Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [272,10,Mod(1,272)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(272, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("272.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 272 = 2^{4} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 272.a (trivial) |
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: | yes |
Analytic conductor: | \(140.089747437\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-5.44491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 272.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −106.475 | −0.758929 | −0.379465 | − | 0.925206i | \(-0.623892\pi\) | ||||
−0.379465 | + | 0.925206i | \(0.623892\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1303.94 | 0.933024 | 0.466512 | − | 0.884515i | \(-0.345511\pi\) | ||||
0.466512 | + | 0.884515i | \(0.345511\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9199.27 | −1.44815 | −0.724073 | − | 0.689723i | \(-0.757732\pi\) | ||||
−0.724073 | + | 0.689723i | \(0.757732\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8346.12 | −0.424027 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −62238.4 | −1.28171 | −0.640857 | − | 0.767660i | \(-0.721421\pi\) | ||||
−0.640857 | + | 0.767660i | \(0.721421\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 141901. | 1.37797 | 0.688985 | − | 0.724775i | \(-0.258056\pi\) | ||||
0.688985 | + | 0.724775i | \(0.258056\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −138837. | −0.708099 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 83521.0 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 941163. | 1.65681 | 0.828407 | − | 0.560127i | \(-0.189247\pi\) | ||||
0.828407 | + | 0.560127i | \(0.189247\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 979491. | 1.09904 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −568165. | −0.423349 | −0.211675 | − | 0.977340i | \(-0.567892\pi\) | ||||
−0.211675 | + | 0.977340i | \(0.567892\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −252865. | −0.129467 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.98439e6 | 1.08074 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.83597e6 | −0.482032 | −0.241016 | − | 0.970521i | \(-0.577481\pi\) | ||||
−0.241016 | + | 0.970521i | \(0.577481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.34903e6 | 1.42923 | 0.714615 | − | 0.699518i | \(-0.246602\pi\) | ||||
0.714615 | + | 0.699518i | \(0.246602\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.62682e6 | 0.972730 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.19953e7 | −1.35115 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.01674e6 | −0.703218 | −0.351609 | − | 0.936147i | \(-0.614365\pi\) | ||||
−0.351609 | + | 0.936147i | \(0.614365\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.51089e7 | −1.04578 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.95674e7 | 1.08145 | 0.540724 | − | 0.841200i | \(-0.318150\pi\) | ||||
0.540724 | + | 0.841200i | \(0.318150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.46966e7 | −1.54767 | −0.773835 | − | 0.633387i | \(-0.781664\pi\) | ||||
−0.773835 | + | 0.633387i | \(0.781664\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.08828e7 | −0.395627 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.63645e7 | 1.68486 | 0.842432 | − | 0.538802i | \(-0.181123\pi\) | ||||
0.842432 | + | 0.538802i | \(0.181123\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.42730e7 | 1.09713 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.89288e6 | −0.184067 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.28783e7 | −0.572359 | −0.286179 | − | 0.958176i | \(-0.592385\pi\) | ||||
−0.286179 | + | 0.958176i | \(0.592385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.11551e7 | −1.19587 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00210e8 | −1.25740 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.04852e8 | −1.12653 | −0.563267 | − | 0.826275i | \(-0.690456\pi\) | ||||
−0.563267 | + | 0.826275i | \(0.690456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.69264e7 | 0.526416 | 0.263208 | − | 0.964739i | \(-0.415219\pi\) | ||||
0.263208 | + | 0.964739i | \(0.415219\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.67782e7 | 0.614052 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.85030e8 | 1.28568 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.58325e7 | 0.0959872 | 0.0479936 | − | 0.998848i | \(-0.484717\pi\) | ||||
0.0479936 | + | 0.998848i | \(0.484717\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.04952e7 | 0.321292 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.81097e7 | 0.458194 | 0.229097 | − | 0.973404i | \(-0.426423\pi\) | ||||
0.229097 | + | 0.973404i | \(0.426423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.27365e7 | −0.258564 | −0.129282 | − | 0.991608i | \(-0.541267\pi\) | ||||
−0.129282 | + | 0.991608i | \(0.541267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.69238e7 | 0.0982563 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.72548e8 | 1.85611 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.38282e8 | 0.399433 | 0.199717 | − | 0.979854i | \(-0.435998\pi\) | ||||
0.199717 | + | 0.979854i | \(0.435998\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.53486e8 | −0.396175 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.69421e8 | 1.54827 | 0.774137 | − | 0.633018i | \(-0.218184\pi\) | ||||
0.774137 | + | 0.633018i | \(0.218184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.08906e8 | 0.226291 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.95485e8 | 0.365828 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.21417e7 | −0.0711963 | −0.0355981 | − | 0.999366i | \(-0.511334\pi\) | ||||
−0.0355981 | + | 0.999366i | \(0.511334\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.30538e9 | −1.99550 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.82486e8 | −1.08468 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.22722e9 | 1.54585 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.11288e8 | −0.471707 | −0.235854 | − | 0.971789i | \(-0.575789\pi\) | ||||
−0.235854 | + | 0.971789i | \(0.575789\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.19449e8 | 0.543481 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.81470e7 | 0.0173524 | 0.00867620 | − | 0.999962i | \(-0.497238\pi\) | ||||
0.00867620 | + | 0.999962i | \(0.497238\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.17681e8 | −0.628296 | −0.314148 | − | 0.949374i | \(-0.601719\pi\) | ||||
−0.314148 | + | 0.949374i | \(0.601719\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.27720e9 | 1.02543 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.18789e8 | 0.530120 | 0.265060 | − | 0.964232i | \(-0.414608\pi\) | ||||
0.265060 | + | 0.964232i | \(0.414608\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.41476e8 | 0.231708 | 0.115854 | − | 0.993266i | \(-0.463040\pi\) | ||||
0.115854 | + | 0.993266i | \(0.463040\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.53581e8 | 0.533693 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.70781e9 | −0.985339 | −0.492670 | − | 0.870216i | \(-0.663979\pi\) | ||||
−0.492670 | + | 0.870216i | \(0.663979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.40853e8 | −0.394995 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.18432e9 | −0.584296 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.68332e8 | −0.351227 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.51567e9 | 0.642792 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.08343e9 | −0.820743 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.87648e9 | −1.05382 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.94335e9 | −0.662880 | −0.331440 | − | 0.943476i | \(-0.607534\pi\) | ||||
−0.331440 | + | 0.943476i | \(0.607534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.69431e9 | 1.17457 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.30692e9 | −0.981075 | −0.490538 | − | 0.871420i | \(-0.663200\pi\) | ||||
−0.490538 | + | 0.871420i | \(0.663200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.65802e9 | −2.39931 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.89147e9 | 1.00835 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.83938e9 | −1.17367 | −0.586836 | − | 0.809706i | \(-0.699627\pi\) | ||||
−0.586836 | + | 0.809706i | \(0.699627\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.57524e9 | −0.812342 | −0.406171 | − | 0.913797i | \(-0.633136\pi\) | ||||
−0.406171 | + | 0.913797i | \(0.633136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00139e9 | −1.27869 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.83168e9 | −1.76616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.39400e9 | −0.449747 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.71396e9 | −0.832641 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.20680e9 | −0.366796 | −0.183398 | − | 0.983039i | \(-0.558710\pi\) | ||||
−0.183398 | + | 0.983039i | \(0.558710\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.78978e9 | −1.21935 | −0.609676 | − | 0.792651i | \(-0.708700\pi\) | ||||
−0.609676 | + | 0.792651i | \(0.708700\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.97076e8 | −0.102842 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.58269e9 | 1.33351 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.99611e9 | 0.787627 | 0.393814 | − | 0.919190i | \(-0.371155\pi\) | ||||
0.393814 | + | 0.919190i | \(0.371155\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.50071e9 | 0.434380 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.22670e9 | 0.613072 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.20096e9 | −0.244212 | −0.122106 | − | 0.992517i | \(-0.538965\pi\) | ||||
−0.122106 | + | 0.992517i | \(0.538965\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.64098e9 | 0.907580 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.54378e9 | 0.153589 | 0.0767946 | − | 0.997047i | \(-0.475531\pi\) | ||||
0.0767946 | + | 0.997047i | \(0.475531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.53135e9 | 0.898802 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.85506e9 | −0.702533 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.36568e10 | 1.15916 | 0.579578 | − | 0.814917i | \(-0.303217\pi\) | ||||
0.579578 | + | 0.814917i | \(0.303217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.32618e9 | 0.187487 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.11641e10 | 0.854959 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.48481e9 | −0.544932 | −0.272466 | − | 0.962165i | \(-0.587839\pi\) | ||||
−0.272466 | + | 0.962165i | \(0.587839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.98188e10 | −1.37254 | −0.686269 | − | 0.727348i | \(-0.740753\pi\) | ||||
−0.686269 | + | 0.727348i | \(0.740753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.06123e9 | −0.399513 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.04534e10 | −0.656119 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.19821e9 | −0.310861 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.74543e10 | −1.56506 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.54665e10 | 1.92827 | 0.964137 | − | 0.265405i | \(-0.0855056\pi\) | ||||
0.964137 | + | 0.265405i | \(0.0855056\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.16540e10 | −0.604599 | −0.302299 | − | 0.953213i | \(-0.597754\pi\) | ||||
−0.302299 | + | 0.953213i | \(0.597754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.97011e10 | −0.975739 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.99943e9 | 0.236495 | 0.118248 | − | 0.992984i | \(-0.462272\pi\) | ||||
0.118248 | + | 0.992984i | \(0.462272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.90482e9 | 0.0861026 | 0.0430513 | − | 0.999073i | \(-0.486292\pi\) | ||||
0.0430513 | + | 0.999073i | \(0.486292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.68576e9 | −0.0728475 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.68896e10 | 0.698052 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.55147e10 | 1.00902 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.74197e9 | 0.179511 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.85765e10 | −2.12356 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.45582e10 | −1.54759 | −0.773797 | − | 0.633434i | \(-0.781645\pi\) | ||||
−0.773797 | + | 0.633434i | \(0.781645\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.04462e10 | −0.347737 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.52422e10 | −1.44401 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.76057e10 | −2.06973 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.67986e9 | 0.196232 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.18517e10 | 0.334207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00748e10 | 0.272812 | 0.136406 | − | 0.990653i | \(-0.456445\pi\) | ||||
0.136406 | + | 0.990653i | \(0.456445\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.11044e9 | 0.0548975 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.51701e10 | −1.87901 | −0.939505 | − | 0.342536i | \(-0.888714\pi\) | ||||
−0.939505 | + | 0.342536i | \(0.888714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.19379e10 | 1.96891 | 0.984453 | − | 0.175647i | \(-0.0562016\pi\) | ||||
0.984453 | + | 0.175647i | \(0.0562016\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.09619e10 | −1.40866 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.97304e10 | −1.10540 | −0.552701 | − | 0.833380i | \(-0.686403\pi\) | ||||
−0.552701 | + | 0.833380i | \(0.686403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.34959e10 | 1.57202 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.47236e10 | −0.303142 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.06399e10 | 0.805680 | 0.402840 | − | 0.915270i | \(-0.368023\pi\) | ||||
0.402840 | + | 0.915270i | \(0.368023\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.05939e10 | −0.584196 | −0.292098 | − | 0.956388i | \(-0.594353\pi\) | ||||
−0.292098 | + | 0.956388i | \(0.594353\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.23994e10 | −0.780067 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.77293e10 | 1.02364 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.33552e11 | 2.28304 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.12765e10 | −1.17503 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.05450e10 | −0.326719 | −0.163359 | − | 0.986567i | \(-0.552233\pi\) | ||||
−0.163359 | + | 0.986567i | \(0.552233\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.53617e10 | 0.542613 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.15958e10 | −0.171739 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.98169e10 | −1.28428 | −0.642139 | − | 0.766588i | \(-0.721953\pi\) | ||||
−0.642139 | + | 0.766588i | \(0.721953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.37482e10 | 1.01836 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.53233e10 | 0.204394 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.43373e11 | −1.84785 | −0.923923 | − | 0.382577i | \(-0.875037\pi\) | ||||
−0.923923 | + | 0.382577i | \(0.875037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.28714e10 | −0.534024 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.48703e9 | 0.0540329 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.67468e11 | −1.95005 | −0.975025 | − | 0.222094i | \(-0.928711\pi\) | ||||
−0.975025 | + | 0.222094i | \(0.928711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.52996e10 | −0.510190 | −0.255095 | − | 0.966916i | \(-0.582107\pi\) | ||||
−0.255095 | + | 0.966916i | \(0.582107\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.38991e11 | 1.51444 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.57379e10 | 0.165940 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.93194e9 | 0.0197167 | 0.00985836 | − | 0.999951i | \(-0.496862\pi\) | ||||
0.00985836 | + | 0.999951i | \(0.496862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.13358e10 | −0.606032 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.16694e11 | 1.11653 | 0.558265 | − | 0.829662i | \(-0.311467\pi\) | ||||
0.558265 | + | 0.829662i | \(0.311467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.65132e8 | 0.00153036 | 0.000765180 | − | 1.00000i | \(-0.499756\pi\) | ||||
0.000765180 | 1.00000i | \(0.499756\pi\) | ||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.30668e11 | −1.17319 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.80006e11 | −1.56609 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.97576e9 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.37918e10 | 0.357993 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.45700e10 | 0.511831 | 0.255915 | − | 0.966699i | \(-0.417623\pi\) | ||||
0.255915 | + | 0.966699i | \(0.417623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.36721e11 | −1.05108 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.85744e11 | −1.38519 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.06230e10 | −0.583363 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.19183e11 | 2.24125 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.93220e9 | −0.0131692 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.42286e10 | 0.491159 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.54538e10 | −0.549046 | −0.274523 | − | 0.961581i | \(-0.588520\pi\) | ||||
−0.274523 | + | 0.961581i | \(0.588520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.64150e10 | 0.476832 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.31980e10 | 0.443688 | 0.221844 | − | 0.975082i | \(-0.428792\pi\) | ||||
0.221844 | + | 0.975082i | \(0.428792\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.60425e10 | 0.0944764 | 0.0472382 | − | 0.998884i | \(-0.484958\pi\) | ||||
0.0472382 | + | 0.998884i | \(0.484958\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00114e11 | 0.572925 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.53822e10 | 0.474899 | 0.237449 | − | 0.971400i | \(-0.423689\pi\) | ||||
0.237449 | + | 0.971400i | \(0.423689\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.14268e11 | 0.617827 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.65329e10 | −0.402324 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.86069e10 | 0.401836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.58818e10 | −0.178402 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.63586e10 | −0.175850 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.18512e11 | −2.43993 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.68636e10 | −0.260380 | −0.130190 | − | 0.991489i | \(-0.541559\pi\) | ||||
−0.130190 | + | 0.991489i | \(0.541559\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.69087e10 | 0.298183 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.06447e10 | 0.0895583 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.07106e11 | 1.29704 | 0.648521 | − | 0.761197i | \(-0.275388\pi\) | ||||
0.648521 | + | 0.761197i | \(0.275388\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.81838e11 | 0.747803 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.57392e11 | −1.83187 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.60556e10 | −0.140653 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.88821e10 | 0.299773 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.34687e10 | −0.123924 | −0.0619621 | − | 0.998079i | \(-0.519736\pi\) | ||||
−0.0619621 | + | 0.998079i | \(0.519736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.80974e11 | −1.37462 | −0.687308 | − | 0.726366i | \(-0.741208\pi\) | ||||
−0.687308 | + | 0.726366i | \(0.741208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.23488e11 | 1.48922 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.09902e11 | 0.719499 | 0.359750 | − | 0.933049i | \(-0.382862\pi\) | ||||
0.359750 | + | 0.933049i | \(0.382862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.27929e11 | 0.427506 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.18080e10 | 0.266556 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.14148e11 | −0.998181 | −0.499091 | − | 0.866550i | \(-0.666332\pi\) | ||||
−0.499091 | + | 0.866550i | \(0.666332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.63101e11 | 1.74503 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.61381e11 | −0.487834 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.18047e10 | −0.241246 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.40379e11 | −0.691671 | −0.345835 | − | 0.938295i | \(-0.612404\pi\) | ||||
−0.345835 | + | 0.938295i | \(0.612404\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.63312e11 | −0.458563 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.02457e11 | 0.828859 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.93908e11 | 0.786179 | 0.393089 | − | 0.919500i | \(-0.371406\pi\) | ||||
0.393089 | + | 0.919500i | \(0.371406\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.06273e11 | 0.799774 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.60526e11 | −0.664225 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.76034e11 | −0.936161 | −0.468081 | − | 0.883686i | \(-0.655054\pi\) | ||||
−0.468081 | + | 0.883686i | \(0.655054\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.06918e11 | 0.503079 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.73836e11 | −0.887741 | −0.443870 | − | 0.896091i | \(-0.646395\pi\) | ||||
−0.443870 | + | 0.896091i | \(0.646395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.46568e11 | 1.73179 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.89582e11 | 0.656253 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.62613e10 | −0.102434 | −0.0512171 | − | 0.998688i | \(-0.516310\pi\) | ||||
−0.0512171 | + | 0.998688i | \(0.516310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.74537e10 | −0.102677 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.52103e11 | 0.744567 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.80312e11 | 0.372681 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.36827e11 | −0.680534 | −0.340267 | − | 0.940329i | \(-0.610517\pi\) | ||||
−0.340267 | + | 0.940329i | \(0.610517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.21861e11 | 1.82091 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.81350e11 | −1.89528 | −0.947642 | − | 0.319335i | \(-0.896541\pi\) | ||||
−0.947642 | + | 0.319335i | \(0.896541\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.04283e12 | 1.96944 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.00137e11 | −0.369640 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.98949e11 | 0.901325 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.17703e11 | 1.44491 | 0.722455 | − | 0.691418i | \(-0.243014\pi\) | ||||
0.722455 | + | 0.691418i | \(0.243014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.15272e11 | 0.890734 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.64566e11 | 1.63139 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.72885e11 | 1.44458 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.80673e11 | 0.616510 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.18196e11 | 0.662852 | 0.331426 | − | 0.943481i | \(-0.392470\pi\) | ||||
0.331426 | + | 0.943481i | \(0.392470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.11784e11 | 0.483709 | 0.241855 | − | 0.970313i | \(-0.422244\pi\) | ||||
0.241855 | + | 0.970313i | \(0.422244\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.70424e11 | −0.714427 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.11196e10 | −0.0314004 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.23681e11 | −0.762328 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.40351e11 | 1.34039 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.66540e11 | −1.20960 | −0.604799 | − | 0.796378i | \(-0.706747\pi\) | ||||
−0.604799 | + | 0.796378i | \(0.706747\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.95119e11 | 0.403461 | 0.201730 | − | 0.979441i | \(-0.435344\pi\) | ||||
0.201730 | + | 0.979441i | \(0.435344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.54901e11 | 0.341326 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.34736e11 | −0.701411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.48786e11 | −0.705201 | −0.352600 | − | 0.935774i | \(-0.614703\pi\) | ||||
−0.352600 | + | 0.935774i | \(0.614703\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.69508e11 | −0.465211 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.03597e12 | 1.27800 | 0.638999 | − | 0.769207i | \(-0.279349\pi\) | ||||
0.638999 | + | 0.769207i | \(0.279349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.49503e10 | −0.0664278 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.34968e11 | 0.278372 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.04924e12 | −1.21833 | −0.609167 | − | 0.793042i | \(-0.708496\pi\) | ||||
−0.609167 | + | 0.793042i | \(0.708496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.21784e12 | −1.38611 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.29415e11 | 0.925401 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.70214e12 | −1.86185 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.13929e11 | 0.122183 | 0.0610917 | − | 0.998132i | \(-0.480542\pi\) | ||||
0.0610917 | + | 0.998132i | \(0.480542\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.49260e11 | 0.262117 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.04783e12 | 1.08053 | 0.540264 | − | 0.841496i | \(-0.318325\pi\) | ||||
0.540264 | + | 0.841496i | \(0.318325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.26218e11 | −0.127646 | −0.0638231 | − | 0.997961i | \(-0.520329\pi\) | ||||
−0.0638231 | + | 0.997961i | \(0.520329\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.02032e12 | −1.01204 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.20765e12 | 1.17494 | 0.587470 | − | 0.809246i | \(-0.300124\pi\) | ||||
0.587470 | + | 0.809246i | \(0.300124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.45648e11 | −0.139003 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.38434e11 | −0.597753 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.15946e12 | 1.98367 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.37988e11 | −0.214503 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.74406e11 | 0.242695 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.58750e12 | 1.37786 | 0.688930 | − | 0.724828i | \(-0.258081\pi\) | ||||
0.688930 | + | 0.724828i | \(0.258081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.13758e12 | −0.969014 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.56512e11 | −0.465278 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.36294e11 | −0.440114 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.39880e11 | −0.757167 | −0.378584 | − | 0.925567i | \(-0.623589\pi\) | ||||
−0.378584 | + | 0.925567i | \(0.623589\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.34347e11 | 0.185340 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.66438e11 | −0.750425 | −0.375213 | − | 0.926939i | \(-0.622430\pi\) | ||||
−0.375213 | + | 0.926939i | \(0.622430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.53342e11 | −0.116910 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.77330e11 | 0.507081 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.02538e11 | −0.663532 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.22995e12 | 0.888045 | 0.444022 | − | 0.896016i | \(-0.353551\pi\) | ||||
0.444022 | + | 0.896016i | \(0.353551\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.64373e11 | −0.116563 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.98521e12 | 1.38277 | 0.691386 | − | 0.722485i | \(-0.257000\pi\) | ||||
0.691386 | + | 0.722485i | \(0.257000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.36626e10 | 0.0161902 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.01485e12 | −0.682127 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.25974e12 | 1.49221 | 0.746104 | − | 0.665830i | \(-0.231922\pi\) | ||||
0.746104 | + | 0.665830i | \(0.231922\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.77130e11 | 0.374438 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.80880e12 | 1.79058 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.35813e11 | −0.586215 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.50803e12 | −2.15952 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.45411e12 | −0.879717 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.78832e11 | 0.284717 | 0.142358 | − | 0.989815i | \(-0.454531\pi\) | ||||
0.142358 | + | 0.989815i | \(0.454531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.37326e11 | 0.547814 | 0.273907 | − | 0.961756i | \(-0.411684\pi\) | ||||
0.273907 | + | 0.961756i | \(0.411684\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.47679e11 | −0.142290 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.13798e11 | 0.346639 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.47834e12 | −0.820775 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.75110e11 | 0.477680 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.77663e12 | 1.49020 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.37257e11 | 0.494614 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.96944e11 | 0.413565 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.75548e12 | −1.40620 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.44109e12 | −1.72706 | −0.863532 | − | 0.504293i | \(-0.831753\pi\) | ||||
−0.863532 | + | 0.504293i | \(0.831753\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.11021e12 | 1.04166 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.45264e11 | 0.216189 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.05238e11 | −0.384575 | −0.192288 | − | 0.981339i | \(-0.561591\pi\) | ||||
−0.192288 | + | 0.981339i | \(0.561591\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.75114e11 | −0.223215 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.72795e12 | −0.798637 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.27210e12 | −0.578438 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.11302e12 | 0.497948 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.13503e11 | −0.0939842 | −0.0469921 | − | 0.998895i | \(-0.514964\pi\) | ||||
−0.0469921 | + | 0.998895i | \(0.514964\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.92347e12 | −2.13264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.53479e11 | 0.235922 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.94290e12 | 0.815010 | 0.407505 | − | 0.913203i | \(-0.366399\pi\) | ||||
0.407505 | + | 0.913203i | \(0.366399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.22688e12 | −0.919345 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.41196e12 | 0.573719 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.66618e11 | −0.386589 | −0.193295 | − | 0.981141i | \(-0.561917\pi\) | ||||
−0.193295 | + | 0.981141i | \(0.561917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.96159e12 | −1.55958 | −0.779788 | − | 0.626043i | \(-0.784673\pi\) | ||||
−0.779788 | + | 0.626043i | \(0.784673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.77629e12 | −1.46342 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.43669e11 | 0.0548098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.21488e12 | 0.831876 | 0.415938 | − | 0.909393i | \(-0.363453\pi\) | ||||
0.415938 | + | 0.909393i | \(0.363453\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.24086e12 | 0.458847 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.15819e12 | −2.24213 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.04629e12 | 0.733600 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.54428e12 | −0.545162 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.70503e11 | 0.233093 | 0.116546 | − | 0.993185i | \(-0.462818\pi\) | ||||
0.116546 | + | 0.993185i | \(0.462818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.91664e12 | 2.36797 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.32314e11 | −0.179483 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.14332e12 | −1.37595 | −0.687975 | − | 0.725735i | \(-0.741500\pi\) | ||||
−0.687975 | + | 0.725735i | \(0.741500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.00186e12 | −0.327703 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.02816e11 | −0.0653458 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.11940e12 | −0.672653 | −0.336327 | − | 0.941745i | \(-0.609185\pi\) | ||||
−0.336327 | + | 0.941745i | \(0.609185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.44856e12 | 1.39086 | 0.695431 | − | 0.718593i | \(-0.255213\pi\) | ||||
0.695431 | + | 0.718593i | \(0.255213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.32140e11 | −0.0407011 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.97634e12 | 0.599740 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.59588e11 | −0.257005 | −0.128502 | − | 0.991709i | \(-0.541017\pi\) | ||||
−0.128502 | + | 0.991709i | \(0.541017\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.79832e12 | −0.529772 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.99816e12 | 2.32169 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.43289e12 | −1.55403 | −0.777013 | − | 0.629484i | \(-0.783266\pi\) | ||||
−0.777013 | + | 0.629484i | \(0.783266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.71667e12 | −0.765772 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.22774e12 | −0.341053 | −0.170527 | − | 0.985353i | \(-0.554547\pi\) | ||||
−0.170527 | + | 0.985353i | \(0.554547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.33143e12 | −1.18583 | −0.592917 | − | 0.805264i | \(-0.702024\pi\) | ||||
−0.592917 | + | 0.805264i | \(0.702024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.69563e12 | −0.457529 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.87673e11 | 0.103103 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.25688e12 | −0.853771 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.23692e12 | 1.61163 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.69566e11 | −0.170555 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.79967e12 | −0.451919 | −0.225959 | − | 0.974137i | \(-0.572552\pi\) | ||||
−0.225959 | + | 0.974137i | \(0.572552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.74433e12 | 1.17451 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.53402e12 | −0.618483 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.28238e12 | 1.51181 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.18835e11 | −0.194286 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.02365e12 | 1.17532 | 0.587662 | − | 0.809106i | \(-0.300048\pi\) | ||||
0.587662 | + | 0.809106i | \(0.300048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.60458e12 | −1.06229 | −0.531143 | − | 0.847283i | \(-0.678237\pi\) | ||||
−0.531143 | + | 0.847283i | \(0.678237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.81716e12 | 1.09590 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.15507e12 | −0.932201 | −0.466100 | − | 0.884732i | \(-0.654341\pi\) | ||||
−0.466100 | + | 0.884732i | \(0.654341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.52584e12 | 1.44390 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.19830e12 | 1.57078 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.43743e11 | 0.0739817 | 0.0369909 | − | 0.999316i | \(-0.488223\pi\) | ||||
0.0369909 | + | 0.999316i | \(0.488223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.31202e12 | −0.915367 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.23606e11 | 0.109638 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.39727e12 | −0.495145 | −0.247572 | − | 0.968869i | \(-0.579633\pi\) | ||||
−0.247572 | + | 0.968869i | \(0.579633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.09899e12 | −0.427665 | −0.213833 | − | 0.976870i | \(-0.568595\pi\) | ||||
−0.213833 | + | 0.976870i | \(0.568595\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.26191e12 | −0.253639 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.12895e13 | −2.23861 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.04314e12 | 0.204068 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.07271e12 | −0.207045 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.54301e12 | −0.674715 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.61276e12 | −0.303042 | −0.151521 | − | 0.988454i | \(-0.548417\pi\) | ||||
−0.151521 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.54650e11 | −0.139920 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.64830e12 | 0.484527 | 0.242264 | − | 0.970210i | \(-0.422110\pi\) | ||||
0.242264 | + | 0.970210i | \(0.422110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.78355e12 | 0.683101 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.00373e12 | 1.42604 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.69821e12 | 1.70529 | 0.852645 | − | 0.522491i | \(-0.174997\pi\) | ||||
0.852645 | + | 0.522491i | \(0.174997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.31026e12 | −1.09506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.72432e12 | −1.49426 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.66546e12 | −0.788693 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.85953e12 | 1.31143 | 0.655715 | − | 0.755008i | \(-0.272367\pi\) | ||||
0.655715 | + | 0.755008i | \(0.272367\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.77855e12 | −0.787040 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.66190e12 | −0.757934 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.63429e12 | 0.262290 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.29503e12 | 0.838922 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.35808e12 | 0.212419 | 0.106210 | − | 0.994344i | \(-0.466129\pi\) | ||||
0.106210 | + | 0.994344i | \(0.466129\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.54506e12 | −1.16510 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.82546e12 | −1.19305 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.66940e11 | −0.0251288 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.38924e12 | 1.24685 | 0.623426 | − | 0.781883i | \(-0.285740\pi\) | ||||
0.623426 | + | 0.781883i | \(0.285740\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.15412e12 | −0.169370 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.17546e12 | −0.605064 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.15160e13 | −1.64787 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.32713e12 | −0.611454 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.05644e12 | −0.147423 | −0.0737117 | − | 0.997280i | \(-0.523484\pi\) | ||||
−0.0737117 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.60214e12 | 0.909864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.25748e12 | 0.443363 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.64254e11 | 0.0624072 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.20219e12 | −0.159614 | −0.0798068 | − | 0.996810i | \(-0.525430\pi\) | ||||
−0.0798068 | + | 0.996810i | \(0.525430\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.53554e12 | 0.988190 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.89789e12 | −0.375365 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.38044e13 | −1.76624 | −0.883121 | − | 0.469146i | \(-0.844562\pi\) | ||||
−0.883121 | + | 0.469146i | \(0.844562\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.14672e12 | −0.776874 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.85390e11 | −0.123028 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.03973e13 | 1.28240 | 0.641198 | − | 0.767375i | \(-0.278438\pi\) | ||||
0.641198 | + | 0.767375i | \(0.278438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.42199e13 | −1.73267 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.06440e12 | −0.850405 | −0.425202 | − | 0.905098i | \(-0.639797\pi\) | ||||
−0.425202 | + | 0.905098i | \(0.639797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.87753e12 | −0.342229 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.58707e12 | −0.656510 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.61233e12 | −0.767691 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.52292e12 | −0.633562 | −0.316781 | − | 0.948499i | \(-0.602602\pi\) | ||||
−0.316781 | + | 0.948499i | \(0.602602\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.18752e12 | 0.247956 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.01574e13 | −1.13768 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.93646e12 | −0.657046 | −0.328523 | − | 0.944496i | \(-0.606551\pi\) | ||||
−0.328523 | + | 0.944496i | \(0.606551\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.76513e12 | −0.411805 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.16527e13 | −1.25949 | −0.629745 | − | 0.776802i | \(-0.716840\pi\) | ||||
−0.629745 | + | 0.776802i | \(0.716840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.14133e12 | −0.335547 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.08945e11 | −0.0959536 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.48786e13 | −1.55233 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.13586e12 | −0.323361 | −0.161681 | − | 0.986843i | \(-0.551691\pi\) | ||||
−0.161681 | + | 0.986843i | \(0.551691\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.56324e12 | 0.974676 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.41981e13 | 1.43029 | 0.715143 | − | 0.698979i | \(-0.246362\pi\) | ||||
0.715143 | + | 0.698979i | \(0.246362\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.85831e12 | −0.185038 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.85232e12 | −0.772865 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.84161e13 | 1.79176 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.10619e12 | −0.587274 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.47927e12 | −0.520949 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.81856e12 | 0.734875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.60742e12 | 0.706889 | 0.353444 | − | 0.935456i | \(-0.385010\pi\) | ||||
0.353444 | + | 0.935456i | \(0.385010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.52656e13 | 1.40238 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.57106e13 | 1.42691 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.07790e12 | 0.725386 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.56472e12 | 0.405286 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.82832e11 | 0.0775025 | 0.0387513 | − | 0.999249i | \(-0.487662\pi\) | ||||
0.0387513 | + | 0.999249i | \(0.487662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.70762e12 | 0.408640 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.51720e11 | 0.0301891 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.90462e12 | 0.331405 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.81530e12 | 0.572010 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.78311e13 | 1.47995 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.36683e13 | 1.12188 | 0.560940 | − | 0.827856i | \(-0.310440\pi\) | ||||
0.560940 | + | 0.827856i | \(0.310440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.63530e13 | 1.32741 | 0.663703 | − | 0.747996i | \(-0.268984\pi\) | ||||
0.663703 | + | 0.747996i | \(0.268984\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.82326e12 | 0.387198 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.86992e12 | −0.227856 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.26551e13 | −2.56420 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.08949e13 | 0.846146 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.83235e12 | −0.371206 | −0.185603 | − | 0.982625i | \(-0.559424\pi\) | ||||
−0.185603 | + | 0.982625i | \(0.559424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.61695e13 | 1.22856 | 0.614282 | − | 0.789087i | \(-0.289446\pi\) | ||||
0.614282 | + | 0.789087i | \(0.289446\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.67569e12 | −0.125937 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.37247e13 | −1.02030 | −0.510149 | − | 0.860086i | \(-0.670410\pi\) | ||||
−0.510149 | + | 0.860086i | \(0.670410\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.58304e13 | 1.89949 | 0.949743 | − | 0.313031i | \(-0.101344\pi\) | ||||
0.949743 | + | 0.313031i | \(0.101344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.05703e11 | −0.0149636 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.69773e12 | 0.266092 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.01299e12 | 0.143302 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.19324e13 | 1.54462 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.42716e11 | 0.0378132 | 0.0189066 | − | 0.999821i | \(-0.493981\pi\) | ||||
0.0189066 | + | 0.999821i | \(0.493981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.11363e13 | −0.767645 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.24250e13 | −0.847368 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.24283e13 | 0.838604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.39431e13 | −0.930857 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.75824e10 | −0.00116143 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.55483e12 | 0.297707 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.71048e13 | −1.10623 | −0.553116 | − | 0.833104i | \(-0.686561\pi\) | ||||
−0.553116 | + | 0.833104i | \(0.686561\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.02425e13 | −0.655480 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.06810e12 | −0.384272 | −0.192136 | − | 0.981368i | \(-0.561542\pi\) | ||||
−0.192136 | + | 0.981368i | \(0.561542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.87986e13 | 1.17803 | 0.589016 | − | 0.808122i | \(-0.299516\pi\) | ||||
0.589016 | + | 0.808122i | \(0.299516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.91661e13 | 1.18855 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.53337e12 | 0.400949 | 0.200474 | − | 0.979699i | \(-0.435752\pi\) | ||||
0.200474 | + | 0.979699i | \(0.435752\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.78077e13 | 1.08152 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.42742e11 | −0.0446429 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.60646e12 | −0.511960 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.24665e12 | 0.132268 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.43265e12 | 0.200017 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.64615e13 | 1.52608 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.60851e13 | −0.918178 | −0.459089 | − | 0.888390i | \(-0.651824\pi\) | ||||
−0.459089 | + | 0.888390i | \(0.651824\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.87507e12 | −0.388443 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.30698e13 | 1.84944 | 0.924720 | − | 0.380647i | \(-0.124299\pi\) | ||||
0.924720 | + | 0.380647i | \(0.124299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.25465e12 | 0.401599 | 0.200800 | − | 0.979632i | \(-0.435646\pi\) | ||||
0.200800 | + | 0.979632i | \(0.435646\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.45574e13 | 0.797697 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.13226e13 | 0.614170 | 0.307085 | − | 0.951682i | \(-0.400646\pi\) | ||||
0.307085 | + | 0.951682i | \(0.400646\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.78774e13 | 0.959947 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.55274e12 | 0.507783 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.30482e13 | 2.79151 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.75974e12 | −0.508434 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.58432e12 | 0.442731 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.34926e13 | −0.688934 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.74603e12 | −0.138817 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.39850e13 | −1.70095 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.58426e13 | −1.28061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.43776e13 | −1.68672 | −0.843360 | − | 0.537348i | \(-0.819426\pi\) | ||||
−0.843360 | + | 0.537348i | \(0.819426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.51457e11 | −0.00735788 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.18306e13 | 0.569082 | 0.284541 | − | 0.958664i | \(-0.408159\pi\) | ||||
0.284541 | + | 0.958664i | \(0.408159\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.16637e13 | −1.98445 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.90348e12 | −0.372755 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.04212e13 | 1.42074 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.68999e13 | 1.24403 | 0.622015 | − | 0.783005i | \(-0.286314\pi\) | ||||
0.622015 | + | 0.783005i | \(0.286314\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.09868e12 | 0.416687 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.39218e13 | 0.631378 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.02716e12 | 0.0910436 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.98985e12 | 0.266414 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.83481e12 | −0.433207 | −0.216603 | − | 0.976260i | \(-0.569498\pi\) | ||||
−0.216603 | + | 0.976260i | \(0.569498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.16681e13 | 1.81773 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.79374e12 | −0.336728 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.77816e12 | −0.290041 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.23144e12 | 0.391238 | 0.195619 | − | 0.980680i | \(-0.437328\pi\) | ||||
0.195619 | + | 0.980680i | \(0.437328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.70812e12 | −0.0717009 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.00553e13 | −0.418062 | −0.209031 | − | 0.977909i | \(-0.567031\pi\) | ||||
−0.209031 | + | 0.977909i | \(0.567031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.11175e13 | −0.457830 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.57987e13 | −1.46024 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.28956e13 | −1.32912 | −0.664558 | − | 0.747237i | \(-0.731380\pi\) | ||||
−0.664558 | + | 0.747237i | \(0.731380\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.90236e12 | −0.356293 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.09106e12 | −0.360414 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.79353e13 | −1.09707 | −0.548537 | − | 0.836126i | \(-0.684815\pi\) | ||||
−0.548537 | + | 0.836126i | \(0.684815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.62463e13 | 1.79913 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.21667e13 | −0.468887 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.45187e13 | 1.69965 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.75686e13 | 1.04270 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.99909e12 | −0.224785 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.51961e13 | −0.564105 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.57620e13 | −1.31523 | −0.657617 | − | 0.753352i | \(-0.728435\pi\) | ||||
−0.657617 | + | 0.753352i | \(0.728435\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.36965e12 | −0.304965 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.49737e12 | 0.198458 | 0.0992290 | − | 0.995065i | \(-0.468362\pi\) | ||||
0.0992290 | + | 0.995065i | \(0.468362\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.28896e13 | 1.17639 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.82051e12 | 0.135394 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.41757e13 | −0.497759 | −0.248879 | − | 0.968534i | \(-0.580062\pi\) | ||||
−0.248879 | + | 0.968534i | \(0.580062\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.62283e12 | 0.0912533 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.85000e12 | −0.0982503 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.48632e13 | −1.53250 | −0.766248 | − | 0.642545i | \(-0.777879\pi\) | ||||
−0.766248 | + | 0.642545i | \(0.777879\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.51896e12 | 0.220656 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.52085e13 | 1.85173 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.97134e13 | 0.655205 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.93025e13 | −0.965101 | −0.482550 | − | 0.875868i | \(-0.660289\pi\) | ||||
−0.482550 | + | 0.875868i | \(0.660289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.05454e12 | 0.197610 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.48378e12 | 0.0803357 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15625e13 | 0.370616 | 0.185308 | − | 0.982680i | \(-0.440672\pi\) | ||||
0.185308 | + | 0.982680i | \(0.440672\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.39251e13 | −0.759993 |
(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 | 272.10.a.g.1.4 | 7 | ||
4.3 | odd | 2 | 17.10.a.b.1.5 | ✓ | 7 | ||
12.11 | even | 2 | 153.10.a.f.1.3 | 7 | |||
68.67 | odd | 2 | 289.10.a.b.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.b.1.5 | ✓ | 7 | 4.3 | odd | 2 | ||
153.10.a.f.1.3 | 7 | 12.11 | even | 2 | |||
272.10.a.g.1.4 | 7 | 1.1 | even | 1 | trivial | ||
289.10.a.b.1.5 | 7 | 68.67 | odd | 2 |