Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(119.955849786\) |
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: | \( x^{4} - 430x^{2} - 2448x + 12138 \) |
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 | \(-13.4480\) 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 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 530.466 | 1.89785 | 0.948926 | − | 0.315499i | \(-0.102172\pi\) | ||||
0.948926 | + | 0.315499i | \(0.102172\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 930.332 | 1.02517 | 0.512584 | − | 0.858637i | \(-0.328688\pi\) | ||||
0.512584 | + | 0.858637i | \(0.328688\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4803.24 | 1.08808 | 0.544038 | − | 0.839060i | \(-0.316895\pi\) | ||||
0.544038 | + | 0.839060i | \(0.316895\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10210.0 | −1.28891 | −0.644455 | − | 0.764642i | \(-0.722916\pi\) | ||||
−0.644455 | + | 0.764642i | \(0.722916\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14322.6 | 1.09573 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −25673.6 | −1.26741 | −0.633703 | − | 0.773577i | \(-0.718466\pi\) | ||||
−0.633703 | + | 0.773577i | \(0.718466\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24444.3 | 0.817597 | 0.408799 | − | 0.912625i | \(-0.365948\pi\) | ||||
0.408799 | + | 0.912625i | \(0.365948\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 25119.0 | 0.591881 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19503.5 | 0.334245 | 0.167122 | − | 0.985936i | \(-0.446552\pi\) | ||||
0.167122 | + | 0.985936i | \(0.446552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 203269. | 2.60184 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 242831. | 1.84889 | 0.924445 | − | 0.381316i | \(-0.124529\pi\) | ||||
0.924445 | + | 0.381316i | \(0.124529\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −137921. | −0.831507 | −0.415753 | − | 0.909477i | \(-0.636482\pi\) | ||||
−0.415753 | + | 0.909477i | \(0.636482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 129687. | 0.628201 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 493509. | 1.94562 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −146746. | −0.476277 | −0.238139 | − | 0.971231i | \(-0.576537\pi\) | ||||
−0.238139 | + | 0.971231i | \(0.576537\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −275669. | −0.744153 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 279862. | 0.634162 | 0.317081 | − | 0.948398i | \(-0.397297\pi\) | ||||
0.317081 | + | 0.948398i | \(0.397297\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 793457. | 1.52189 | 0.760946 | − | 0.648815i | \(-0.224735\pi\) | ||||
0.760946 | + | 0.648815i | \(0.224735\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 386709. | 0.632617 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.15302e6 | −1.61992 | −0.809962 | − | 0.586482i | \(-0.800512\pi\) | ||||
−0.809962 | + | 0.586482i | \(0.800512\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41974.2 | 0.0509678 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −693187. | −0.731737 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 681439. | 0.628726 | 0.314363 | − | 0.949303i | \(-0.398209\pi\) | ||||
0.314363 | + | 0.949303i | \(0.398209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.54795e6 | 2.06501 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 659995. | 0.472040 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −40009.7 | −0.0253620 | −0.0126810 | − | 0.999920i | \(-0.504037\pi\) | ||||
−0.0126810 | + | 0.999920i | \(0.504037\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.32040e6 | 1.30890 | 0.654452 | − | 0.756103i | \(-0.272899\pi\) | ||||
0.654452 | + | 0.756103i | \(0.272899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 678212. | 0.341722 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.41604e6 | −2.44616 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.63837e6 | −0.665505 | −0.332753 | − | 0.943014i | \(-0.607977\pi\) | ||||
−0.332753 | + | 0.943014i | \(0.607977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 526594. | 0.192976 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.79092e6 | −1.25701 | −0.628507 | − | 0.777804i | \(-0.716334\pi\) | ||||
−0.628507 | + | 0.777804i | \(0.716334\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −969505. | −0.291689 | −0.145845 | − | 0.989308i | \(-0.546590\pi\) | ||||
−0.145845 | + | 0.989308i | \(0.546590\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.48826e6 | 1.50217 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.46860e6 | 1.11546 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.24969e6 | 1.42614 | 0.713072 | − | 0.701091i | \(-0.247303\pi\) | ||||
0.713072 | + | 0.701091i | \(0.247303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.63631e6 | −1.46592 | −0.732960 | − | 0.680272i | \(-0.761862\pi\) | ||||
−0.732960 | + | 0.680272i | \(0.761862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.36190e7 | −2.40535 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.55643e6 | 1.06746 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.65733e6 | 0.700280 | 0.350140 | − | 0.936697i | \(-0.386134\pi\) | ||||
0.350140 | + | 0.936697i | \(0.386134\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.49866e6 | −1.32135 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.72388e6 | −0.480071 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.29668e7 | 1.55168 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.23448e6 | −0.582334 | −0.291167 | − | 0.956672i | \(-0.594044\pi\) | ||||
−0.291167 | + | 0.956672i | \(0.594044\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.50156e6 | 0.362692 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 514976. | 0.0497351 | 0.0248675 | − | 0.999691i | \(-0.492084\pi\) | ||||
0.0248675 | + | 0.999691i | \(0.492084\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.04823e6 | 0.545379 | 0.272689 | − | 0.962102i | \(-0.412087\pi\) | ||||
0.272689 | + | 0.962102i | \(0.412087\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.33247e7 | 1.12330 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.00697e7 | −0.794647 | −0.397324 | − | 0.917679i | \(-0.630061\pi\) | ||||
−0.397324 | + | 0.917679i | \(0.630061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.47212e6 | 0.108881 | 0.0544403 | − | 0.998517i | \(-0.482663\pi\) | ||||
0.0544403 | + | 0.998517i | \(0.482663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.96214e6 | −0.274979 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.75618e6 | −0.570874 | −0.285437 | − | 0.958397i | \(-0.592139\pi\) | ||||
−0.285437 | + | 0.958397i | \(0.592139\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.03459e7 | 0.634347 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.44307e6 | −0.429637 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.38850e7 | −1.29930 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.58390e6 | 0.183911 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.55627e6 | 0.366134 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.63845e7 | 3.04006 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.05516e7 | 0.890293 | 0.445146 | − | 0.895458i | \(-0.353152\pi\) | ||||
0.445146 | + | 0.895458i | \(0.353152\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.14234e7 | 0.878665 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.06403e7 | −1.19081 | −0.595406 | − | 0.803425i | \(-0.703009\pi\) | ||||
−0.595406 | + | 0.803425i | \(0.703009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.27413e7 | 0.838174 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.04412e7 | 0.365242 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.19457e7 | 0.396906 | 0.198453 | − | 0.980110i | \(-0.436408\pi\) | ||||
0.198453 | + | 0.980110i | \(0.436408\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.07490e7 | 0.655308 | 0.327654 | − | 0.944798i | \(-0.393742\pi\) | ||||
0.327654 | + | 0.944798i | \(0.393742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.11316e7 | −0.935264 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.90409e7 | −1.40243 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.28813e8 | 3.50892 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.13330e6 | 0.0294263 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.75243e7 | 1.91993 | 0.959966 | − | 0.280118i | \(-0.0903735\pi\) | ||||
0.959966 | + | 0.280118i | \(0.0903735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.43978e7 | −1.52213 | −0.761065 | − | 0.648676i | \(-0.775323\pi\) | ||||
−0.761065 | + | 0.648676i | \(0.775323\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.87161e7 | −0.422469 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.31626e7 | −1.57808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.72664e7 | −0.562315 | −0.281157 | − | 0.959662i | \(-0.590718\pi\) | ||||
−0.281157 | + | 0.959662i | \(0.590718\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.83989e7 | 0.362995 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.81447e7 | 0.342657 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.03321e7 | −0.910309 | −0.455154 | − | 0.890413i | \(-0.650416\pi\) | ||||
−0.455154 | + | 0.890413i | \(0.650416\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.87947e7 | 1.19223 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.57706e7 | 1.09276 | 0.546379 | − | 0.837538i | \(-0.316006\pi\) | ||||
0.546379 | + | 0.837538i | \(0.316006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.14949e7 | 0.661289 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.78199e7 | 0.272532 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.83635e7 | −1.00384 | −0.501918 | − | 0.864915i | \(-0.667372\pi\) | ||||
−0.501918 | + | 0.864915i | \(0.667372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.89107e8 | 2.66732 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.08026e6 | −0.0146427 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.03905e8 | −1.35410 | −0.677049 | − | 0.735938i | \(-0.736742\pi\) | ||||
−0.677049 | + | 0.735938i | \(0.736742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.89023e7 | 0.863691 | 0.431846 | − | 0.901948i | \(-0.357863\pi\) | ||||
0.431846 | + | 0.901948i | \(0.357863\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.26507e7 | 0.755696 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.78437e7 | −0.903904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.23316e8 | −1.37903 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.83117e7 | 0.197294 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.14992e7 | 0.119412 | 0.0597062 | − | 0.998216i | \(-0.480984\pi\) | ||||
0.0597062 | + | 0.998216i | \(0.480984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.41140e7 | 0.641952 | 0.320976 | − | 0.947087i | \(-0.395989\pi\) | ||||
0.320976 | + | 0.947087i | \(0.395989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.46233e8 | −1.41229 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.77703e8 | −1.65601 | −0.828003 | − | 0.560723i | \(-0.810523\pi\) | ||||
−0.828003 | + | 0.560723i | \(0.810523\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.66111e6 | 0.0149422 | 0.00747108 | − | 0.999972i | \(-0.497622\pi\) | ||||
0.00747108 | + | 0.999972i | \(0.497622\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.42361e7 | −0.384230 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.25913e8 | 1.89542 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.48457e8 | 1.20355 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.42180e7 | 0.111415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.17412e8 | 0.889609 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.25200e8 | 1.65036 | 0.825181 | − | 0.564868i | \(-0.191073\pi\) | ||||
0.825181 | + | 0.564868i | \(0.191073\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.02355e8 | −0.725738 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.20902e8 | 2.88833 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.28313e8 | −0.852433 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.61766e7 | −0.168407 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.62127e8 | 1.63357 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.93794e7 | 0.298180 | 0.149090 | − | 0.988824i | \(-0.452366\pi\) | ||||
0.149090 | + | 0.988824i | \(0.452366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.48183e8 | 0.867280 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.34336e8 | −1.89711 | −0.948557 | − | 0.316608i | \(-0.897456\pi\) | ||||
−0.948557 | + | 0.316608i | \(0.897456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.66610e8 | 0.916804 | 0.458402 | − | 0.888745i | \(-0.348422\pi\) | ||||
0.458402 | + | 0.888745i | \(0.348422\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.20652e8 | 0.644011 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.77181e8 | 1.43555 | 0.717773 | − | 0.696277i | \(-0.245161\pi\) | ||||
0.717773 | + | 0.696277i | \(0.245161\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.11638e8 | −3.07438 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.68742e8 | 0.823385 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.33182e8 | 1.10485 | 0.552424 | − | 0.833564i | \(-0.313703\pi\) | ||||
0.552424 | + | 0.833564i | \(0.313703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.53512e7 | −0.392781 | −0.196390 | − | 0.980526i | \(-0.562922\pi\) | ||||
−0.196390 | + | 0.980526i | \(0.562922\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.22659e7 | 0.0967294 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.49575e8 | −1.05381 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.06180e8 | −0.846349 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.43007e8 | 0.969974 | 0.484987 | − | 0.874521i | \(-0.338824\pi\) | ||||
0.484987 | + | 0.874521i | \(0.338824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.36798e7 | 0.363684 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.67712e8 | −1.38873 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.64384e7 | 0.317644 | 0.158822 | − | 0.987307i | \(-0.449230\pi\) | ||||
0.158822 | + | 0.987307i | \(0.449230\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.36522e8 | −0.488264 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.77024e8 | 0.616296 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.11540e7 | 0.139497 | 0.0697487 | − | 0.997565i | \(-0.477780\pi\) | ||||
0.0697487 | + | 0.997565i | \(0.477780\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.61480e8 | 1.19323 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.25748e8 | 0.404307 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.01524e8 | 1.25770 | 0.628852 | − | 0.777525i | \(-0.283525\pi\) | ||||
0.628852 | + | 0.777525i | \(0.283525\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.33296e8 | −1.01727 | −0.508637 | − | 0.860981i | \(-0.669850\pi\) | ||||
−0.508637 | + | 0.860981i | \(0.669850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.56464e8 | −0.762881 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.76348e8 | 2.83100 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.54553e8 | −0.436916 | −0.218458 | − | 0.975846i | \(-0.570103\pi\) | ||||
−0.218458 | + | 0.975846i | \(0.570103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00545e8 | −0.277169 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.22342e8 | 0.866652 | 0.433326 | − | 0.901237i | \(-0.357340\pi\) | ||||
0.433326 | + | 0.901237i | \(0.357340\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.98182e8 | −1.30658 | −0.653289 | − | 0.757108i | \(-0.726611\pi\) | ||||
−0.653289 | + | 0.757108i | \(0.726611\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.50105e8 | 0.895862 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.60365e8 | 0.650122 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.48795e8 | 0.606317 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.41331e8 | −0.336211 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.39648e8 | −1.02110 | −0.510550 | − | 0.859848i | \(-0.670558\pi\) | ||||
−0.510550 | + | 0.859848i | \(0.670558\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.12238e7 | −0.0481332 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.45421e7 | 0.209400 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.99130e8 | −0.430811 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.38179e8 | 1.56019 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.39044e7 | 0.0287145 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.23089e9 | 2.48411 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.03335e8 | 1.38732 | 0.693662 | − | 0.720301i | \(-0.255996\pi\) | ||||
0.693662 | + | 0.720301i | \(0.255996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.63302e8 | 0.314874 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.05993e7 | 0.0953857 | 0.0476929 | − | 0.998862i | \(-0.484813\pi\) | ||||
0.0476929 | + | 0.998862i | \(0.484813\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.44273e8 | −0.818926 | −0.409463 | − | 0.912327i | \(-0.634284\pi\) | ||||
−0.409463 | + | 0.912327i | \(0.634284\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.59768e8 | 0.648538 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.80797e7 | 0.137667 | 0.0688337 | − | 0.997628i | \(-0.478072\pi\) | ||||
0.0688337 | + | 0.997628i | \(0.478072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.16637e9 | 2.01173 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.71882e8 | −0.458790 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.27573e8 | −1.03623 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.07537e9 | −3.35354 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.97472e7 | 0.0628622 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.07269e9 | −1.66069 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.34081e8 | 0.809485 | 0.404743 | − | 0.914431i | \(-0.367361\pi\) | ||||
0.404743 | + | 0.914431i | \(0.367361\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.06978e8 | −0.158759 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.69102e8 | −1.26303 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.55509e7 | −0.0363665 | −0.0181832 | − | 0.999835i | \(-0.505788\pi\) | ||||
−0.0181832 | + | 0.999835i | \(0.505788\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.36417e8 | −0.329594 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.62469e8 | −0.904743 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.27118e8 | −0.972917 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.79340e8 | 0.366240 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.01189e9 | −1.30011 | −0.650055 | − | 0.759887i | \(-0.725254\pi\) | ||||
−0.650055 | + | 0.759887i | \(0.725254\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.15695e9 | −1.45689 | −0.728443 | − | 0.685107i | \(-0.759756\pi\) | ||||
−0.728443 | + | 0.685107i | \(0.759756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00963e8 | −0.248051 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.31242e9 | −1.58804 | −0.794022 | − | 0.607890i | \(-0.792016\pi\) | ||||
−0.794022 | + | 0.607890i | \(0.792016\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.01095e9 | −2.38563 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.44894e8 | −0.750153 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.62022e7 | 0.0527026 | 0.0263513 | − | 0.999653i | \(-0.491611\pi\) | ||||
0.0263513 | + | 0.999653i | \(0.491611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.96349e8 | −0.331535 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.67653e7 | 0.106181 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.14289e8 | −0.553583 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.17215e8 | −0.862989 | −0.431494 | − | 0.902116i | \(-0.642014\pi\) | ||||
−0.431494 | + | 0.902116i | \(0.642014\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.04019e8 | 0.211387 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.33965e8 | 0.644550 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.08683e8 | −0.208212 | −0.104106 | − | 0.994566i | \(-0.533198\pi\) | ||||
−0.104106 | + | 0.994566i | \(0.533198\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.79238e9 | 1.75518 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.47930e9 | −2.38305 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.11653e9 | −1.05350 | −0.526748 | − | 0.850022i | \(-0.676589\pi\) | ||||
−0.526748 | + | 0.850022i | \(0.676589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.54894e8 | 0.514011 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.90286e8 | −0.627818 | −0.313909 | − | 0.949453i | \(-0.601639\pi\) | ||||
−0.313909 | + | 0.949453i | \(0.601639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.37044e9 | 2.11698 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.78431e8 | 0.507298 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.85656e9 | 1.59914 | 0.799569 | − | 0.600574i | \(-0.205061\pi\) | ||||
0.799569 | + | 0.600574i | \(0.205061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.00725e8 | −0.423624 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.27288e8 | −0.687516 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.31524e9 | 2.70661 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.59743e7 | 0.0128131 | 0.00640655 | − | 0.999979i | \(-0.497961\pi\) | ||||
0.00640655 | + | 0.999979i | \(0.497961\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.14015e8 | 0.483920 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.07966e8 | 0.548286 | 0.274143 | − | 0.961689i | \(-0.411606\pi\) | ||||
0.274143 | + | 0.961689i | \(0.411606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.40817e9 | 1.07174 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.81911e8 | 0.210872 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.04855e8 | −0.518226 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.54308e9 | −1.11521 | −0.557606 | − | 0.830105i | \(-0.688280\pi\) | ||||
−0.557606 | + | 0.830105i | \(0.688280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.22533e8 | 0.229154 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.72223e7 | −0.0260003 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.05080e9 | −2.78210 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.60223e8 | 0.378342 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.64486e8 | −0.242065 | −0.121032 | − | 0.992649i | \(-0.538620\pi\) | ||||
−0.121032 | + | 0.992649i | \(0.538620\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.97063e9 | −1.28712 | −0.643560 | − | 0.765396i | \(-0.722543\pi\) | ||||
−0.643560 | + | 0.765396i | \(0.722543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.40552e8 | −0.539975 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.21864e9 | −3.29759 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.15874e9 | 1.34185 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.32410e9 | −0.809695 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.29837e9 | 0.781136 | 0.390568 | − | 0.920574i | \(-0.372279\pi\) | ||||
0.390568 | + | 0.920574i | \(0.372279\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.48225e9 | 1.46939 | 0.734696 | − | 0.678397i | \(-0.237325\pi\) | ||||
0.734696 | + | 0.678397i | \(0.237325\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.47796e9 | 2.02587 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.76748e8 | 0.273278 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.40045e8 | −0.473889 | −0.236945 | − | 0.971523i | \(-0.576146\pi\) | ||||
−0.236945 | + | 0.971523i | \(0.576146\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.05992e7 | 0.0169893 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.91489e8 | −0.541845 | −0.270922 | − | 0.962601i | \(-0.587329\pi\) | ||||
−0.270922 | + | 0.962601i | \(0.587329\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.47055e9 | 1.32903 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.09316e9 | 1.10847 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.22228e8 | 0.115861 | 0.0579305 | − | 0.998321i | \(-0.481550\pi\) | ||||
0.0579305 | + | 0.998321i | \(0.481550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.34424e9 | 0.690017 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.73874e9 | −0.878802 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.03871e9 | −2.50772 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.72029e8 | 0.133324 | 0.0666620 | − | 0.997776i | \(-0.478765\pi\) | ||||
0.0666620 | + | 0.997776i | \(0.478765\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.05334e8 | −0.243912 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.29484e9 | 1.09093 | 0.545467 | − | 0.838132i | \(-0.316352\pi\) | ||||
0.545467 | + | 0.838132i | \(0.316352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.05198e9 | −0.492579 | −0.246289 | − | 0.969196i | \(-0.579211\pi\) | ||||
−0.246289 | + | 0.969196i | \(0.579211\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.97539e9 | −0.911103 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.36844e9 | −0.621750 | −0.310875 | − | 0.950451i | \(-0.600622\pi\) | ||||
−0.310875 | + | 0.950451i | \(0.600622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.52423e9 | −0.682254 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.36193e8 | −0.324653 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.81116e9 | 1.65594 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.96876e9 | 2.12726 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.96769e8 | 0.209575 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.98936e8 | 0.332152 | 0.166076 | − | 0.986113i | \(-0.446890\pi\) | ||||
0.166076 | + | 0.986113i | \(0.446890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.49827e9 | 0.613879 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.89907e8 | 0.197833 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.77671e9 | −1.10518 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.57453e9 | 1.01006 | 0.505029 | − | 0.863102i | \(-0.331482\pi\) | ||||
0.505029 | + | 0.863102i | \(0.331482\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.35897e9 | −0.525567 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.77530e9 | 0.676842 | 0.338421 | − | 0.940995i | \(-0.390107\pi\) | ||||
0.338421 | + | 0.940995i | \(0.390107\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.23434e9 | −2.34329 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.85746e9 | 0.688336 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.52681e9 | −1.28865 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.41248e9 | −1.22947 | −0.614735 | − | 0.788734i | \(-0.710737\pi\) | ||||
−0.614735 | + | 0.788734i | \(0.710737\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.77581e9 | 0.630904 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.25973e9 | 0.441356 | 0.220678 | − | 0.975347i | \(-0.429173\pi\) | ||||
0.220678 | + | 0.975347i | \(0.429173\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.73177e8 | 0.0943898 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.12036e9 | 0.381795 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.42432e9 | 1.48708 | 0.743540 | − | 0.668692i | \(-0.233145\pi\) | ||||
0.743540 | + | 0.668692i | \(0.233145\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.01962e8 | −0.299030 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.81137e8 | 0.157347 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.20838e9 | 1.03505 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.53823e9 | −1.76260 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.84581e9 | −0.579565 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.01665e9 | −0.934529 | −0.467264 | − | 0.884118i | \(-0.654760\pi\) | ||||
−0.467264 | + | 0.884118i | \(0.654760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.45237e9 | −1.66659 | −0.833297 | − | 0.552826i | \(-0.813549\pi\) | ||||
−0.833297 | + | 0.552826i | \(0.813549\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.10590e9 | 1.53998 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.54094e9 | 1.05386 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.02444e9 | −0.888280 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.91670e7 | −0.00845399 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.85738e9 | −0.817378 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.34164e9 | −1.50812 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.80543e9 | −0.781789 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.01612e8 | 0.0554569 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.27780e9 | 0.346955 | 0.173478 | − | 0.984838i | \(-0.444500\pi\) | ||||
0.173478 | + | 0.984838i | \(0.444500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.86036e9 | 0.498652 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.80909e8 | 0.206639 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.90809e9 | −1.54345 | −0.771724 | − | 0.635958i | \(-0.780605\pi\) | ||||
−0.771724 | + | 0.635958i | \(0.780605\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.69157e9 | 0.436301 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.93582e9 | 1.51165 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.81428e9 | 1.46204 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.10178e9 | −0.521869 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.13395e9 | 0.278035 | 0.139018 | − | 0.990290i | \(-0.455606\pi\) | ||||
0.139018 | + | 0.990290i | \(0.455606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.10117e9 | −1.96158 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.32954e9 | −0.796186 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.21605e9 | 0.523360 | 0.261680 | − | 0.965155i | \(-0.415724\pi\) | ||||
0.261680 | + | 0.965155i | \(0.415724\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.64485e9 | −1.08343 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.94416e8 | 0.113907 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.95125e9 | −0.444039 | −0.222019 | − | 0.975042i | \(-0.571265\pi\) | ||||
−0.222019 | + | 0.975042i | \(0.571265\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.28413e9 | −1.41260 | −0.706299 | − | 0.707914i | \(-0.749637\pi\) | ||||
−0.706299 | + | 0.707914i | \(0.749637\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.10477e8 | 0.0689427 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.96445e9 | 0.869652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.95604e9 | −1.29075 | −0.645375 | − | 0.763866i | \(-0.723299\pi\) | ||||
−0.645375 | + | 0.763866i | \(0.723299\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.73108e9 | 0.370631 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.10430e9 | −1.50281 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.27311e9 | 0.684102 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.94829e9 | −0.815387 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.03096e9 | −0.414447 | −0.207223 | − | 0.978294i | \(-0.566443\pi\) | ||||
−0.207223 | + | 0.978294i | \(0.566443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.37139e9 | −0.679838 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.79797e9 | −0.956096 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.80592e8 | 0.153721 | 0.0768604 | − | 0.997042i | \(-0.475510\pi\) | ||||
0.0768604 | + | 0.997042i | \(0.475510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.26702e10 | −2.46588 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.48500e7 | 0.00862686 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.85326e9 | −0.352325 | −0.176162 | − | 0.984361i | \(-0.556368\pi\) | ||||
−0.176162 | + | 0.984361i | \(0.556368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.50306e9 | 0.282434 | 0.141217 | − | 0.989979i | \(-0.454898\pi\) | ||||
0.141217 | + | 0.989979i | \(0.454898\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.19438e9 | −0.221835 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.90114e9 | 0.349035 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.89042e9 | 0.343082 | 0.171541 | − | 0.985177i | \(-0.445125\pi\) | ||||
0.171541 | + | 0.985177i | \(0.445125\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.09966e9 | 1.09432 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.17723e10 | 2.08794 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.21094e9 | 1.43973 | 0.719865 | − | 0.694114i | \(-0.244204\pi\) | ||||
0.719865 | + | 0.694114i | \(0.244204\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.00834e9 | 0.694868 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.13340e9 | 1.56543 | 0.782717 | − | 0.622378i | \(-0.213833\pi\) | ||||
0.782717 | + | 0.622378i | \(0.213833\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.93564e9 | −0.666957 | −0.333479 | − | 0.942758i | \(-0.608222\pi\) | ||||
−0.333479 | + | 0.942758i | \(0.608222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.83887e8 | 0.0643254 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.33286e9 | 0.717904 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.93343e10 | 3.16773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.17011e9 | 0.513616 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.76750e9 | 0.603637 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.29696e9 | 0.839313 | 0.419656 | − | 0.907683i | \(-0.362151\pi\) | ||||
0.419656 | + | 0.907683i | \(0.362151\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.08040e9 | 0.952837 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.09019e10 | 1.68964 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.28555e8 | −0.0656929 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.76358e9 | −0.419005 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.15727e9 | 1.37329 | 0.686646 | − | 0.726992i | \(-0.259082\pi\) | ||||
0.686646 | + | 0.726992i | \(0.259082\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.18605e9 | −0.175940 | −0.0879698 | − | 0.996123i | \(-0.528038\pi\) | ||||
−0.0879698 | + | 0.996123i | \(0.528038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.13644e10 | 1.66758 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.58435e9 | −0.955757 | −0.477879 | − | 0.878426i | \(-0.658594\pi\) | ||||
−0.477879 | + | 0.878426i | \(0.658594\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.92176e8 | −0.0275958 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.46444e9 | −0.492153 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.87870e9 | 0.264035 | 0.132018 | − | 0.991247i | \(-0.457854\pi\) | ||||
0.132018 | + | 0.991247i | \(0.457854\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.62536e10 | −2.25999 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.06769e8 | −0.0972297 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.00667e10 | −1.37022 | −0.685108 | − | 0.728441i | \(-0.740245\pi\) | ||||
−0.685108 | + | 0.728441i | \(0.740245\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.98681e9 | 1.07564 | 0.537821 | − | 0.843059i | \(-0.319247\pi\) | ||||
0.537821 | + | 0.843059i | \(0.319247\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.07742e9 | 0.943143 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.20635e10 | 1.59073 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.73605e9 | 0.617982 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.33324e9 | 0.172154 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.11454e10 | 1.42419 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.79369e9 | 0.732660 | 0.366330 | − | 0.930485i | \(-0.380614\pi\) | ||||
0.366330 | + | 0.930485i | \(0.380614\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.00094e9 | 0.500724 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.23248e9 | −0.152657 | −0.0763287 | − | 0.997083i | \(-0.524320\pi\) | ||||
−0.0763287 | + | 0.997083i | \(0.524320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.86980e9 | −0.596990 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.02708e9 | −1.09530 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.18833e9 | 0.983383 | 0.491691 | − | 0.870770i | \(-0.336379\pi\) | ||||
0.491691 | + | 0.870770i | \(0.336379\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.33676e9 | 0.753269 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.49847e9 | 0.529317 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.95747e9 | −0.810372 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.52637e9 | −0.175990 | −0.0879948 | − | 0.996121i | \(-0.528046\pi\) | ||||
−0.0879948 | + | 0.996121i | \(0.528046\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.25761e9 | 0.371820 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.10066e10 | 1.24368 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.18507e9 | −0.803741 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.48388e9 | 0.828813 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.00901e9 | −0.329921 | −0.164961 | − | 0.986300i | \(-0.552750\pi\) | ||||
−0.164961 | + | 0.986300i | \(0.552750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.58710e9 | −0.389403 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.65142e10 | −1.77499 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.79099e8 | 0.0509867 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.60947e9 | −0.696474 | −0.348237 | − | 0.937407i | \(-0.613220\pi\) | ||||
−0.348237 | + | 0.937407i | \(0.613220\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.55602e9 | 0.475381 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.68995e9 | −0.277927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.60145e10 | −2.66161 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.29591e9 | 0.637884 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.58311e9 | 0.961513 | 0.480757 | − | 0.876854i | \(-0.340362\pi\) | ||||
0.480757 | + | 0.876854i | \(0.340362\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.62686e9 | 0.559104 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.30448e9 | −0.226772 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.93599e10 | 4.81052 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.40647e9 | 0.714893 | 0.357447 | − | 0.933934i | \(-0.383647\pi\) | ||||
0.357447 | + | 0.933934i | \(0.383647\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.03709e10 | −1.92886 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.58074e10 | −1.48251 | −0.741255 | − | 0.671223i | \(-0.765769\pi\) | ||||
−0.741255 | + | 0.671223i | \(0.765769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.01178e8 | 0.0558467 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.86950e9 | −0.724121 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.33337e9 | 0.850713 | 0.425356 | − | 0.905026i | \(-0.360149\pi\) | ||||
0.425356 | + | 0.905026i | \(0.360149\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.73853e9 | −0.608417 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.19221e10 | 1.06633 | 0.533163 | − | 0.846012i | \(-0.321003\pi\) | ||||
0.533163 | + | 0.846012i | \(0.321003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.11240e10 | 3.64374 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.56687e9 | −0.488640 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.36818e9 | −0.814646 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.55698e10 | 1.34135 | 0.670677 | − | 0.741750i | \(-0.266004\pi\) | ||||
0.670677 | + | 0.741750i | \(0.266004\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.56118e9 | 0.560015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.41608e10 | −2.88878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.36270e9 | −0.197958 | −0.0989790 | − | 0.995090i | \(-0.531558\pi\) | ||||
−0.0989790 | + | 0.995090i | \(0.531558\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.52935e9 | 0.209973 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.55817e10 | −1.28165 | −0.640823 | − | 0.767689i | \(-0.721407\pi\) | ||||
−0.640823 | + | 0.767689i | \(0.721407\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.36956e9 | 0.111621 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.92823e9 | −0.801783 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.08497e8 | 0.0326893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.29713e9 | −0.340750 | −0.170375 | − | 0.985379i | \(-0.554498\pi\) | ||||
−0.170375 | + | 0.985379i | \(0.554498\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.33384e9 | 0.183392 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.93932e9 | 0.540367 | 0.270184 | − | 0.962809i | \(-0.412916\pi\) | ||||
0.270184 | + | 0.962809i | \(0.412916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.80351e10 | −2.16345 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.68610e9 | −0.281899 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.84102e9 | 0.518489 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.82087e10 | −1.36773 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.77964e9 | 0.355819 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.44639e10 | −1.06719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.00164e10 | 1.46377 | 0.731886 | − | 0.681427i | \(-0.238640\pi\) | ||||
0.731886 | + | 0.681427i | \(0.238640\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.11116e9 | 0.0805389 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.14615e9 | −0.585241 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.36912e10 | −1.68706 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.75996e9 | 0.688911 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.77813e9 | 0.334313 | 0.167157 | − | 0.985930i | \(-0.446541\pi\) | ||||
0.167157 | + | 0.985930i | \(0.446541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.96022e10 | 2.05310 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.39519e9 | 0.233427 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.65676e9 | −0.317380 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.62514e9 | 0.650312 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.08411e10 | 0.726136 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.64254e10 | −1.75470 | −0.877349 | − | 0.479853i | \(-0.840690\pi\) | ||||
−0.877349 | + | 0.479853i | \(0.840690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.71149e10 | −1.78498 | −0.892492 | − | 0.451063i | \(-0.851045\pi\) | ||||
−0.892492 | + | 0.451063i | \(0.851045\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.99900e9 | −0.587323 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.66995e10 | −1.72763 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.93955e10 | 1.24430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.92452e9 | −0.440449 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.07029e10 | −1.30566 | −0.652830 | − | 0.757505i | \(-0.726418\pi\) | ||||
−0.652830 | + | 0.757505i | \(0.726418\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.03545e9 | 0.189812 | 0.0949059 | − | 0.995486i | \(-0.469745\pi\) | ||||
0.0949059 | + | 0.995486i | \(0.469745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.63614e10 | 1.63448 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.59965e9 | −0.0983460 | −0.0491730 | − | 0.998790i | \(-0.515659\pi\) | ||||
−0.0491730 | + | 0.998790i | \(0.515659\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.37869e10 | 0.840477 | 0.420239 | − | 0.907414i | \(-0.361946\pi\) | ||||
0.420239 | + | 0.907414i | \(0.361946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.17293e9 | −0.252254 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.07763e9 | −0.0645969 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.48890e10 | 2.07389 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.71471e9 | −0.160024 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.87002e9 | 0.226228 | 0.113114 | − | 0.993582i | \(-0.463917\pi\) | ||||
0.113114 | + | 0.993582i | \(0.463917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.17170e10 | 2.41839 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.70323e9 | 0.500362 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.20116e10 | 1.25503 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.33422e9 | 0.188539 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.34509e10 | −0.754354 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.86206e9 | −0.159193 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.20942e9 | −0.508055 | −0.254027 | − | 0.967197i | \(-0.581755\pi\) | ||||
−0.254027 | + | 0.967197i | \(0.581755\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.45283e9 | 0.517226 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.21307e10 | 1.74376 | 0.871882 | − | 0.489715i | \(-0.162899\pi\) | ||||
0.871882 | + | 0.489715i | \(0.162899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.17662e10 | −1.70997 | −0.854987 | − | 0.518650i | \(-0.826435\pi\) | ||||
−0.854987 | + | 0.518650i | \(0.826435\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.02984e9 | 0.375348 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.41602e10 | 1.27957 | 0.639784 | − | 0.768555i | \(-0.279024\pi\) | ||||
0.639784 | + | 0.768555i | \(0.279024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.62645e10 | −1.90513 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.71747e9 | 0.350057 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00187e10 | 1.55175 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.67278e10 | 0.857776 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.81594e9 | −0.194111 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.17596e10 | 3.11657 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.85014e8 | −0.0242804 | −0.0121402 | − | 0.999926i | \(-0.503864\pi\) | ||||
−0.0121402 | + | 0.999926i | \(0.503864\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.18705e10 | −0.589532 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.92738e10 | −0.949626 | −0.474813 | − | 0.880087i | \(-0.657484\pi\) | ||||
−0.474813 | + | 0.880087i | \(0.657484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.80412e10 | −1.37067 | −0.685336 | − | 0.728227i | \(-0.740345\pi\) | ||||
−0.685336 | + | 0.728227i | \(0.740345\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.73041e8 | −0.0277897 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.01064e10 | −1.44853 | −0.724263 | − | 0.689524i | \(-0.757820\pi\) | ||||
−0.724263 | + | 0.689524i | \(0.757820\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.91198e10 | 0.912699 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.55264e9 | 0.120897 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.81848e10 | −1.32445 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.51180e10 | −2.56988 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.37651e9 | −0.248729 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.34916e10 | −1.53736 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.74950e10 | −0.796851 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.99308e10 | 0.900779 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.65503e10 | 1.63916 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.84680e10 | 1.71188 | 0.855942 | − | 0.517072i | \(-0.172978\pi\) | ||||
0.855942 | + | 0.517072i | \(0.172978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.75418e8 | 0.0165784 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.36782e10 | −1.03761 | −0.518805 | − | 0.854892i | \(-0.673623\pi\) | ||||
−0.518805 | + | 0.854892i | \(0.673623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.66790e10 | −1.59503 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.32341e10 | 1.43420 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.85056e10 | −1.22078 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.49843e10 | −1.91186 | −0.955932 | − | 0.293588i | \(-0.905150\pi\) | ||||
−0.955932 | + | 0.293588i | \(0.905150\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.89900e10 | 0.800972 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.87052e10 | 1.62018 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.98289e10 | −1.23920 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.40916e9 | 0.181793 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.23071e9 | −0.295887 | −0.147944 | − | 0.988996i | \(-0.547265\pi\) | ||||
−0.147944 | + | 0.988996i | \(0.547265\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.02603e9 | 0.0416712 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.36618e9 | 0.0550710 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.54151e10 | −2.61720 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.00467e10 | 1.59030 | 0.795148 | − | 0.606415i | \(-0.207393\pi\) | ||||
0.795148 | + | 0.606415i | \(0.207393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.19954e10 | −0.472807 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.15429e10 | −1.23406 | −0.617032 | − | 0.786938i | \(-0.711665\pi\) | ||||
−0.617032 | + | 0.786938i | \(0.711665\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.45828e9 | 0.211965 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.71374e9 | 0.374434 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.45818e10 | −0.557940 | −0.278970 | − | 0.960300i | \(-0.589993\pi\) | ||||
−0.278970 | + | 0.960300i | \(0.589993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.89862e9 | 0.375961 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.10815e9 | 0.0794823 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.47800e10 | −0.553158 | −0.276579 | − | 0.960991i | \(-0.589201\pi\) | ||||
−0.276579 | + | 0.960991i | \(0.589201\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.09991e9 | 0.226627 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.14921e10 | 1.16147 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.11134e10 | 0.406895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.49030e9 | −0.308597 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.34083e9 | −0.264882 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.40103e10 | 1.21833 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.51653e10 | −1.25061 | −0.625304 | − | 0.780381i | \(-0.715025\pi\) | ||||
−0.625304 | + | 0.780381i | \(0.715025\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.69445e10 | −0.598266 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.36232e9 | −0.152915 | −0.0764576 | − | 0.997073i | \(-0.524361\pi\) | ||||
−0.0764576 | + | 0.997073i | \(0.524361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.93035e10 | 0.671800 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.60349e10 | −1.93617 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.19268e10 | −0.409159 | −0.204579 | − | 0.978850i | \(-0.565583\pi\) | ||||
−0.204579 | + | 0.978850i | \(0.565583\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.23702e10 | 0.761958 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.07318e9 | 0.0362935 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.38784e9 | 0.180916 | 0.0904581 | − | 0.995900i | \(-0.471167\pi\) | ||||
0.0904581 | + | 0.995900i | \(0.471167\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.42652e10 | −3.14286 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.89627e10 | −0.958802 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.54752e10 | 0.508685 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.25517e10 | 1.06247 | 0.531234 | − | 0.847225i | \(-0.321728\pi\) | ||||
0.531234 | + | 0.847225i | \(0.321728\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.44202e10 | 0.467357 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.81163e8 | 0.0283580 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.55618e9 | −0.113645 | −0.0568225 | − | 0.998384i | \(-0.518097\pi\) | ||||
−0.0568225 | + | 0.998384i | \(0.518097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.88840e9 | −0.0916596 |
(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 | 384.8.a.s.1.4 | yes | 4 | |
4.3 | odd | 2 | 384.8.a.o.1.4 | yes | 4 | ||
8.3 | odd | 2 | 384.8.a.r.1.1 | yes | 4 | ||
8.5 | even | 2 | 384.8.a.n.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.a.n.1.1 | ✓ | 4 | 8.5 | even | 2 | ||
384.8.a.o.1.4 | yes | 4 | 4.3 | odd | 2 | ||
384.8.a.r.1.1 | yes | 4 | 8.3 | odd | 2 | ||
384.8.a.s.1.4 | yes | 4 | 1.1 | even | 1 | trivial |