Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,8,Mod(1,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.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: | \(179.933774679\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{235}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 235 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 96) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-15.3297\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −155.275 | −0.555530 | −0.277765 | − | 0.960649i | \(-0.589594\pi\) | ||||
−0.277765 | + | 0.960649i | \(0.589594\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1742.38 | −1.91999 | −0.959995 | − | 0.280017i | \(-0.909660\pi\) | ||||
−0.959995 | + | 0.280017i | \(0.909660\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 51.6521 | 0.0117008 | 0.00585038 | − | 0.999983i | \(-0.498138\pi\) | ||||
0.00585038 | + | 0.999983i | \(0.498138\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10471.6 | 1.32193 | 0.660967 | − | 0.750415i | \(-0.270146\pi\) | ||||
0.660967 | + | 0.750415i | \(0.270146\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −24021.5 | −1.18585 | −0.592923 | − | 0.805259i | \(-0.702026\pi\) | ||||
−0.592923 | + | 0.805259i | \(0.702026\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1149.27 | −0.0384403 | −0.0192201 | − | 0.999815i | \(-0.506118\pi\) | ||||
−0.0192201 | + | 0.999815i | \(0.506118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 86508.9 | 1.48256 | 0.741282 | − | 0.671194i | \(-0.234218\pi\) | ||||
0.741282 | + | 0.671194i | \(0.234218\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −54014.6 | −0.691386 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 153332. | 1.16746 | 0.583728 | − | 0.811949i | \(-0.301593\pi\) | ||||
0.583728 | + | 0.811949i | \(0.301593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 132760. | 0.800392 | 0.400196 | − | 0.916430i | \(-0.368942\pi\) | ||||
0.400196 | + | 0.916430i | \(0.368942\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 270548. | 1.06661 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −504967. | −1.63892 | −0.819458 | − | 0.573139i | \(-0.805725\pi\) | ||||
−0.819458 | + | 0.573139i | \(0.805725\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −99416.4 | −0.225276 | −0.112638 | − | 0.993636i | \(-0.535930\pi\) | ||||
−0.112638 | + | 0.993636i | \(0.535930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 84318.7 | 0.161728 | 0.0808638 | − | 0.996725i | \(-0.474232\pi\) | ||||
0.0808638 | + | 0.996725i | \(0.474232\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 998165. | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.21233e6 | 2.68636 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.24958e6 | 1.15292 | 0.576458 | − | 0.817127i | \(-0.304434\pi\) | ||||
0.576458 | + | 0.817127i | \(0.304434\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8020.30 | −0.00650012 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.67870e6 | 1.06412 | 0.532061 | − | 0.846706i | \(-0.321418\pi\) | ||||
0.532061 | + | 0.846706i | \(0.321418\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 405326. | 0.228639 | 0.114320 | − | 0.993444i | \(-0.463531\pi\) | ||||
0.114320 | + | 0.993444i | \(0.463531\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.62598e6 | −0.734374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.16414e6 | −0.879072 | −0.439536 | − | 0.898225i | \(-0.644857\pi\) | ||||
−0.439536 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.57024e6 | 0.520669 | 0.260335 | − | 0.965518i | \(-0.416167\pi\) | ||||
0.260335 | + | 0.965518i | \(0.416167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.88524e6 | −0.868065 | −0.434032 | − | 0.900897i | \(-0.642910\pi\) | ||||
−0.434032 | + | 0.900897i | \(0.642910\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −89997.5 | −0.0224653 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.87170e6 | −0.883500 | −0.441750 | − | 0.897138i | \(-0.645642\pi\) | ||||
−0.441750 | + | 0.897138i | \(0.645642\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −796558. | −0.152913 | −0.0764564 | − | 0.997073i | \(-0.524361\pi\) | ||||
−0.0764564 | + | 0.997073i | \(0.524361\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.72994e6 | 0.658773 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.41571e6 | −0.212867 | −0.106434 | − | 0.994320i | \(-0.533943\pi\) | ||||
−0.106434 | + | 0.994320i | \(0.533943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.82454e7 | −2.53810 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 178454. | 0.0213547 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −238942. | −0.0265822 | −0.0132911 | − | 0.999912i | \(-0.504231\pi\) | ||||
−0.0132911 | + | 0.999912i | \(0.504231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.87275e7 | −1.80865 | −0.904324 | − | 0.426847i | \(-0.859624\pi\) | ||||
−0.904324 | + | 0.426847i | \(0.859624\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.67587e6 | 0.421630 | 0.210815 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210815 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.38526e7 | −1.09317 | −0.546585 | − | 0.837404i | \(-0.684072\pi\) | ||||
−0.546585 | + | 0.837404i | \(0.684072\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.05778e6 | −0.374083 | −0.187041 | − | 0.982352i | \(-0.559890\pi\) | ||||
−0.187041 | + | 0.982352i | \(0.559890\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.79817e7 | 1.82431 | 0.912157 | − | 0.409841i | \(-0.134416\pi\) | ||||
0.912157 | + | 0.409841i | \(0.134416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.34327e7 | −0.823608 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.18545e7 | 2.27681 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.94845e7 | −0.999863 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.05180e7 | 0.939616 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.22490e6 | 0.183022 | 0.0915109 | − | 0.995804i | \(-0.470830\pi\) | ||||
0.0915109 | + | 0.995804i | \(0.470830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.16738e7 | 1.61962 | 0.809812 | − | 0.586690i | \(-0.199569\pi\) | ||||
0.809812 | + | 0.586690i | \(0.199569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00247e6 | 0.0738049 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.58796e7 | −0.859876 | −0.429938 | − | 0.902858i | \(-0.641465\pi\) | ||||
−0.429938 | + | 0.902858i | \(0.641465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.07048e7 | −1.60139 | −0.800696 | − | 0.599071i | \(-0.795537\pi\) | ||||
−0.800696 | + | 0.599071i | \(0.795537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 540879. | 0.0154676 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.38087e7 | −0.648557 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.36811e7 | −1.08179 | −0.540893 | − | 0.841091i | \(-0.681914\pi\) | ||||
−0.540893 | + | 0.841091i | \(0.681914\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.81915e7 | 1.61180 | 0.805900 | − | 0.592052i | \(-0.201682\pi\) | ||||
0.805900 | + | 0.592052i | \(0.201682\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.06144e7 | −0.444642 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.99359e6 | −0.206098 | −0.103049 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103049 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50731e8 | −2.84651 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.77375e6 | 0.0863382 | 0.0431691 | − | 0.999068i | \(-0.486255\pi\) | ||||
0.0431691 | + | 0.999068i | \(0.486255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.90961e7 | 1.48030 | 0.740152 | − | 0.672440i | \(-0.234754\pi\) | ||||
0.740152 | + | 0.672440i | \(0.234754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.69052e7 | 0.747510 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.58721e7 | −0.379901 | −0.189950 | − | 0.981794i | \(-0.560833\pi\) | ||||
−0.189950 | + | 0.981794i | \(0.560833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.41137e7 | 1.32745 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.29009e7 | −0.559089 | −0.279545 | − | 0.960133i | \(-0.590183\pi\) | ||||
−0.279545 | + | 0.960133i | \(0.590183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.28747e8 | −1.61384 | −0.806920 | − | 0.590661i | \(-0.798867\pi\) | ||||
−0.806920 | + | 0.590661i | \(0.798867\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.84089e7 | 0.910467 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.24076e6 | −0.0138753 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.60958e8 | −1.67146 | −0.835730 | − | 0.549140i | \(-0.814955\pi\) | ||||
−0.835730 | + | 0.549140i | \(0.814955\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.61920e8 | 1.62125 | 0.810625 | − | 0.585566i | \(-0.199128\pi\) | ||||
0.810625 | + | 0.585566i | \(0.199128\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.27020e8 | 1.18370 | 0.591848 | − | 0.806049i | \(-0.298398\pi\) | ||||
0.591848 | + | 0.806049i | \(0.298398\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.74928e7 | 0.157353 | 0.0786763 | − | 0.996900i | \(-0.474931\pi\) | ||||
0.0786763 | + | 0.996900i | \(0.474931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.67163e8 | −2.24151 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.54369e7 | 0.125147 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −59362.5 | −0.000449780 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.40594e7 | −0.322887 | −0.161443 | − | 0.986882i | \(-0.551615\pi\) | ||||
−0.161443 | + | 0.986882i | \(0.551615\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.30926e7 | −0.0898445 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.31319e8 | −1.53674 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.51542e8 | −1.56761 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.25971e8 | 0.760685 | 0.380343 | − | 0.924846i | \(-0.375806\pi\) | ||||
0.380343 | + | 0.924846i | \(0.375806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.13624e8 | −0.644733 | −0.322366 | − | 0.946615i | \(-0.604478\pi\) | ||||
−0.322366 | + | 0.946615i | \(0.604478\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.65608e8 | 0.911289 | 0.455645 | − | 0.890162i | \(-0.349409\pi\) | ||||
0.455645 | + | 0.890162i | \(0.349409\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.77584e8 | −1.43764 | −0.718818 | − | 0.695199i | \(-0.755316\pi\) | ||||
−0.718818 | + | 0.695199i | \(0.755316\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.54990e8 | −0.779054 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00082e8 | −1.42183 | −0.710915 | − | 0.703278i | \(-0.751719\pi\) | ||||
−0.710915 | + | 0.703278i | \(0.751719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.72418e8 | −1.71384 | −0.856922 | − | 0.515446i | \(-0.827626\pi\) | ||||
−0.856922 | + | 0.515446i | \(0.827626\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.43521e8 | −1.49235 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.20347e7 | −0.0508155 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.44996e8 | 0.977916 | 0.488958 | − | 0.872307i | \(-0.337377\pi\) | ||||
0.488958 | + | 0.872307i | \(0.337377\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.46837e6 | 0.0173471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.71767e7 | 0.210113 | 0.105057 | − | 0.994466i | \(-0.466498\pi\) | ||||
0.105057 | + | 0.994466i | \(0.466498\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.79842e8 | 3.14670 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.63071e7 | 0.292551 | 0.146275 | − | 0.989244i | \(-0.453271\pi\) | ||||
0.146275 | + | 0.989244i | \(0.453271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.94029e8 | −0.640479 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.72851e8 | −0.541425 | −0.270712 | − | 0.962660i | \(-0.587259\pi\) | ||||
−0.270712 | + | 0.962660i | \(0.587259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.93066e8 | −0.894484 | −0.447242 | − | 0.894413i | \(-0.647594\pi\) | ||||
−0.447242 | + | 0.894413i | \(0.647594\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.78997e6 | −0.00808974 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.02094e8 | −1.13671 | −0.568353 | − | 0.822785i | \(-0.692419\pi\) | ||||
−0.568353 | + | 0.822785i | \(0.692419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.56183e8 | −0.688777 | −0.344388 | − | 0.938827i | \(-0.611914\pi\) | ||||
−0.344388 | + | 0.938827i | \(0.611914\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.55378e7 | −0.198112 | −0.0990562 | − | 0.995082i | \(-0.531582\pi\) | ||||
−0.0990562 | + | 0.995082i | \(0.531582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.73221e8 | 0.432527 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.66693e8 | 0.406232 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.87808e8 | −1.59746 | −0.798731 | − | 0.601688i | \(-0.794495\pi\) | ||||
−0.798731 | + | 0.601688i | \(0.794495\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.60661e8 | −0.591152 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.05883e8 | 1.95985 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.46915e8 | −0.310515 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.29372e7 | −0.127016 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.58303e8 | −0.509501 | −0.254751 | − | 0.967007i | \(-0.581993\pi\) | ||||
−0.254751 | + | 0.967007i | \(0.581993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.14264e8 | 0.403913 | 0.201957 | − | 0.979394i | \(-0.435270\pi\) | ||||
0.201957 | + | 0.979394i | \(0.435270\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.31251e8 | 0.794923 | 0.397461 | − | 0.917619i | \(-0.369891\pi\) | ||||
0.397461 | + | 0.917619i | \(0.369891\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.13425e8 | 0.199986 | 0.0999932 | − | 0.994988i | \(-0.468118\pi\) | ||||
0.0999932 | + | 0.994988i | \(0.468118\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.91994e6 | 0.0136601 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.76073e7 | 0.0455842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.65617e8 | −0.913967 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.73918e9 | −2.69252 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.46930e8 | 1.13209 | 0.566046 | − | 0.824374i | \(-0.308472\pi\) | ||||
0.566046 | + | 0.824374i | \(0.308472\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.36038e8 | 0.488351 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.55138e8 | −0.790126 | −0.395063 | − | 0.918654i | \(-0.629277\pi\) | ||||
−0.395063 | + | 0.918654i | \(0.629277\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.85736e6 | 0.00936519 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.41980e9 | −3.23780 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45452e9 | 1.86881 | 0.934407 | − | 0.356206i | \(-0.115930\pi\) | ||||
0.934407 | + | 0.356206i | \(0.115930\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.79394e7 | 0.0981450 | 0.0490725 | − | 0.998795i | \(-0.484373\pi\) | ||||
0.0490725 | + | 0.998795i | \(0.484373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.54961e8 | −1.03451 | −0.517255 | − | 0.855831i | \(-0.673046\pi\) | ||||
−0.517255 | + | 0.855831i | \(0.673046\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.43820e8 | −0.289248 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.81451e8 | −0.549189 | −0.274595 | − | 0.961560i | \(-0.588544\pi\) | ||||
−0.274595 | + | 0.961560i | \(0.588544\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.92551e8 | −0.998522 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.48007e8 | 0.482236 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.01203e9 | 1.06872 | 0.534359 | − | 0.845257i | \(-0.320553\pi\) | ||||
0.534359 | + | 0.845257i | \(0.320553\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.17723e9 | −2.21359 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.31785e9 | −1.31487 | −0.657437 | − | 0.753510i | \(-0.728359\pi\) | ||||
−0.657437 | + | 0.753510i | \(0.728359\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.60563e9 | 1.54330 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.26791e9 | −1.19633 | −0.598167 | − | 0.801372i | \(-0.704104\pi\) | ||||
−0.598167 | + | 0.801372i | \(0.704104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.44181e8 | −0.676835 | −0.338417 | − | 0.940996i | \(-0.609892\pi\) | ||||
−0.338417 | + | 0.940996i | \(0.609892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.39744e7 | 0.0124802 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.14243e8 | −0.356806 | −0.178403 | − | 0.983958i | \(-0.557093\pi\) | ||||
−0.178403 | + | 0.983958i | \(0.557093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.07807e9 | −1.75809 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.01179e8 | 0.490810 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.05816e8 | 0.165087 | 0.0825436 | − | 0.996587i | \(-0.473696\pi\) | ||||
0.0825436 | + | 0.996587i | \(0.473696\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.86415e9 | −1.44369 | −0.721846 | − | 0.692054i | \(-0.756706\pi\) | ||||
−0.721846 | + | 0.692054i | \(0.756706\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.39021e9 | 1.05807 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.60826e7 | −0.0191766 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.07532e8 | 0.655889 | 0.327944 | − | 0.944697i | \(-0.393644\pi\) | ||||
0.327944 | + | 0.944697i | \(0.393644\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.92493e9 | −2.04311 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.23686e8 | 0.0849477 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.53137e8 | 0.300941 | 0.150470 | − | 0.988615i | \(-0.451921\pi\) | ||||
0.150470 | + | 0.988615i | \(0.451921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.62727e9 | 1.06285 | 0.531425 | − | 0.847106i | \(-0.321657\pi\) | ||||
0.531425 | + | 0.847106i | \(0.321657\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.29751e9 | 0.819878 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.06231e8 | −0.438985 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.84387e8 | −0.592237 | −0.296118 | − | 0.955151i | \(-0.595692\pi\) | ||||
−0.296118 | + | 0.955151i | \(0.595692\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.67333e9 | 0.990545 | 0.495273 | − | 0.868738i | \(-0.335068\pi\) | ||||
0.495273 | + | 0.868738i | \(0.335068\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.94225e7 | −0.0569901 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.78714e9 | 1.57229 | 0.786147 | − | 0.618040i | \(-0.212073\pi\) | ||||
0.786147 | + | 0.618040i | \(0.212073\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.72313e9 | 0.941683 | 0.470841 | − | 0.882218i | \(-0.343950\pi\) | ||||
0.470841 | + | 0.882218i | \(0.343950\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.19824e8 | 0.118254 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.13732e9 | 1.11431 | 0.557157 | − | 0.830407i | \(-0.311892\pi\) | ||||
0.557157 | + | 0.830407i | \(0.311892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.13507e6 | −0.00263590 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.83306e9 | 1.40999 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.56149e9 | −1.25541 | −0.627706 | − | 0.778451i | \(-0.716006\pi\) | ||||
−0.627706 | + | 0.778451i | \(0.716006\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.96595e8 | 0.473768 | 0.236884 | − | 0.971538i | \(-0.423874\pi\) | ||||
0.236884 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.61394e9 | 1.22395 | 0.611973 | − | 0.790879i | \(-0.290376\pi\) | ||||
0.611973 | + | 0.790879i | \(0.290376\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.57019e9 | −1.16777 | −0.583883 | − | 0.811838i | \(-0.698467\pi\) | ||||
−0.583883 | + | 0.811838i | \(0.698467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.77075e9 | 1.68781 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.35524e6 | 0.00189233 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.20776e7 | 0.0265771 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.93225e8 | 0.329778 | 0.164889 | − | 0.986312i | \(-0.447273\pi\) | ||||
0.164889 | + | 0.986312i | \(0.447273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.28779e9 | −2.16654 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.71018e7 | 0.0147672 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.26410e9 | 0.495940 | 0.247970 | − | 0.968768i | \(-0.420237\pi\) | ||||
0.247970 | + | 0.968768i | \(0.420237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.37678e9 | −1.28741 | −0.643706 | − | 0.765273i | \(-0.722604\pi\) | ||||
−0.643706 | + | 0.765273i | \(0.722604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.68327e9 | −1.38442 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.73595e9 | −0.999680 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.76331e8 | 0.351759 | 0.175879 | − | 0.984412i | \(-0.443723\pi\) | ||||
0.175879 | + | 0.984412i | \(0.443723\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.35477e9 | 0.474654 | 0.237327 | − | 0.971430i | \(-0.423729\pi\) | ||||
0.237327 | + | 0.971430i | \(0.423729\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.90791e9 | 1.00476 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.02597e9 | 0.680959 | 0.340479 | − | 0.940252i | \(-0.389411\pi\) | ||||
0.340479 | + | 0.940252i | \(0.389411\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.02718e9 | 1.66668 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.26047e8 | −0.234228 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.15573e7 | 0.0164087 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.99361e8 | 0.0617601 | 0.0308800 | − | 0.999523i | \(-0.490169\pi\) | ||||
0.0308800 | + | 0.999523i | \(0.490169\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.02783e9 | −1.23116 | −0.615581 | − | 0.788074i | \(-0.711079\pi\) | ||||
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.18910e9 | −0.949142 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.07896e9 | 1.19799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.04105e9 | −0.297800 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.15096e9 | 0.607288 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.14272e8 | 0.0314325 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.55841e9 | −0.423148 | −0.211574 | − | 0.977362i | \(-0.567859\pi\) | ||||
−0.211574 | + | 0.977362i | \(0.567859\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.85349e8 | 0.207814 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.01460e9 | 0.787542 | 0.393771 | − | 0.919209i | \(-0.371170\pi\) | ||||
0.393771 | + | 0.919209i | \(0.371170\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.76221e8 | −0.0448773 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.74595e9 | 1.69631 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.97397e9 | 1.70996 | 0.854981 | − | 0.518659i | \(-0.173569\pi\) | ||||
0.854981 | + | 0.518659i | \(0.173569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.82948e8 | 0.213793 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.91575e9 | −1.16094 | −0.580471 | − | 0.814281i | \(-0.697131\pi\) | ||||
−0.580471 | + | 0.814281i | \(0.697131\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.34487e9 | −1.01346 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.91661e9 | 0.663720 | 0.331860 | − | 0.943329i | \(-0.392324\pi\) | ||||
0.331860 | + | 0.943329i | \(0.392324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.78071e9 | −0.625071 | −0.312536 | − | 0.949906i | \(-0.601178\pi\) | ||||
−0.312536 | + | 0.949906i | \(0.601178\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.67274e9 | −1.02502 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.95173e9 | −0.422965 | −0.211482 | − | 0.977382i | \(-0.567829\pi\) | ||||
−0.211482 | + | 0.977382i | \(0.567829\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.38790e9 | 0.293591 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.45433e7 | 0.0134900 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.31559e9 | −1.08472 | −0.542361 | − | 0.840146i | \(-0.682469\pi\) | ||||
−0.542361 | + | 0.840146i | \(0.682469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.52578e8 | −0.0307673 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.17508e9 | 0.231407 | 0.115703 | − | 0.993284i | \(-0.463088\pi\) | ||||
0.115703 | + | 0.993284i | \(0.463088\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.49897e9 | −1.26484 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.88790e8 | 0.0929242 | 0.0464621 | − | 0.998920i | \(-0.485205\pi\) | ||||
0.0464621 | + | 0.998920i | \(0.485205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.92744e9 | −0.362176 | −0.181088 | − | 0.983467i | \(-0.557962\pi\) | ||||
−0.181088 | + | 0.983467i | \(0.557962\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.02546e9 | 0.555454 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.50300e9 | −1.18019 | −0.590097 | − | 0.807332i | \(-0.700911\pi\) | ||||
−0.590097 | + | 0.807332i | \(0.700911\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.04523e10 | 1.85383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.40924e9 | −0.422444 | −0.211222 | − | 0.977438i | \(-0.567744\pi\) | ||||
−0.211222 | + | 0.977438i | \(0.567744\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.02270e9 | 1.37506 | 0.687531 | − | 0.726155i | \(-0.258694\pi\) | ||||
0.687531 | + | 0.726155i | \(0.258694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.38409e9 | −1.25135 | −0.625677 | − | 0.780083i | \(-0.715177\pi\) | ||||
−0.625677 | + | 0.780083i | \(0.715177\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.46670e9 | 0.408703 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.03395e9 | 0.169402 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.21300e10 | 1.94350 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.86728e8 | −0.124659 | −0.0623293 | − | 0.998056i | \(-0.519853\pi\) | ||||
−0.0623293 | + | 0.998056i | \(0.519853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.56022e8 | −0.101674 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.31666e10 | 3.55119 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.81312e8 | −0.0871779 | −0.0435890 | − | 0.999050i | \(-0.513879\pi\) | ||||
−0.0435890 | + | 0.999050i | \(0.513879\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.39677e9 | 1.24559 | 0.622793 | − | 0.782386i | \(-0.285998\pi\) | ||||
0.622793 | + | 0.782386i | \(0.285998\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.27887e9 | 1.20173 | 0.600864 | − | 0.799351i | \(-0.294823\pi\) | ||||
0.600864 | + | 0.799351i | \(0.294823\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.67086e7 | 0.0124510 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.05982e9 | −0.992195 | −0.496098 | − | 0.868267i | \(-0.665234\pi\) | ||||
−0.496098 | + | 0.868267i | \(0.665234\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.47092e9 | −0.899749 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.61653e9 | −0.356145 | −0.178072 | − | 0.984017i | \(-0.556986\pi\) | ||||
−0.178072 | + | 0.984017i | \(0.556986\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.77438e9 | 1.18171 | 0.590855 | − | 0.806778i | \(-0.298790\pi\) | ||||
0.590855 | + | 0.806778i | \(0.298790\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.10934e8 | −0.0410008 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.32646e10 | 1.73083 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.09360e7 | 0.00267525 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.93417e9 | 0.623967 | 0.311983 | − | 0.950088i | \(-0.399007\pi\) | ||||
0.311983 | + | 0.950088i | \(0.399007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.15194e10 | −1.42682 | −0.713411 | − | 0.700746i | \(-0.752851\pi\) | ||||
−0.713411 | + | 0.700746i | \(0.752851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.16327e8 | 0.0510376 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.83610e9 | 0.700891 | 0.350445 | − | 0.936583i | \(-0.386030\pi\) | ||||
0.350445 | + | 0.936583i | \(0.386030\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.01847e9 | 0.477687 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.30850e10 | 1.52408 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.34502e10 | −1.55080 | −0.775402 | − | 0.631468i | \(-0.782453\pi\) | ||||
−0.775402 | + | 0.631468i | \(0.782453\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.87321e9 | 0.889621 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.38813e9 | 0.267142 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.35211e9 | 1.02541 | 0.512704 | − | 0.858565i | \(-0.328644\pi\) | ||||
0.512704 | + | 0.858565i | \(0.328644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.80346e8 | 0.0630004 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.26303e10 | 3.47259 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.07639e10 | −1.13425 | −0.567126 | − | 0.823631i | \(-0.691945\pi\) | ||||
−0.567126 | + | 0.823631i | \(0.691945\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.14850e10 | 1.18663 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.39851e7 | −0.00859273 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.95823e8 | 0.0296811 | 0.0148406 | − | 0.999890i | \(-0.495276\pi\) | ||||
0.0148406 | + | 0.999890i | \(0.495276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.14712e9 | −0.809526 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.28218e9 | −0.807164 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.92934e9 | −0.765362 | −0.382681 | − | 0.923881i | \(-0.624999\pi\) | ||||
−0.382681 | + | 0.923881i | \(0.624999\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.02546e9 | −0.191784 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.06379e10 | −0.997681 | −0.498841 | − | 0.866694i | \(-0.666241\pi\) | ||||
−0.498841 | + | 0.866694i | \(0.666241\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.11783e8 | −0.0102858 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.21560e10 | 1.10799 | 0.553993 | − | 0.832522i | \(-0.313104\pi\) | ||||
0.553993 | + | 0.832522i | \(0.313104\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.04486e9 | −0.451220 | −0.225610 | − | 0.974218i | \(-0.572438\pi\) | ||||
−0.225610 | + | 0.974218i | \(0.572438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.78260e9 | 0.600965 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.41364e10 | 2.09887 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.58691e10 | −1.36714 | −0.683568 | − | 0.729887i | \(-0.739573\pi\) | ||||
−0.683568 | + | 0.729887i | \(0.739573\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.05885e10 | −0.895403 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.76028e9 | −0.315054 | −0.157527 | − | 0.987515i | \(-0.550352\pi\) | ||||
−0.157527 | + | 0.987515i | \(0.550352\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.38635e9 | 0.196285 | 0.0981427 | − | 0.995172i | \(-0.468710\pi\) | ||||
0.0981427 | + | 0.995172i | \(0.468710\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.81256e9 | 0.718235 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.75786e10 | 1.40670 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.63901e9 | −0.129969 | −0.0649845 | − | 0.997886i | \(-0.520700\pi\) | ||||
−0.0649845 | + | 0.997886i | \(0.520700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.01355e9 | 0.624017 | 0.312009 | − | 0.950079i | \(-0.398998\pi\) | ||||
0.312009 | + | 0.950079i | \(0.398998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.17100e9 | −0.553380 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.14257e8 | 0.00865966 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.11063e7 | 0.00609223 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.55176e9 | 0.114493 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.21205e9 | −0.0886361 | −0.0443181 | − | 0.999017i | \(-0.514111\pi\) | ||||
−0.0443181 | + | 0.999017i | \(0.514111\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.87547e10 | −3.50267 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.24440e9 | 0.302246 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.31165e8 | 0.0651512 | 0.0325756 | − | 0.999469i | \(-0.489629\pi\) | ||||
0.0325756 | + | 0.999469i | \(0.489629\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.39774e10 | −1.66298 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.49029e8 | −0.0101570 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.34048e10 | 1.58132 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.48310e9 | −0.496891 | −0.248446 | − | 0.968646i | \(-0.579920\pi\) | ||||
−0.248446 | + | 0.968646i | \(0.579920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.60208e10 | 1.71296 | 0.856479 | − | 0.516181i | \(-0.172647\pi\) | ||||
0.856479 | + | 0.516181i | \(0.172647\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.41246e8 | −0.0479635 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.69053e7 | −0.00621685 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.24111e9 | 0.141339 | 0.0706695 | − | 0.997500i | \(-0.477486\pi\) | ||||
0.0706695 | + | 0.997500i | \(0.477486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.16414e10 | 1.35327 | 0.676636 | − | 0.736317i | \(-0.263437\pi\) | ||||
0.676636 | + | 0.736317i | \(0.263437\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.18759e10 | 0.730125 | 0.365062 | − | 0.930983i | \(-0.381048\pi\) | ||||
0.365062 | + | 0.930983i | \(0.381048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.14265e9 | −0.557354 | −0.278677 | − | 0.960385i | \(-0.589896\pi\) | ||||
−0.278677 | + | 0.960385i | \(0.589896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.31435e10 | −3.18561 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.38344e10 | −0.822353 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.27491e10 | −0.745267 | −0.372633 | − | 0.927979i | \(-0.621545\pi\) | ||||
−0.372633 | + | 0.927979i | \(0.621545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.26094e9 | 0.362956 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.28321e9 | −0.415264 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.39493e10 | 1.91973 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.36841e10 | −2.42980 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.72779e10 | −0.953167 | −0.476583 | − | 0.879129i | \(-0.658125\pi\) | ||||
−0.476583 | + | 0.879129i | \(0.658125\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.14152e10 | 0.619514 | 0.309757 | − | 0.950816i | \(-0.399752\pi\) | ||||
0.309757 | + | 0.950816i | \(0.399752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.27618e10 | 0.686965 | 0.343483 | − | 0.939159i | \(-0.388393\pi\) | ||||
0.343483 | + | 0.939159i | \(0.388393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.19302e8 | 0.0169108 | 0.00845540 | − | 0.999964i | \(-0.497309\pi\) | ||||
0.00845540 | + | 0.999964i | \(0.497309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.01730e9 | 0.211046 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.99981e8 | −0.0103376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.26620e10 | −1.16208 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.57501e10 | −1.80405 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.51426e9 | −0.426234 | −0.213117 | − | 0.977027i | \(-0.568362\pi\) | ||||
−0.213117 | + | 0.977027i | \(0.568362\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.20262e9 | 0.404145 | 0.202072 | − | 0.979371i | \(-0.435232\pi\) | ||||
0.202072 | + | 0.979371i | \(0.435232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.57333e10 | −0.769054 | −0.384527 | − | 0.923114i | \(-0.625635\pi\) | ||||
−0.384527 | + | 0.923114i | \(0.625635\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.84173e10 | −0.886124 | −0.443062 | − | 0.896491i | \(-0.646108\pi\) | ||||
−0.443062 | + | 0.896491i | \(0.646108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.36136e9 | −0.351400 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.14717e9 | −0.0539071 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.66146e9 | 0.310591 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.03565e10 | 0.934423 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.00167e10 | −1.36718 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.99912e10 | 0.896537 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.44837e9 | 0.197959 | 0.0989796 | − | 0.995089i | \(-0.468442\pi\) | ||||
0.0989796 | + | 0.995089i | \(0.468442\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.83330e10 | 0.803377 | 0.401688 | − | 0.915776i | \(-0.368424\pi\) | ||||
0.401688 | + | 0.915776i | \(0.368424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.11439e7 | −0.00178920 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.26115e10 | −3.10966 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.38356e10 | 1.43803 | 0.719017 | − | 0.694993i | \(-0.244592\pi\) | ||||
0.719017 | + | 0.694993i | \(0.244592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.64429e10 | 0.688291 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.72756e10 | 1.13312 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.27055e10 | −1.33834 | −0.669169 | − | 0.743110i | \(-0.733350\pi\) | ||||
−0.669169 | + | 0.743110i | \(0.733350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.54258e9 | −0.103264 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.92660e8 | 0.00770814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.13238e10 | −0.846791 | −0.423395 | − | 0.905945i | \(-0.639162\pi\) | ||||
−0.423395 | + | 0.905945i | \(0.639162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.37346e10 | 0.928578 | 0.464289 | − | 0.885684i | \(-0.346310\pi\) | ||||
0.464289 | + | 0.885684i | \(0.346310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.60040e9 | −0.333986 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.23219e9 | 0.0471470 | 0.0235735 | − | 0.999722i | \(-0.492496\pi\) | ||||
0.0235735 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.02130e10 | −1.14752 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.42965e10 | 0.909325 | 0.454662 | − | 0.890664i | \(-0.349760\pi\) | ||||
0.454662 | + | 0.890664i | \(0.349760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.49928e10 | 0.928547 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.50921e10 | 1.65095 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.88727e9 | −0.359372 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.51422e10 | −0.900653 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.54395e10 | 1.61600 | 0.807998 | − | 0.589185i | \(-0.200551\pi\) | ||||
0.807998 | + | 0.589185i | \(0.200551\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.55196e9 | 0.0894555 | 0.0447277 | − | 0.998999i | \(-0.485758\pi\) | ||||
0.0447277 | + | 0.998999i | \(0.485758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.83469e10 | 3.07466 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.12078e9 | −0.175673 | −0.0878365 | − | 0.996135i | \(-0.527995\pi\) | ||||
−0.0878365 | + | 0.996135i | \(0.527995\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.31243e7 | −0.00249071 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.49695e10 | 0.838442 | 0.419221 | − | 0.907884i | \(-0.362303\pi\) | ||||
0.419221 | + | 0.907884i | \(0.362303\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.97231e10 | −0.657579 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.29431e9 | 0.239771 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.79851e9 | 0.0913417 | 0.0456709 | − | 0.998957i | \(-0.485457\pi\) | ||||
0.0456709 | + | 0.998957i | \(0.485457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.71620e9 | −0.0874141 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.32195e10 | 0.742026 | 0.371013 | − | 0.928628i | \(-0.379010\pi\) | ||||
0.371013 | + | 0.928628i | \(0.379010\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 576.8.a.bl.1.1 | 2 | ||
3.2 | odd | 2 | 192.8.a.u.1.2 | 2 | |||
4.3 | odd | 2 | 576.8.a.bm.1.1 | 2 | |||
8.3 | odd | 2 | 288.8.a.j.1.2 | 2 | |||
8.5 | even | 2 | 288.8.a.i.1.2 | 2 | |||
12.11 | even | 2 | 192.8.a.r.1.2 | 2 | |||
24.5 | odd | 2 | 96.8.a.d.1.1 | ✓ | 2 | ||
24.11 | even | 2 | 96.8.a.g.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.8.a.d.1.1 | ✓ | 2 | 24.5 | odd | 2 | ||
96.8.a.g.1.1 | yes | 2 | 24.11 | even | 2 | ||
192.8.a.r.1.2 | 2 | 12.11 | even | 2 | |||
192.8.a.u.1.2 | 2 | 3.2 | odd | 2 | |||
288.8.a.i.1.2 | 2 | 8.5 | even | 2 | |||
288.8.a.j.1.2 | 2 | 8.3 | odd | 2 | |||
576.8.a.bl.1.1 | 2 | 1.1 | even | 1 | trivial | ||
576.8.a.bm.1.1 | 2 | 4.3 | odd | 2 |