Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 14124x^{2} - 170336x + 18391464 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(119.418\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1818.41 | 1.30115 | 0.650575 | − | 0.759442i | \(-0.274528\pi\) | ||||
0.650575 | + | 0.759442i | \(0.274528\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3817.40 | −0.600933 | −0.300467 | − | 0.953792i | \(-0.597142\pi\) | ||||
−0.300467 | + | 0.953792i | \(0.597142\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 79487.2 | 1.63693 | 0.818465 | − | 0.574556i | \(-0.194825\pi\) | ||||
0.818465 | + | 0.574556i | \(0.194825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 154447. | 1.49980 | 0.749902 | − | 0.661549i | \(-0.230101\pi\) | ||||
0.749902 | + | 0.661549i | \(0.230101\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 147291. | 0.751219 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 343554. | 0.997643 | 0.498822 | − | 0.866705i | \(-0.333766\pi\) | ||||
0.498822 | + | 0.866705i | \(0.333766\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25500.6 | 0.0448909 | 0.0224455 | − | 0.999748i | \(-0.492855\pi\) | ||||
0.0224455 | + | 0.999748i | \(0.492855\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −309209. | −0.346949 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.10072e6 | 1.56529 | 0.782643 | − | 0.622470i | \(-0.213871\pi\) | ||||
0.782643 | + | 0.622470i | \(0.213871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.35350e6 | 0.692990 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.13554e6 | 0.298133 | 0.149067 | − | 0.988827i | \(-0.452373\pi\) | ||||
0.149067 | + | 0.988827i | \(0.452373\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.73826e6 | 1.11597 | 0.557985 | − | 0.829851i | \(-0.311574\pi\) | ||||
0.557985 | + | 0.829851i | \(0.311574\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.43847e6 | 0.945082 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.94160e6 | −0.781904 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.67864e6 | −0.848998 | −0.424499 | − | 0.905429i | \(-0.639550\pi\) | ||||
−0.424499 | + | 0.905429i | \(0.639550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.25102e7 | 0.865912 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.08921e7 | −0.601982 | −0.300991 | − | 0.953627i | \(-0.597317\pi\) | ||||
−0.300991 | + | 0.953627i | \(0.597317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −108899. | −0.00485754 | −0.00242877 | − | 0.999997i | \(-0.500773\pi\) | ||||
−0.00242877 | + | 0.999997i | \(0.500773\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.19306e7 | 0.433717 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.24010e7 | −1.26747 | −0.633733 | − | 0.773552i | \(-0.718478\pi\) | ||||
−0.633733 | + | 0.773552i | \(0.718478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.57811e7 | −0.638879 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.78279e7 | 0.575990 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.58656e7 | −1.32070 | −0.660349 | − | 0.750959i | \(-0.729592\pi\) | ||||
−0.660349 | + | 0.750959i | \(0.729592\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.44541e8 | 2.12989 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.06555e6 | 0.0259178 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.39466e7 | 1.00936 | 0.504681 | − | 0.863306i | \(-0.331610\pi\) | ||||
0.504681 | + | 0.863306i | \(0.331610\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.38466e8 | −1.28044 | −0.640221 | − | 0.768190i | \(-0.721157\pi\) | ||||
−0.640221 | + | 0.768190i | \(0.721157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.50459e7 | −0.200311 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.80848e8 | 1.95147 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.57461e7 | 0.398597 | 0.199298 | − | 0.979939i | \(-0.436134\pi\) | ||||
0.199298 | + | 0.979939i | \(0.436134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.70159e8 | 0.903719 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.75829e7 | 0.175520 | 0.0877602 | − | 0.996142i | \(-0.472029\pi\) | ||||
0.0877602 | + | 0.996142i | \(0.472029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.83407e8 | 1.16804 | 0.584019 | − | 0.811740i | \(-0.301479\pi\) | ||||
0.584019 | + | 0.811740i | \(0.301479\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.09633e8 | 0.400098 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.03434e8 | −0.983686 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.68780e8 | 1.35409 | 0.677045 | − | 0.735942i | \(-0.263260\pi\) | ||||
0.677045 | + | 0.735942i | \(0.263260\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.19210e8 | −0.969573 | −0.484786 | − | 0.874633i | \(-0.661103\pi\) | ||||
−0.484786 | + | 0.874633i | \(0.661103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.24723e8 | 1.29808 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.19785e7 | 0.172127 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.32398e8 | 1.40629 | 0.703147 | − | 0.711045i | \(-0.251778\pi\) | ||||
0.703147 | + | 0.711045i | \(0.251778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.89586e8 | −0.901282 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.64799e8 | 0.644306 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.63705e7 | 0.0584098 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.37090e9 | −1.57229 | −0.786143 | − | 0.618044i | \(-0.787925\pi\) | ||||
−0.786143 | + | 0.618044i | \(0.787925\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.21516e8 | 0.545643 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.29635e9 | 1.23958 | 0.619791 | − | 0.784767i | \(-0.287218\pi\) | ||||
0.619791 | + | 0.784767i | \(0.287218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.02804e8 | −0.177545 | −0.0887727 | − | 0.996052i | \(-0.528294\pi\) | ||||
−0.0887727 | + | 0.996052i | \(0.528294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.62270e8 | −0.451433 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.25915e9 | −1.66616 | −0.833082 | − | 0.553150i | \(-0.813426\pi\) | ||||
−0.833082 | + | 0.553150i | \(0.813426\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.66475e8 | 0.180816 | 0.0904082 | − | 0.995905i | \(-0.471183\pi\) | ||||
0.0904082 | + | 0.995905i | \(0.471183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.83970e8 | −0.490169 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.42429e9 | −1.39872 | −0.699360 | − | 0.714770i | \(-0.746532\pi\) | ||||
−0.699360 | + | 0.714770i | \(0.746532\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.81998e9 | 2.03667 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.01333e9 | 0.499935 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.31148e9 | −0.599517 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.96027e9 | 1.67954 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.82259e8 | −0.347555 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.09037e9 | −0.399465 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.12647e8 | −0.311305 | −0.155652 | − | 0.987812i | \(-0.549748\pi\) | ||||
−0.155652 | + | 0.987812i | \(0.549748\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.82084e6 | −0.00280450 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.96692e9 | −1.77023 | −0.885114 | − | 0.465375i | \(-0.845920\pi\) | ||||
−0.885114 | + | 0.465375i | \(0.845920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.73458e7 | −0.0269764 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.66379e8 | 0.250406 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.06316e9 | −1.71300 | −0.856498 | − | 0.516150i | \(-0.827365\pi\) | ||||
−0.856498 | + | 0.516150i | \(0.827365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.13879e9 | −0.485961 | −0.242980 | − | 0.970031i | \(-0.578125\pi\) | ||||
−0.242980 | + | 0.970031i | \(0.578125\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.43448e9 | −0.731772 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.22766e10 | 2.45508 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.06487e9 | 0.387916 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.08827e9 | −0.368857 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.97318e9 | 0.327965 | 0.163983 | − | 0.986463i | \(-0.447566\pi\) | ||||
0.163983 | + | 0.986463i | \(0.447566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.03152e8 | −0.0317998 | −0.0158999 | − | 0.999874i | \(-0.505061\pi\) | ||||
−0.0158999 | + | 0.999874i | \(0.505061\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.25406e9 | 0.332548 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.04345e10 | 1.45205 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.37720e10 | 1.80904 | 0.904520 | − | 0.426432i | \(-0.140230\pi\) | ||||
0.904520 | + | 0.426432i | \(0.140230\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.14511e9 | −0.762505 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.01930e9 | −0.940633 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.01690e9 | 0.334747 | 0.167374 | − | 0.985894i | \(-0.446471\pi\) | ||||
0.167374 | + | 0.985894i | \(0.446471\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.17078e10 | 1.22969 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.92894e9 | 0.490376 | 0.245188 | − | 0.969476i | \(-0.421150\pi\) | ||||
0.245188 | + | 0.969476i | \(0.421150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.32494e10 | 1.24941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.67309e8 | 0.0149636 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.34775e10 | −1.14393 | −0.571967 | − | 0.820277i | \(-0.693819\pi\) | ||||
−0.571967 | + | 0.820277i | \(0.693819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.16684e9 | −0.416441 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.60968e9 | 0.582756 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.28594e10 | 0.936231 | 0.468116 | − | 0.883667i | \(-0.344933\pi\) | ||||
0.468116 | + | 0.883667i | \(0.344933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.46209e10 | −1.01256 | −0.506281 | − | 0.862368i | \(-0.668980\pi\) | ||||
−0.506281 | + | 0.862368i | \(0.668980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.12158e10 | −0.739264 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.75997e10 | −1.10467 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.73082e10 | 1.63307 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.02872e9 | −0.115650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.49838e10 | 1.35834 | 0.679170 | − | 0.733981i | \(-0.262340\pi\) | ||||
0.679170 | + | 0.733981i | \(0.262340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.45447e10 | −1.27336 | −0.636678 | − | 0.771129i | \(-0.719692\pi\) | ||||
−0.636678 | + | 0.771129i | \(0.719692\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.27487e10 | 1.12668 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.14198e10 | −0.540209 | −0.270104 | − | 0.962831i | \(-0.587058\pi\) | ||||
−0.270104 | + | 0.962831i | \(0.587058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.08567e10 | 0.490747 | 0.245373 | − | 0.969429i | \(-0.421089\pi\) | ||||
0.245373 | + | 0.969429i | \(0.421089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.32544e9 | 0.230130 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.33480e9 | −0.179158 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.98063e10 | −0.783269 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.37829e10 | 0.521762 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.02697e9 | 0.0734833 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.64028e10 | 1.61166 | 0.805830 | − | 0.592147i | \(-0.201719\pi\) | ||||
0.805830 | + | 0.592147i | \(0.201719\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.04422e9 | 0.101337 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.98024e8 | −0.00632039 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.19052e10 | −0.670624 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.29559e10 | 0.674367 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.30610e10 | 1.49627 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.71348e10 | 0.734775 | 0.367388 | − | 0.930068i | \(-0.380252\pi\) | ||||
0.367388 | + | 0.930068i | \(0.380252\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.88029e9 | 0.230997 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.40226e9 | −0.185032 | −0.0925162 | − | 0.995711i | \(-0.529491\pi\) | ||||
−0.0925162 | + | 0.995711i | \(0.529491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.21764e10 | 1.01347 | 0.506733 | − | 0.862103i | \(-0.330853\pi\) | ||||
0.506733 | + | 0.862103i | \(0.330853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.45782e10 | −0.567931 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.28793e10 | −1.61995 | −0.809977 | − | 0.586462i | \(-0.800520\pi\) | ||||
−0.809977 | + | 0.586462i | \(0.800520\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.71026e10 | −1.64916 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.79712e10 | 0.781784 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.38185e10 | 0.273950 | 0.136975 | − | 0.990574i | \(-0.456262\pi\) | ||||
0.136975 | + | 0.990574i | \(0.456262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.86065e10 | −0.928148 | −0.464074 | − | 0.885796i | \(-0.653613\pi\) | ||||
−0.464074 | + | 0.885796i | \(0.653613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.68806e10 | −0.831277 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.93849e9 | 0.0673276 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.39560e10 | −0.559783 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.95300e10 | −1.58279 | −0.791393 | − | 0.611308i | \(-0.790644\pi\) | ||||
−0.791393 | + | 0.611308i | \(0.790644\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.66981e11 | 2.56227 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.06026e10 | 0.749449 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.82008e10 | 0.689216 | 0.344608 | − | 0.938747i | \(-0.388012\pi\) | ||||
0.344608 | + | 0.938747i | \(0.388012\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.69472e10 | 0.510191 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.45026e9 | 0.0993777 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.11820e10 | 0.401886 | 0.200943 | − | 0.979603i | \(-0.435599\pi\) | ||||
0.200943 | + | 0.979603i | \(0.435599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.37955e11 | −1.71843 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.74243e10 | 0.811924 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.79418e10 | 0.558251 | 0.279125 | − | 0.960255i | \(-0.409955\pi\) | ||||
0.279125 | + | 0.960255i | \(0.409955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.20036e10 | −0.698321 | −0.349160 | − | 0.937063i | \(-0.613533\pi\) | ||||
−0.349160 | + | 0.937063i | \(0.613533\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.77565e10 | −0.520356 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.07586e11 | 1.13438 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.51491e10 | 0.766946 | 0.383473 | − | 0.923552i | \(-0.374728\pi\) | ||||
0.383473 | + | 0.923552i | \(0.374728\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.76487e10 | 0.371990 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.27701e9 | 0.0696265 | 0.0348133 | − | 0.999394i | \(-0.488916\pi\) | ||||
0.0348133 | + | 0.999394i | \(0.488916\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.07526e11 | 0.996492 | 0.498246 | − | 0.867036i | \(-0.333978\pi\) | ||||
0.498246 | + | 0.867036i | \(0.333978\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.75601e9 | 0.0337229 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.15794e10 | 0.361751 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.58306e8 | −0.00470795 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.11043e11 | −0.907760 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.31989e10 | −0.183892 | −0.0919462 | − | 0.995764i | \(-0.529309\pi\) | ||||
−0.0919462 | + | 0.995764i | \(0.529309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.70834e11 | 1.31333 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.22428e10 | 0.315027 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.24451e11 | 2.34762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.15712e8 | 0.00291906 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.05004e11 | 0.715672 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.51789e11 | −1.66605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.84503e11 | 1.18544 | 0.592721 | − | 0.805408i | \(-0.298054\pi\) | ||||
0.592721 | + | 0.805408i | \(0.298054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.64271e10 | −0.102506 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.83522e11 | 1.11241 | 0.556205 | − | 0.831045i | \(-0.312257\pi\) | ||||
0.556205 | + | 0.831045i | \(0.312257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.67363e11 | 0.985620 | 0.492810 | − | 0.870137i | \(-0.335970\pi\) | ||||
0.492810 | + | 0.870137i | \(0.335970\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.55439e10 | −0.260635 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.07406e11 | 1.70980 | 0.854899 | − | 0.518794i | \(-0.173619\pi\) | ||||
0.854899 | + | 0.518794i | \(0.173619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.02607e10 | 0.488023 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.82991e11 | −0.961960 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.76083e9 | 0.0447851 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.09044e11 | 1.03935 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.15845e10 | 0.104394 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.61862e11 | 0.761662 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.22502e10 | −0.101884 | −0.0509421 | − | 0.998702i | \(-0.516222\pi\) | ||||
−0.0509421 | + | 0.998702i | \(0.516222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.35015e10 | −0.282999 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.19554e11 | 0.518634 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.04892e10 | −0.255472 | −0.127736 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127736 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.96367e11 | −0.807551 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.56119e11 | 1.82677 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.52462e11 | 0.984857 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.09419e11 | 1.17587 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.97594e11 | 0.731628 | 0.365814 | − | 0.930688i | \(-0.380791\pi\) | ||||
0.365814 | + | 0.930688i | \(0.380791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.32441e11 | −1.56032 | −0.780159 | − | 0.625582i | \(-0.784862\pi\) | ||||
−0.780159 | + | 0.625582i | \(0.784862\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.20795e10 | 0.288637 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.49455e10 | 0.119786 | 0.0598928 | − | 0.998205i | \(-0.480924\pi\) | ||||
0.0598928 | + | 0.998205i | \(0.480924\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.83412e10 | 0.228378 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.06230e11 | −0.346131 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.44648e10 | −0.0777351 | −0.0388676 | − | 0.999244i | \(-0.512375\pi\) | ||||
−0.0388676 | + | 0.999244i | \(0.512375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.22037e11 | −0.997985 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.20782e11 | 0.969684 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.15350e11 | 1.51979 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.54134e11 | 0.443508 | 0.221754 | − | 0.975103i | \(-0.428822\pi\) | ||||
0.221754 | + | 0.975103i | \(0.428822\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.14630e10 | −0.200661 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.89609e11 | 0.793651 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.83594e11 | −0.758590 | −0.379295 | − | 0.925276i | \(-0.623833\pi\) | ||||
−0.379295 | + | 0.925276i | \(0.623833\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.83200e10 | −0.230631 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.75380e11 | 0.447141 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.98473e11 | −1.24098 | −0.620490 | − | 0.784214i | \(-0.713066\pi\) | ||||
−0.620490 | + | 0.784214i | \(0.713066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.39244e10 | −0.179732 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.80570e11 | 0.666264 | 0.333132 | − | 0.942880i | \(-0.391895\pi\) | ||||
0.333132 | + | 0.942880i | \(0.391895\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.51769e11 | −1.27992 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.14488e8 | −0.00161918 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.48132e10 | 0.0770853 | 0.0385426 | − | 0.999257i | \(-0.487728\pi\) | ||||
0.0385426 | + | 0.999257i | \(0.487728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.21713e11 | 1.56160 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.83320e11 | −1.02204 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.52436e11 | 1.76187 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.60260e10 | −0.0525835 | −0.0262917 | − | 0.999654i | \(-0.508370\pi\) | ||||
−0.0262917 | + | 0.999654i | \(0.508370\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.88501e9 | −0.0155749 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.66429e11 | −1.48021 | −0.740103 | − | 0.672494i | \(-0.765223\pi\) | ||||
−0.740103 | + | 0.672494i | \(0.765223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.86258e11 | 1.67374 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.82767e10 | 0.144572 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.69328e11 | −1.38975 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.76343e11 | −0.665011 | −0.332506 | − | 0.943101i | \(-0.607894\pi\) | ||||
−0.332506 | + | 0.943101i | \(0.607894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.72116e11 | −0.988999 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.58632e11 | −0.606559 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.62297e11 | −1.26156 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.73242e11 | −0.280569 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.24941e11 | −1.46606 | −0.733028 | − | 0.680198i | \(-0.761894\pi\) | ||||
−0.733028 | + | 0.680198i | \(0.761894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.98004e11 | −0.927758 | −0.463879 | − | 0.885899i | \(-0.653543\pi\) | ||||
−0.463879 | + | 0.885899i | \(0.653543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.78193e11 | −0.422489 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.65000e11 | 0.691357 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.28581e11 | 0.769461 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.94402e11 | 1.41744 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.60269e10 | 0.0502897 | 0.0251448 | − | 0.999684i | \(-0.491995\pi\) | ||||
0.0251448 | + | 0.999684i | \(0.491995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.52251e11 | −1.16512 | −0.582562 | − | 0.812786i | \(-0.697950\pi\) | ||||
−0.582562 | + | 0.812786i | \(0.697950\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.67255e11 | 0.223963 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.35697e10 | 0.0702672 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.94785e11 | −0.250302 | −0.125151 | − | 0.992138i | \(-0.539942\pi\) | ||||
−0.125151 | + | 0.992138i | \(0.539942\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.69150e11 | −0.212960 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.03960e11 | 0.251611 | 0.125805 | − | 0.992055i | \(-0.459849\pi\) | ||||
0.125805 | + | 0.992055i | \(0.459849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.51364e12 | 1.82980 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.59827e11 | 0.189351 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.72352e11 | 0.432360 | 0.216180 | − | 0.976354i | \(-0.430640\pi\) | ||||
0.216180 | + | 0.976354i | \(0.430640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.65782e11 | −0.985403 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.64553e10 | −0.0183596 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.07211e12 | −1.17270 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.43400e12 | 1.53789 | 0.768947 | − | 0.639313i | \(-0.220781\pi\) | ||||
0.768947 | + | 0.639313i | \(0.220781\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.82579e11 | 0.191997 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.21208e12 | 1.24991 | 0.624953 | − | 0.780662i | \(-0.285118\pi\) | ||||
0.624953 | + | 0.780662i | \(0.285118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.68275e12 | −1.70179 | −0.850895 | − | 0.525336i | \(-0.823939\pi\) | ||||
−0.850895 | + | 0.525336i | \(0.823939\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.45197e11 | 0.838339 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.42499e11 | −0.916969 | −0.458485 | − | 0.888702i | \(-0.651608\pi\) | ||||
−0.458485 | + | 0.888702i | \(0.651608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.50979e11 | −0.239530 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.11553e12 | 1.04445 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.65610e9 | −0.00795146 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.45149e10 | 0.0311090 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.97754e11 | −0.440233 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.15579e11 | −0.794669 | −0.397334 | − | 0.917674i | \(-0.630065\pi\) | ||||
−0.397334 | + | 0.917674i | \(0.630065\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.49484e12 | −1.27333 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.49564e11 | −0.543075 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.49285e12 | −2.04578 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.70542e12 | 1.37389 | 0.686943 | − | 0.726712i | \(-0.258952\pi\) | ||||
0.686943 | + | 0.726712i | \(0.258952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.44369e11 | 0.193266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.95142e12 | −1.51525 | −0.757625 | − | 0.652690i | \(-0.773640\pi\) | ||||
−0.757625 | + | 0.652690i | \(0.773640\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.90119e11 | 0.297431 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.48330e11 | 0.709964 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.43469e11 | −0.105476 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.72335e12 | 1.96630 | 0.983152 | − | 0.182790i | \(-0.0585127\pi\) | ||||
0.983152 | + | 0.182790i | \(0.0585127\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.99244e11 | 0.283119 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.70028e12 | 1.88084 | 0.940422 | − | 0.340011i | \(-0.110431\pi\) | ||||
0.940422 | + | 0.340011i | \(0.110431\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.35729e12 | 1.61288 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.07320e12 | 0.721349 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.15879e12 | −1.42554 | −0.712770 | − | 0.701398i | \(-0.752560\pi\) | ||||
−0.712770 | + | 0.701398i | \(0.752560\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.08188e12 | −0.701913 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.35520e10 | 0.00863926 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.68782e11 | −0.231013 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.37034e12 | −2.07475 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.09167e12 | −0.660450 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.59041e11 | 0.391871 | 0.195935 | − | 0.980617i | \(-0.437226\pi\) | ||||
0.195935 | + | 0.980617i | \(0.437226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.33748e11 | 0.428834 | 0.214417 | − | 0.976742i | \(-0.431215\pi\) | ||||
0.214417 | + | 0.976742i | \(0.431215\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.18514e11 | −0.240432 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.97141e12 | 1.11334 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.61189e12 | 1.45012 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.16384e11 | 0.336454 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.68225e12 | −0.902856 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.10806e12 | −2.16793 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.04161e12 | 0.540533 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.04927e12 | −1.04580 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.56238e12 | 1.28604 | 0.643022 | − | 0.765848i | \(-0.277680\pi\) | ||||
0.643022 | + | 0.765848i | \(0.277680\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.18430e12 | −0.584603 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.84562e11 | 0.235269 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.42235e12 | −1.15689 | −0.578447 | − | 0.815720i | \(-0.696341\pi\) | ||||
−0.578447 | + | 0.815720i | \(0.696341\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.08478e11 | −0.426814 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.89568e10 | 0.0133835 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.78952e12 | −0.813718 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.42558e12 | −0.637783 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.99530e11 | −0.131854 | −0.0659269 | − | 0.997824i | \(-0.521000\pi\) | ||||
−0.0659269 | + | 0.997824i | \(0.521000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.68192e10 | −0.00728537 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.21196e12 | 0.942855 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.58923e12 | 1.08613 | 0.543066 | − | 0.839690i | \(-0.317263\pi\) | ||||
0.543066 | + | 0.839690i | \(0.317263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.40835e12 | −1.81994 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.64326e11 | −0.0667704 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.09519e12 | 1.23789 | 0.618945 | − | 0.785434i | \(-0.287560\pi\) | ||||
0.618945 | + | 0.785434i | \(0.287560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.97701e12 | −0.778298 | −0.389149 | − | 0.921175i | \(-0.627231\pi\) | ||||
−0.389149 | + | 0.921175i | \(0.627231\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.02369e12 | 0.784238 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.84332e12 | 1.08473 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.50291e11 | −0.169123 | −0.0845614 | − | 0.996418i | \(-0.526949\pi\) | ||||
−0.0845614 | + | 0.996418i | \(0.526949\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.98812e12 | −0.735173 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.60029e12 | 0.582648 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.03035e12 | −2.16189 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.84265e12 | 0.650490 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.02724e12 | −1.05239 | −0.526193 | − | 0.850365i | \(-0.676381\pi\) | ||||
−0.526193 | + | 0.850365i | \(0.676381\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.46329e11 | 0.0500970 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.25007e11 | −0.311890 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.55472e12 | −1.51257 | −0.756284 | − | 0.654243i | \(-0.772987\pi\) | ||||
−0.756284 | + | 0.654243i | \(0.772987\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.38482e12 | −0.780061 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.79390e11 | 0.283333 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.02438e12 | 0.642497 | 0.321249 | − | 0.946995i | \(-0.395897\pi\) | ||||
0.321249 | + | 0.946995i | \(0.395897\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.89526e11 | 0.184318 | 0.0921591 | − | 0.995744i | \(-0.470623\pi\) | ||||
0.0921591 | + | 0.995744i | \(0.470623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.31360e11 | 0.132866 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.20140e12 | 2.18533 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.99382e12 | 1.79207 | 0.896035 | − | 0.443984i | \(-0.146435\pi\) | ||||
0.896035 | + | 0.443984i | \(0.146435\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.51119e11 | −0.103437 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.54872e12 | −1.90095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.98091e12 | −1.13870 | −0.569351 | − | 0.822094i | \(-0.692806\pi\) | ||||
−0.569351 | + | 0.822094i | \(0.692806\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.60431e12 | −0.452221 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.04076e12 | 1.67806 | 0.839032 | − | 0.544082i | \(-0.183122\pi\) | ||||
0.839032 | + | 0.544082i | \(0.183122\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.19083e12 | −0.326019 | −0.163010 | − | 0.986624i | \(-0.552120\pi\) | ||||
−0.163010 | + | 0.986624i | \(0.552120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.11641e12 | 0.301240 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.17760e12 | −0.845089 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.62629e12 | −1.21275 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.64184e11 | 0.0424256 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.32514e12 | −0.846997 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.09497e12 | −1.78163 | −0.890816 | − | 0.454363i | \(-0.849867\pi\) | ||||
−0.890816 | + | 0.454363i | \(0.849867\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.75863e12 | 0.930493 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.65957e12 | −0.405054 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.98181e12 | −0.958194 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.46581e11 | 0.0585068 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.21353e12 | 0.985792 | 0.492896 | − | 0.870088i | \(-0.335938\pi\) | ||||
0.492896 | + | 0.870088i | \(0.335938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.10169e12 | 0.484864 | 0.242432 | − | 0.970168i | \(-0.422055\pi\) | ||||
0.242432 | + | 0.970168i | \(0.422055\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.60399e10 | −0.00364908 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.45447e12 | −0.775018 | −0.387509 | − | 0.921866i | \(-0.626664\pi\) | ||||
−0.387509 | + | 0.921866i | \(0.626664\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.46755e12 | 1.65226 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.77432e12 | −0.387185 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.38398e12 | −1.15876 | −0.579380 | − | 0.815057i | \(-0.696705\pi\) | ||||
−0.579380 | + | 0.815057i | \(0.696705\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.08503e13 | −2.30333 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.85943e12 | 0.389346 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.08428e12 | 1.25668 | 0.628340 | − | 0.777939i | \(-0.283735\pi\) | ||||
0.628340 | + | 0.777939i | \(0.283735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.81235e12 | 0.980506 | 0.490253 | − | 0.871580i | \(-0.336904\pi\) | ||||
0.490253 | + | 0.871580i | \(0.336904\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.29794e12 | 0.863872 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.77015e11 | −0.0351004 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.38545e12 | 0.466664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.19792e12 | 0.424223 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.10063e13 | −2.09600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.82624e12 | −1.65847 | −0.829235 | − | 0.558899i | \(-0.811224\pi\) | ||||
−0.829235 | + | 0.558899i | \(0.811224\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.19304e11 | 0.133366 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.95703e12 | −0.723969 | −0.361984 | − | 0.932184i | \(-0.617901\pi\) | ||||
−0.361984 | + | 0.932184i | \(0.617901\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.23326e12 | 0.944839 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.99583e11 | −0.106829 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.76613e12 | −1.01389 | −0.506946 | − | 0.861978i | \(-0.669226\pi\) | ||||
−0.506946 | + | 0.861978i | \(0.669226\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.28437e13 | −2.22887 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.41629e12 | 0.585125 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.17172e13 | −1.98079 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.26637e12 | −0.711881 | −0.355941 | − | 0.934509i | \(-0.615839\pi\) | ||||
−0.355941 | + | 0.934509i | \(0.615839\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.99083e12 | −0.327895 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.88920e12 | −0.632307 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.74202e12 | −0.600564 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.90322e12 | −0.935281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.62492e12 | 0.879802 | 0.439901 | − | 0.898046i | \(-0.355013\pi\) | ||||
0.439901 | + | 0.898046i | \(0.355013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.46811e11 | −0.0381123 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.24531e12 | −0.952144 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.94867e12 | −0.744906 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.74160e12 | −0.407470 | −0.203735 | − | 0.979026i | \(-0.565308\pi\) | ||||
−0.203735 | + | 0.979026i | \(0.565308\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.07567e12 | 0.451363 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.20545e13 | 1.74681 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.23239e13 | 3.19442 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.11930e12 | 0.158165 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.15437e12 | 0.440182 | 0.220091 | − | 0.975479i | \(-0.429365\pi\) | ||||
0.220091 | + | 0.975479i | \(0.429365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.74184e11 | 0.106693 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.93712e12 | −0.535866 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.53695e12 | 0.206603 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.74710e12 | −1.16134 | −0.580670 | − | 0.814139i | \(-0.697209\pi\) | ||||
−0.580670 | + | 0.814139i | \(0.697209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.74128e10 | −0.00484610 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.44871e10 | −0.0120894 | −0.00604470 | − | 0.999982i | \(-0.501924\pi\) | ||||
−0.00604470 | + | 0.999982i | \(0.501924\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.79733e12 | −0.479938 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.22598e12 | 0.652475 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.12664e12 | 0.878992 | 0.439496 | − | 0.898244i | \(-0.355157\pi\) | ||||
0.439496 | + | 0.898244i | \(0.355157\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.19017e11 | 0.0388716 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.11604e11 | 0.0856621 | 0.0428310 | − | 0.999082i | \(-0.486362\pi\) | ||||
0.0428310 | + | 0.999082i | \(0.486362\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.58805e12 | 0.426732 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.75044e12 | −0.323191 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.62407e12 | 1.00125 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.09650e13 | 1.25785 | 0.628927 | − | 0.777464i | \(-0.283494\pi\) | ||||
0.628927 | + | 0.777464i | \(0.283494\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.06193e12 | −0.913822 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.69414e11 | −0.0413763 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.22871e13 | −1.35993 | −0.679966 | − | 0.733243i | \(-0.738006\pi\) | ||||
−0.679966 | + | 0.733243i | \(0.738006\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.35254e13 | 1.47932 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.02506e13 | 1.10794 | 0.553971 | − | 0.832536i | \(-0.313112\pi\) | ||||
0.553971 | + | 0.832536i | \(0.313112\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.01724e12 | −0.108659 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.09881e12 | 0.432694 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.45098e13 | 1.51385 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.06562e12 | −0.934822 | −0.467411 | − | 0.884040i | \(-0.654813\pi\) | ||||
−0.467411 | + | 0.884040i | \(0.654813\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.90427e12 | 0.397919 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.84509e13 | −1.85870 | −0.929350 | − | 0.369201i | \(-0.879632\pi\) | ||||
−0.929350 | + | 0.369201i | \(0.879632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.76672e12 | 0.773357 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.99272e12 | 0.294559 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.77754e11 | −0.0270235 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.98736e12 | 0.287315 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.03471e11 | 0.0573758 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.50431e13 | 2.35383 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.03454e12 | 0.281972 | 0.140986 | − | 0.990012i | \(-0.454973\pi\) | ||||
0.140986 | + | 0.990012i | \(0.454973\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.52574e12 | 0.232029 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.25446e12 | 0.840537 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.13857e13 | −1.92041 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.11743e13 | −0.992134 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.71637e13 | 1.50677 | 0.753386 | − | 0.657579i | \(-0.228419\pi\) | ||||
0.753386 | + | 0.657579i | \(0.228419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45671e13 | −1.26448 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.46136e12 | 0.468765 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.25272e13 | 1.91200 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.45824e13 | −1.22390 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.88329e12 | 0.322306 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.84376e12 | −0.315491 | −0.157746 | − | 0.987480i | \(-0.550423\pi\) | ||||
−0.157746 | + | 0.987480i | \(0.550423\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.81504e12 | 0.472019 | 0.236009 | − | 0.971751i | \(-0.424160\pi\) | ||||
0.236009 | + | 0.971751i | \(0.424160\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.02229e12 | −0.403176 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.48597e12 | 0.435556 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.77699e9 | −0.000218060 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.86827e12 | −0.300427 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.98531e13 | 1.52505 | 0.762526 | − | 0.646957i | \(-0.223959\pi\) | ||||
0.762526 | + | 0.646957i | \(0.223959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.43301e13 | −1.08881 | −0.544403 | − | 0.838824i | \(-0.683244\pi\) | ||||
−0.544403 | + | 0.838824i | \(0.683244\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.71444e12 | 0.654933 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.25152e12 | 0.613422 | 0.306711 | − | 0.951803i | \(-0.400772\pi\) | ||||
0.306711 | + | 0.951803i | \(0.400772\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.31194e12 | −0.243549 | −0.121775 | − | 0.992558i | \(-0.538859\pi\) | ||||
−0.121775 | + | 0.992558i | \(0.538859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.08708e12 | 0.442797 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.85720e12 | −0.637373 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.96284e12 | 0.638053 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.04955e12 | 0.214769 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.20859e13 | −0.842072 | −0.421036 | − | 0.907044i | \(-0.638333\pi\) | ||||
−0.421036 | + | 0.907044i | \(0.638333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.32177e13 | −0.911117 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.89438e11 | 0.0401989 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.40929e13 | 1.62567 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.51179e13 | −1.00929 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.70959e12 | 0.575325 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.03322e13 | −1.32892 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.65968e12 | −0.236686 | −0.118343 | − | 0.992973i | \(-0.537758\pi\) | ||||
−0.118343 | + | 0.992973i | \(0.537758\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.04237e11 | 0.0194699 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.91677e13 | −1.21383 | −0.606913 | − | 0.794768i | \(-0.707592\pi\) | ||||
−0.606913 | + | 0.794768i | \(0.707592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.06228e13 | 1.29234 | 0.646172 | − | 0.763192i | \(-0.276369\pi\) | ||||
0.646172 | + | 0.763192i | \(0.276369\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.36793e12 | 0.208857 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.08452e12 | −0.189295 | −0.0946475 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946475 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.45076e13 | −1.48843 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.52228e10 | −0.00271814 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.72621e13 | 2.21655 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.01543e13 | 0.597817 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.99445e12 | −0.524096 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.16238e12 | 0.240052 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.90264e13 | 1.65689 | 0.828446 | − | 0.560069i | \(-0.189225\pi\) | ||||
0.828446 | + | 0.560069i | \(0.189225\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.87911e12 | −0.106170 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.69337e13 | −0.947021 | −0.473511 | − | 0.880788i | \(-0.657013\pi\) | ||||
−0.473511 | + | 0.880788i | \(0.657013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.73642e13 | −0.961242 | −0.480621 | − | 0.876928i | \(-0.659589\pi\) | ||||
−0.480621 | + | 0.876928i | \(0.659589\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.38375e13 | 0.758252 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.69498e13 | 0.919406 | 0.459703 | − | 0.888073i | \(-0.347956\pi\) | ||||
0.459703 | + | 0.888073i | \(0.347956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.48394e12 | 0.187073 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.42166e12 | 0.181881 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.08125e12 | −0.0568977 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.33837e13 | 1.21818 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.62805e13 | 1.35540 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.51601e12 | 0.332708 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.60640e13 | −1.31759 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.36726e10 | 0.00168532 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.65869e13 | −1.31750 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.95992e13 | −0.961622 | −0.480811 | − | 0.876824i | \(-0.659658\pi\) | ||||
−0.480811 | + | 0.876824i | \(0.659658\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.50533e12 | 0.413194 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.77979e13 | 0.856124 | 0.428062 | − | 0.903749i | \(-0.359197\pi\) | ||||
0.428062 | + | 0.903749i | \(0.359197\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.33218e13 | −1.58712 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.03949e13 | −0.961893 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.27781e13 | 1.06379 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.61520e11 | 0.0305931 | 0.0152965 | − | 0.999883i | \(-0.495131\pi\) | ||||
0.0152965 | + | 0.999883i | \(0.495131\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.49447e13 | 0.684415 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.80457e12 | 0.263246 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.31000e13 | −0.588347 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.33060e12 | −0.0591818 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.85586e12 | 0.0817475 | 0.0408737 | − | 0.999164i | \(-0.486986\pi\) | ||||
0.0408737 | + | 0.999164i | \(0.486986\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.57432e11 | −0.0286799 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.48652e13 | 0.642251 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.96575e13 | 2.12487 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.97151e13 | −0.835548 | −0.417774 | − | 0.908551i | \(-0.637190\pi\) | ||||
−0.417774 | + | 0.908551i | \(0.637190\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.35564e13 | 0.569048 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.18755e13 | −0.493739 | −0.246869 | − | 0.969049i | \(-0.579402\pi\) | ||||
−0.246869 | + | 0.969049i | \(0.579402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.28813e13 | −0.942275 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.68905e12 | −0.150478 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.15724e13 | −0.467572 | −0.233786 | − | 0.972288i | \(-0.575112\pi\) | ||||
−0.233786 | + | 0.972288i | \(0.575112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.37713e13 | 1.75183 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.48998e13 | 0.987153 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.16575e13 | 1.63597 | 0.817985 | − | 0.575239i | \(-0.195091\pi\) | ||||
0.817985 | + | 0.575239i | \(0.195091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.54309e13 | 1.76740 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.31112e12 | 0.281760 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.69629e13 | 1.02940 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.48804e12 | 0.245391 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.48223e13 | −0.555388 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.46324e13 | −1.65683 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.31308e13 | −0.850692 | −0.425346 | − | 0.905031i | \(-0.639848\pi\) | ||||
−0.425346 | + | 0.905031i | \(0.639848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.09627e11 | 0.0258567 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.35529e13 | −0.850272 | −0.425136 | − | 0.905129i | \(-0.639774\pi\) | ||||
−0.425136 | + | 0.905129i | \(0.639774\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.16460e12 | 0.292030 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.69325e13 | 0.600069 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.82311e13 | 1.34243 | 0.671215 | − | 0.741263i | \(-0.265773\pi\) | ||||
0.671215 | + | 0.741263i | \(0.265773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.61650e13 | 2.30201 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.74834e12 | 0.0602721 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.76306e13 | 0.943843 | 0.471922 | − | 0.881641i | \(-0.343561\pi\) | ||||
0.471922 | + | 0.881641i | \(0.343561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.07660e13 | −0.702893 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.31108e13 | 0.439746 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.28767e11 | −0.00760345 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.13754e13 | −0.704017 | −0.352008 | − | 0.935997i | \(-0.614501\pi\) | ||||
−0.352008 | + | 0.935997i | \(0.614501\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.80226e12 | −0.0588229 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.97419e13 | 0.638535 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.63793e12 | −0.180714 | −0.0903569 | − | 0.995909i | \(-0.528801\pi\) | ||||
−0.0903569 | + | 0.995909i | \(0.528801\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.14362e12 | −0.163390 |
(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 | 384.10.a.h.1.4 | yes | 4 | |
4.3 | odd | 2 | 384.10.a.d.1.4 | yes | 4 | ||
8.3 | odd | 2 | 384.10.a.e.1.1 | yes | 4 | ||
8.5 | even | 2 | 384.10.a.a.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.a.a.1.1 | ✓ | 4 | 8.5 | even | 2 | ||
384.10.a.d.1.4 | yes | 4 | 4.3 | odd | 2 | ||
384.10.a.e.1.1 | yes | 4 | 8.3 | odd | 2 | ||
384.10.a.h.1.4 | yes | 4 | 1.1 | even | 1 | trivial |