12i | 0.974801 | − | 1.68840i | 0.294210 | − | 0.955741i | \(-0.404944\pi\) |
0.680591 | − | 0.732664i | \(-0.261723\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.21647e11 | + | 1.59634e12i | 0.925342 | + | 1.60274i |
(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 | 84.9.p.a.53.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 84.9.p.a.53.1 | ✓ | 2 | |
7.2 | even | 3 | inner | 84.9.p.a.65.1 | yes | 2 | |
21.2 | odd | 6 | inner | 84.9.p.a.65.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.p.a.53.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
84.9.p.a.53.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
84.9.p.a.65.1 | yes | 2 | 7.2 | even | 3 | inner | |
84.9.p.a.65.1 | yes | 2 | 21.2 | odd | 6 | inner |