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: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 286x - 1680 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-12.1582\) 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 | ||||||||
\(5\) | 223.082 | 0.798124 | 0.399062 | − | 0.916924i | \(-0.369336\pi\) | ||||
0.399062 | + | 0.916924i | \(0.369336\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1526.43 | −1.68203 | −0.841017 | − | 0.541009i | \(-0.818043\pi\) | ||||
−0.841017 | + | 0.541009i | \(0.818043\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1604.21 | −0.363401 | −0.181700 | − | 0.983354i | \(-0.558160\pi\) | ||||
−0.181700 | + | 0.983354i | \(0.558160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2959.89 | −0.373657 | −0.186829 | − | 0.982393i | \(-0.559821\pi\) | ||||
−0.186829 | + | 0.982393i | \(0.559821\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6023.23 | 0.460797 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −20142.8 | −0.994372 | −0.497186 | − | 0.867644i | \(-0.665633\pi\) | ||||
−0.497186 | + | 0.867644i | \(0.665633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7745.63 | −0.259071 | −0.129536 | − | 0.991575i | \(-0.541349\pi\) | ||||
−0.129536 | + | 0.991575i | \(0.541349\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −41213.7 | −0.971123 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 71478.4 | 1.22498 | 0.612488 | − | 0.790480i | \(-0.290169\pi\) | ||||
0.612488 | + | 0.790480i | \(0.290169\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −28359.2 | −0.362998 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25181.4 | −0.191729 | −0.0958645 | − | 0.995394i | \(-0.530562\pi\) | ||||
−0.0958645 | + | 0.995394i | \(0.530562\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 270532. | 1.63099 | 0.815496 | − | 0.578762i | \(-0.196464\pi\) | ||||
0.815496 | + | 0.578762i | \(0.196464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −43313.6 | −0.209810 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −340520. | −1.34247 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −394033. | −1.27887 | −0.639435 | − | 0.768845i | \(-0.720832\pi\) | ||||
−0.639435 | + | 0.768845i | \(0.720832\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −79917.0 | −0.215731 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 181640. | 0.411594 | 0.205797 | − | 0.978595i | \(-0.434021\pi\) | ||||
0.205797 | + | 0.978595i | \(0.434021\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 555492. | 1.06546 | 0.532731 | − | 0.846285i | \(-0.321166\pi\) | ||||
0.532731 | + | 0.846285i | \(0.321166\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 162627. | 0.266041 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 669993. | 0.941299 | 0.470649 | − | 0.882320i | \(-0.344020\pi\) | ||||
0.470649 | + | 0.882320i | \(0.344020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50646e6 | 1.82924 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −543856. | −0.574101 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 772991. | 0.713196 | 0.356598 | − | 0.934258i | \(-0.383937\pi\) | ||||
0.356598 | + | 0.934258i | \(0.383937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −357870. | −0.290039 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −209132. | −0.149575 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.30252e6 | 0.825659 | 0.412830 | − | 0.910808i | \(-0.364541\pi\) | ||||
0.412830 | + | 0.910808i | \(0.364541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.68711e6 | 0.951677 | 0.475838 | − | 0.879533i | \(-0.342145\pi\) | ||||
0.475838 | + | 0.879533i | \(0.342145\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.11277e6 | −0.560678 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −660299. | −0.298225 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.08822e6 | 0.442032 | 0.221016 | − | 0.975270i | \(-0.429063\pi\) | ||||
0.221016 | + | 0.975270i | \(0.429063\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.92992e6 | 0.707240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −859754. | −0.285082 | −0.142541 | − | 0.989789i | \(-0.545527\pi\) | ||||
−0.142541 | + | 0.989789i | \(0.545527\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.61965e6 | 0.788158 | 0.394079 | − | 0.919077i | \(-0.371064\pi\) | ||||
0.394079 | + | 0.919077i | \(0.371064\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −765699. | −0.209577 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.44871e6 | 0.611253 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.33710e6 | 1.44609 | 0.723046 | − | 0.690800i | \(-0.242741\pi\) | ||||
0.723046 | + | 0.690800i | \(0.242741\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.43435e6 | −1.61912 | −0.809559 | − | 0.587038i | \(-0.800294\pi\) | ||||
−0.809559 | + | 0.587038i | \(0.800294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.49351e6 | −0.793632 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −679899. | −0.110695 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.18695e7 | −1.78471 | −0.892354 | − | 0.451337i | \(-0.850947\pi\) | ||||
−0.892354 | + | 0.451337i | \(0.850947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.51807e6 | 0.628504 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.30435e6 | 0.941654 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.72791e6 | −0.206771 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.05179e6 | 0.450761 | 0.225380 | − | 0.974271i | \(-0.427638\pi\) | ||||
0.225380 | + | 0.974271i | \(0.427638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.16947e6 | −0.121134 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.68684e6 | 0.452643 | 0.226321 | − | 0.974053i | \(-0.427330\pi\) | ||||
0.226321 | + | 0.974053i | \(0.427330\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.57360e7 | 1.41894 | 0.709468 | − | 0.704737i | \(-0.248935\pi\) | ||||
0.709468 | + | 0.704737i | \(0.248935\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.19405e6 | −0.775076 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.17323e7 | −0.925849 | −0.462924 | − | 0.886398i | \(-0.653200\pi\) | ||||
−0.462924 | + | 0.886398i | \(0.653200\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.64178e6 | −0.121429 | −0.0607144 | − | 0.998155i | \(-0.519338\pi\) | ||||
−0.0607144 | + | 0.998155i | \(0.519338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.06389e7 | −0.738356 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.65935e7 | −1.08184 | −0.540921 | − | 0.841073i | \(-0.681924\pi\) | ||||
−0.540921 | + | 0.841073i | \(0.681924\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.59456e7 | 0.977682 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.15776e6 | −0.124552 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.07467e7 | 1.67257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.69137e7 | −0.867940 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.90429e6 | 0.237634 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.37548e7 | −1.08784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.38888e7 | −1.03486 | −0.517431 | − | 0.855725i | \(-0.673111\pi\) | ||||
−0.517431 | + | 0.855725i | \(0.673111\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.49983e7 | 0.615145 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.03484e7 | 1.17947 | 0.589735 | − | 0.807597i | \(-0.299232\pi\) | ||||
0.589735 | + | 0.807597i | \(0.299232\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.18232e7 | 0.435767 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.39093e6 | 0.153599 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.84774e7 | 1.27845 | 0.639225 | − | 0.769020i | \(-0.279255\pi\) | ||||
0.639225 | + | 0.769020i | \(0.279255\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.72666e7 | 1.80863 | 0.904315 | − | 0.426867i | \(-0.140383\pi\) | ||||
0.904315 | + | 0.426867i | \(0.140383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.80898e7 | 0.543459 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.74827e6 | 0.135787 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.61754e6 | −0.153024 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.06743e7 | 1.05611 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.12193e7 | 1.26847 | 0.634237 | − | 0.773139i | \(-0.281314\pi\) | ||||
0.634237 | + | 0.773139i | \(0.281314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.07825e6 | 0.0491223 | 0.0245612 | − | 0.999698i | \(-0.492181\pi\) | ||||
0.0245612 | + | 0.999698i | \(0.492181\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.46841e7 | −0.331457 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.03508e7 | 1.30173 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.49433e7 | 1.54555 | 0.772777 | − | 0.634678i | \(-0.218867\pi\) | ||||
0.772777 | + | 0.634678i | \(0.218867\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.08707e7 | 0.411764 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.09107e8 | −2.06045 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.32916e7 | −0.421252 | −0.210626 | − | 0.977567i | \(-0.567550\pi\) | ||||
−0.210626 | + | 0.977567i | \(0.567550\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.66250e6 | −0.167454 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.24114e7 | 0.704653 | 0.352326 | − | 0.935877i | \(-0.385391\pi\) | ||||
0.352326 | + | 0.935877i | \(0.385391\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.39876e7 | −0.860380 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.64657e6 | −0.0863571 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.97832e7 | −1.17152 | −0.585760 | − | 0.810484i | \(-0.699204\pi\) | ||||
−0.585760 | + | 0.810484i | \(0.699204\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.32885e7 | 0.610575 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.51679e7 | 0.476694 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.19077e6 | −0.0285503 | −0.0142751 | − | 0.999898i | \(-0.504544\pi\) | ||||
−0.0142751 | + | 0.999898i | \(0.504544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.36384e7 | 0.672358 | 0.336179 | − | 0.941798i | \(-0.390865\pi\) | ||||
0.336179 | + | 0.941798i | \(0.390865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.55520e7 | 0.549451 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.79018e7 | −1.02070 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.23132e7 | 0.361356 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.00448e7 | −0.323708 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.09646e8 | 1.13861 | 0.569305 | − | 0.822127i | \(-0.307213\pi\) | ||||
0.569305 | + | 0.822127i | \(0.307213\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.15412e8 | −1.15558 | −0.577788 | − | 0.816187i | \(-0.696084\pi\) | ||||
−0.577788 | + | 0.816187i | \(0.696084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.78281e7 | −0.172180 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.78654e8 | 1.66487 | 0.832435 | − | 0.554122i | \(-0.186946\pi\) | ||||
0.832435 | + | 0.554122i | \(0.186946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.06694e8 | −0.959745 | −0.479873 | − | 0.877338i | \(-0.659317\pi\) | ||||
−0.479873 | + | 0.877338i | \(0.659317\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.93819e7 | 0.255208 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.84378e7 | 0.322495 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.05208e7 | 0.328503 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.21078e7 | 0.408325 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.24256e7 | 0.0941467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.79426e8 | −1.31491 | −0.657456 | − | 0.753493i | \(-0.728368\pi\) | ||||
−0.657456 | + | 0.753493i | \(0.728368\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.32133e7 | −0.164592 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.23920e8 | 0.850371 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.12948e8 | −2.74338 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.07305e7 | 0.455043 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.96205e7 | 0.371554 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.37823e8 | 1.43611 | 0.718054 | − | 0.695988i | \(-0.245033\pi\) | ||||
0.718054 | + | 0.695988i | \(0.245033\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.06739e7 | −0.120999 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.34015e8 | 1.32786 | 0.663932 | − | 0.747793i | \(-0.268886\pi\) | ||||
0.663932 | + | 0.747793i | \(0.268886\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.47626e8 | 1.36261 | 0.681306 | − | 0.731998i | \(-0.261412\pi\) | ||||
0.681306 | + | 0.731998i | \(0.261412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.61153e7 | 0.352907 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.29473e8 | 1.18846 | 0.594231 | − | 0.804295i | \(-0.297457\pi\) | ||||
0.594231 | + | 0.804295i | \(0.297457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.49464e8 | 0.751273 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.71102e8 | 0.834902 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.21111e7 | −0.104766 | −0.0523828 | − | 0.998627i | \(-0.516682\pi\) | ||||
−0.0523828 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.31724e8 | 1.06638 | 0.533189 | − | 0.845996i | \(-0.320994\pi\) | ||||
0.533189 | + | 0.845996i | \(0.320994\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.36064e8 | 1.45996 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.29262e7 | 0.0968039 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.27728e8 | −0.934798 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.22516e6 | 0.0248481 | 0.0124240 | − | 0.999923i | \(-0.496045\pi\) | ||||
0.0124240 | + | 0.999923i | \(0.496045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.14666e8 | −0.445157 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.21325e8 | −0.458204 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.02916e8 | 0.745675 | 0.372837 | − | 0.927897i | \(-0.378385\pi\) | ||||
0.372837 | + | 0.927897i | \(0.378385\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.01465e8 | 2.15110 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.83573e7 | −0.0639097 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.91567e7 | 0.302210 | 0.151105 | − | 0.988518i | \(-0.451717\pi\) | ||||
0.151105 | + | 0.988518i | \(0.451717\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.72441e8 | 0.569219 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.20476e8 | −1.03040 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.29913e8 | 1.03339 | 0.516697 | − | 0.856168i | \(-0.327161\pi\) | ||||
0.516697 | + | 0.856168i | \(0.327161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.51563e8 | 0.767810 | 0.383905 | − | 0.923372i | \(-0.374579\pi\) | ||||
0.383905 | + | 0.923372i | \(0.374579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.21988e8 | 0.362867 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.54940e7 | 0.131914 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.19740e8 | −0.903894 | −0.451947 | − | 0.892045i | \(-0.649270\pi\) | ||||
−0.451947 | + | 0.892045i | \(0.649270\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.97218e8 | 0.543664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.79730e8 | −1.55867 | −0.779334 | − | 0.626609i | \(-0.784442\pi\) | ||||
−0.779334 | + | 0.626609i | \(0.784442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.52928e8 | 0.401082 | 0.200541 | − | 0.979685i | \(-0.435730\pi\) | ||||
0.200541 | + | 0.979685i | \(0.435730\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.66537e7 | −0.119379 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.77262e8 | −0.692315 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.60590e6 | −0.0112246 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.09398e8 | 0.260247 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.33108e7 | 0.147042 | 0.0735210 | − | 0.997294i | \(-0.476576\pi\) | ||||
0.0735210 | + | 0.997294i | \(0.476576\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.90568e8 | 0.658978 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.15756e7 | −0.0699365 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.11568e8 | −0.457721 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.47921e8 | −1.79214 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.26545e8 | 0.261333 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.76365e8 | 0.759556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.53352e8 | 0.302485 | 0.151243 | − | 0.988497i | \(-0.451673\pi\) | ||||
0.151243 | + | 0.988497i | \(0.451673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.24871e8 | 0.819224 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.53440e8 | −0.477764 | −0.238882 | − | 0.971049i | \(-0.576781\pi\) | ||||
−0.238882 | + | 0.971049i | \(0.576781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.34566e8 | −0.801033 | −0.400517 | − | 0.916290i | \(-0.631169\pi\) | ||||
−0.400517 | + | 0.916290i | \(0.631169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.48239e8 | −0.447491 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.39819e8 | −0.951789 | −0.475895 | − | 0.879502i | \(-0.657876\pi\) | ||||
−0.475895 | + | 0.879502i | \(0.657876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.03963e7 | 0.0696745 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.16772e8 | −0.534539 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.56019e8 | 0.257613 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.39401e7 | 0.135637 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.43280e7 | −0.0701069 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.02270e9 | −1.58330 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.78667e7 | −0.0877062 | −0.0438531 | − | 0.999038i | \(-0.513963\pi\) | ||||
−0.0438531 | + | 0.999038i | \(0.513963\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.87250e8 | −0.426290 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.42762e8 | 0.352797 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.27253e8 | 0.181118 | 0.0905592 | − | 0.995891i | \(-0.471135\pi\) | ||||
0.0905592 | + | 0.995891i | \(0.471135\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.48025e8 | −0.624602 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.33989e8 | −0.592704 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.04242e9 | −1.39481 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.30531e8 | 0.564465 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.70640e8 | −1.11863 | −0.559314 | − | 0.828956i | \(-0.688935\pi\) | ||||
−0.559314 | + | 0.828956i | \(0.688935\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.54583e8 | −0.824282 | −0.412141 | − | 0.911120i | \(-0.635219\pi\) | ||||
−0.412141 | + | 0.911120i | \(0.635219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.82595e7 | −0.0719104 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.18126e9 | 1.42933 | 0.714667 | − | 0.699464i | \(-0.246578\pi\) | ||||
0.714667 | + | 0.699464i | \(0.246578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.91796e8 | −0.227531 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.30160e8 | 0.965657 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.73290e8 | −0.311740 | −0.155870 | − | 0.987778i | \(-0.549818\pi\) | ||||
−0.155870 | + | 0.987778i | \(0.549818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.33877e8 | −0.932882 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.56670e8 | −0.501105 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.84398e8 | 0.629048 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.33000e9 | −1.40449 | −0.702246 | − | 0.711935i | \(-0.747819\pi\) | ||||
−0.702246 | + | 0.711935i | \(0.747819\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.32416e8 | 0.137198 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.17992e9 | −1.19962 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.52311e8 | 0.451290 | 0.225645 | − | 0.974210i | \(-0.427551\pi\) | ||||
0.225645 | + | 0.974210i | \(0.427551\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.41379e8 | −0.628066 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.45343e7 | 0.0716409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.64402e9 | 1.55121 | 0.775603 | − | 0.631221i | \(-0.217446\pi\) | ||||
0.775603 | + | 0.631221i | \(0.217446\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.44999e8 | −0.597477 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.98969e7 | 0.0635714 | 0.0317857 | − | 0.999495i | \(-0.489881\pi\) | ||||
0.0317857 | + | 0.999495i | \(0.489881\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.46265e8 | 0.487855 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.04953e8 | 0.355154 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.76666e8 | 0.755110 | 0.377555 | − | 0.925987i | \(-0.376765\pi\) | ||||
0.377555 | + | 0.925987i | \(0.376765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.43978e9 | −1.21808 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.19408e8 | 0.680967 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.41370e9 | 1.15416 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.95321e9 | −1.56669 | −0.783344 | − | 0.621588i | \(-0.786488\pi\) | ||||
−0.783344 | + | 0.621588i | \(0.786488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.19226e8 | 0.251590 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.56622e9 | 1.21296 | 0.606481 | − | 0.795098i | \(-0.292580\pi\) | ||||
0.606481 | + | 0.795098i | \(0.292580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00743e8 | −0.609432 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.18555e8 | 0.0886805 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.32110e8 | 0.464742 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.15083e9 | 0.831724 | 0.415862 | − | 0.909428i | \(-0.363480\pi\) | ||||
0.415862 | + | 0.909428i | \(0.363480\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.03889e9 | 0.738113 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.98820e9 | −1.38879 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.88156e9 | −1.29226 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.54620e9 | 1.04421 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.67886e9 | −1.11498 | −0.557488 | − | 0.830185i | \(-0.688235\pi\) | ||||
−0.557488 | + | 0.830185i | \(0.688235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.42077e9 | 0.927976 | 0.463988 | − | 0.885842i | \(-0.346418\pi\) | ||||
0.463988 | + | 0.885842i | \(0.346418\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.88425e8 | 0.313766 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.71234e8 | 0.360955 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.57526e9 | −1.60075 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.28203e8 | 0.0783969 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.76731e8 | 0.346978 | 0.173489 | − | 0.984836i | \(-0.444496\pi\) | ||||
0.173489 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.29171e9 | −0.764642 | −0.382321 | − | 0.924030i | \(-0.624875\pi\) | ||||
−0.382321 | + | 0.924030i | \(0.624875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.51674e8 | −0.0883482 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.53645e8 | −0.317356 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.60873e9 | −0.907523 | −0.453761 | − | 0.891123i | \(-0.649918\pi\) | ||||
−0.453761 | + | 0.891123i | \(0.649918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.09821e9 | 0.609746 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.37709e9 | −1.29907 | −0.649534 | − | 0.760333i | \(-0.725036\pi\) | ||||
−0.649534 | + | 0.760333i | \(0.725036\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.64787e9 | −1.42442 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.38292e9 | 0.732353 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.25417e9 | 1.69659 | 0.848297 | − | 0.529520i | \(-0.177628\pi\) | ||||
0.848297 | + | 0.529520i | \(0.177628\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.91389e8 | −0.149574 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.61128e7 | 0.0283608 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00790e9 | 0.501624 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.30664e9 | −1.62062 | −0.810309 | − | 0.586003i | \(-0.800701\pi\) | ||||
−0.810309 | + | 0.586003i | \(0.800701\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.96471e8 | −0.191367 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.00472e9 | −1.90379 | −0.951894 | − | 0.306428i | \(-0.900866\pi\) | ||||
−0.951894 | + | 0.306428i | \(0.900866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.35702e9 | −0.635407 | −0.317703 | − | 0.948190i | \(-0.602912\pi\) | ||||
−0.317703 | + | 0.948190i | \(0.602912\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.62947e9 | 0.751557 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.42473e9 | −1.55603 | −0.778014 | − | 0.628247i | \(-0.783773\pi\) | ||||
−0.778014 | + | 0.628247i | \(0.783773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.66109e9 | −0.743513 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.02347e9 | 0.892326 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.91124e8 | −0.387190 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.19660e8 | 0.0940423 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.63510e8 | 0.237732 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.35267e8 | 0.0562366 | 0.0281183 | − | 0.999605i | \(-0.491048\pi\) | ||||
0.0281183 | + | 0.999605i | \(0.491048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.16629e9 | 0.477859 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.94589e9 | −1.18960 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.03884e8 | 0.359763 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.21620e9 | 0.477148 | 0.238574 | − | 0.971124i | \(-0.423320\pi\) | ||||
0.238574 | + | 0.971124i | \(0.423320\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.28873e8 | −0.243210 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.04610e8 | 0.0398831 | 0.0199416 | − | 0.999801i | \(-0.493652\pi\) | ||||
0.0199416 | + | 0.999801i | \(0.493652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.07225e8 | 0.190650 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.60888e8 | −0.0966797 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.31236e9 | 0.479517 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.71953e9 | 1.70038 | 0.850192 | − | 0.526473i | \(-0.176486\pi\) | ||||
0.850192 | + | 0.526473i | \(0.176486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.14511e9 | 0.406831 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.98374e9 | 1.04538 | 0.522689 | − | 0.852524i | \(-0.324929\pi\) | ||||
0.522689 | + | 0.852524i | \(0.324929\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.04555e9 | 0.361265 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.45766e9 | −0.496741 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.51373e9 | 1.18102 | 0.590509 | − | 0.807031i | \(-0.298927\pi\) | ||||
0.590509 | + | 0.807031i | \(0.298927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.99872e9 | −1.32571 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.52457e8 | −0.0498583 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.51042e9 | 1.13249 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.07481e9 | −0.342069 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.15415e9 | −0.676378 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.74420e7 | −0.00540335 | −0.00270168 | − | 0.999996i | \(-0.500860\pi\) | ||||
−0.00270168 | + | 0.999996i | \(0.500860\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.15669e9 | −0.659222 | −0.329611 | − | 0.944117i | \(-0.606918\pi\) | ||||
−0.329611 | + | 0.944117i | \(0.606918\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.16879e9 | 0.352516 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.44927e9 | −1.62181 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.70434e9 | 0.500565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.49534e8 | 0.275220 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.37635e8 | −0.153795 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.61727e9 | −0.738942 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.91507e7 | −0.0164835 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.41667e9 | −0.664746 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.97673e9 | −1.35131 | −0.675653 | − | 0.737220i | \(-0.736138\pi\) | ||||
−0.675653 | + | 0.737220i | \(0.736138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.44824e9 | 0.388186 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.66252e8 | −0.0969152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.97379e9 | 1.03812 | 0.519062 | − | 0.854737i | \(-0.326281\pi\) | ||||
0.519062 | + | 0.854737i | \(0.326281\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.22990e9 | 0.317226 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.95046e8 | 0.0496715 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.67316e9 | −2.43238 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.37335e9 | −0.589299 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.21200e9 | 0.787558 | 0.393779 | − | 0.919205i | \(-0.371167\pi\) | ||||
0.393779 | + | 0.919205i | \(0.371167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.64419e9 | −0.398118 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.72457e8 | 0.208629 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.69409e9 | −1.81710 | −0.908548 | − | 0.417781i | \(-0.862808\pi\) | ||||
−0.908548 | + | 0.417781i | \(0.862808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.70172e9 | −0.863444 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.11209e8 | −0.186893 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.21967e9 | 1.64295 | 0.821475 | − | 0.570244i | \(-0.193152\pi\) | ||||
0.821475 | + | 0.570244i | \(0.193152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.66999e9 | 1.49934 | 0.749668 | − | 0.661814i | \(-0.230213\pi\) | ||||
0.749668 | + | 0.661814i | \(0.230213\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.96043e9 | 0.657376 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.02707e9 | −0.444664 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.52193e9 | 0.329822 | 0.164911 | − | 0.986308i | \(-0.447266\pi\) | ||||
0.164911 | + | 0.986308i | \(0.447266\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.11611e9 | −0.667172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.28745e10 | 2.72341 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.24004e9 | −0.259176 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.81358e8 | −0.0994083 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.26742e9 | 1.89115 | 0.945574 | − | 0.325408i | \(-0.105502\pi\) | ||||
0.945574 | + | 0.325408i | \(0.105502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.09544e9 | −0.422543 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.82365e9 | 0.961214 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.62133e9 | −0.713142 | −0.356571 | − | 0.934268i | \(-0.616054\pi\) | ||||
−0.356571 | + | 0.934268i | \(0.616054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.85904e9 | 1.33492 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.88075e9 | −0.554109 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.87148e9 | −1.30634 | −0.653170 | − | 0.757211i | \(-0.726561\pi\) | ||||
−0.653170 | + | 0.757211i | \(0.726561\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.37454e9 | −0.822001 | −0.411000 | − | 0.911635i | \(-0.634820\pi\) | ||||
−0.411000 | + | 0.911635i | \(0.634820\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.93311e8 | 0.147344 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.77315e9 | −0.692724 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.79016e9 | 0.324887 | 0.162443 | − | 0.986718i | \(-0.448063\pi\) | ||||
0.162443 | + | 0.986718i | \(0.448063\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.03782e9 | 0.186192 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.98310e9 | −0.351723 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.18426e9 | −1.25971 | −0.629855 | − | 0.776713i | \(-0.716886\pi\) | ||||
−0.629855 | + | 0.776713i | \(0.716886\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.09406e9 | 0.189661 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.00365e9 | −0.686212 | −0.343106 | − | 0.939297i | \(-0.611479\pi\) | ||||
−0.343106 | + | 0.939297i | \(0.611479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.14329e9 | 1.38001 | 0.690006 | − | 0.723804i | \(-0.257608\pi\) | ||||
0.690006 | + | 0.723804i | \(0.257608\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.40691e9 | 0.235747 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.81180e10 | 3.00194 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.08371e9 | −0.505235 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.35491e8 | 0.0543556 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.93693e9 | 1.27167 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.92407e9 | 0.780229 | 0.390114 | − | 0.920766i | \(-0.372435\pi\) | ||||
0.390114 | + | 0.920766i | \(0.372435\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.84450e9 | −0.759165 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.32918e9 | −0.825948 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.45894e9 | −0.683508 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.26760e8 | −0.0950273 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.25248e9 | −0.637734 | −0.318867 | − | 0.947800i | \(-0.603302\pi\) | ||||
−0.318867 | + | 0.947800i | \(0.603302\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.99844e9 | −0.296452 | −0.148226 | − | 0.988954i | \(-0.547356\pi\) | ||||
−0.148226 | + | 0.988954i | \(0.547356\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.34585e9 | 0.490962 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.98078e9 | 0.722990 | 0.361495 | − | 0.932374i | \(-0.382267\pi\) | ||||
0.361495 | + | 0.932374i | \(0.382267\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.08950e9 | −0.300045 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.11496e10 | −1.58389 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.24503e8 | 0.129931 | 0.0649654 | − | 0.997888i | \(-0.479306\pi\) | ||||
0.0649654 | + | 0.997888i | \(0.479306\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.77020e9 | 0.941363 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.90972e9 | 0.262719 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.40009e9 | 1.27948 | 0.639740 | − | 0.768592i | \(-0.279042\pi\) | ||||
0.639740 | + | 0.768592i | \(0.279042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.20065e10 | −1.61700 | −0.808501 | − | 0.588495i | \(-0.799721\pi\) | ||||
−0.808501 | + | 0.588495i | \(0.799721\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.60975e9 | 0.214517 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.63755e9 | 0.347796 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.79993e9 | −0.234863 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.42122e9 | 0.829137 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.70648e9 | −0.345840 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.23701e10 | −1.56431 | −0.782154 | − | 0.623086i | \(-0.785879\pi\) | ||||
−0.782154 | + | 0.623086i | \(0.785879\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.58194e8 | −0.0698590 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.27900e9 | −0.530007 | −0.265004 | − | 0.964247i | \(-0.585373\pi\) | ||||
−0.265004 | + | 0.964247i | \(0.585373\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.18479e9 | −0.758195 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.31841e9 | 0.766643 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.62834e10 | 1.95557 | 0.977786 | − | 0.209607i | \(-0.0672185\pi\) | ||||
0.977786 | + | 0.209607i | \(0.0672185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.58363e9 | 1.02036 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.68591e9 | 0.786705 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.28797e9 | −0.266491 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.32503e10 | 1.52775 | 0.763875 | − | 0.645364i | \(-0.223294\pi\) | ||||
0.763875 | + | 0.645364i | \(0.223294\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.78511e9 | 0.203751 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.27752e10 | 1.44351 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.65875e9 | −0.409277 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.19576e9 | 0.686159 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.06887e9 | 0.446130 | 0.223065 | − | 0.974804i | \(-0.428394\pi\) | ||||
0.223065 | + | 0.974804i | \(0.428394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.05203e9 | 0.331318 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.03552e9 | 0.433748 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.15415e9 | −0.761360 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.59855e10 | 1.68447 | 0.842236 | − | 0.539109i | \(-0.181239\pi\) | ||||
0.842236 | + | 0.539109i | \(0.181239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.61975e9 | 0.482031 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.93372e10 | 1.99793 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.05926e9 | 0.108375 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.97001e8 | −0.0604864 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.52111e9 | −0.453622 | −0.226811 | − | 0.973939i | \(-0.572830\pi\) | ||||
−0.226811 | + | 0.973939i | \(0.572830\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.40199e10 | −2.38670 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.25654e9 | 0.615673 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.14126e8 | 0.0695972 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.67194e10 | −1.61380 | −0.806899 | − | 0.590689i | \(-0.798856\pi\) | ||||
−0.806899 | + | 0.590689i | \(0.798856\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.11892e10 | −1.05947 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.84678e9 | 0.923486 | 0.461743 | − | 0.887014i | \(-0.347224\pi\) | ||||
0.461743 | + | 0.887014i | \(0.347224\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.07372e9 | 0.842907 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.74573e9 | −0.160635 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.02442e9 | 0.366816 | 0.183408 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183408 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.19007e8 | 0.0558897 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.10258e10 | 0.986161 | 0.493080 | − | 0.869984i | \(-0.335871\pi\) | ||||
0.493080 | + | 0.869984i | \(0.335871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.14261e10 | 1.01240 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.14864e9 | −0.539706 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.79086e10 | 1.55731 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.87188e9 | −0.592019 | −0.296010 | − | 0.955185i | \(-0.595656\pi\) | ||||
−0.296010 | + | 0.955185i | \(0.595656\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.68079e8 | 0.0143460 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.63622e8 | 0.0392057 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.04576e10 | 1.71404 | 0.857018 | − | 0.515287i | \(-0.172315\pi\) | ||||
0.857018 | + | 0.515287i | \(0.172315\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.09599e9 | −0.257012 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.23380e10 | −1.83737 | −0.918686 | − | 0.394989i | \(-0.870748\pi\) | ||||
−0.918686 | + | 0.394989i | \(0.870748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.50606e9 | 0.204247 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.27577e9 | −0.264544 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.85530e9 | −0.308514 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.68174e9 | −0.371249 | −0.185624 | − | 0.982621i | \(-0.559431\pi\) | ||||
−0.185624 | + | 0.982621i | \(0.559431\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.47872e9 | 0.430515 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.45602e9 | −0.424862 | −0.212431 | − | 0.977176i | \(-0.568138\pi\) | ||||
−0.212431 | + | 0.977176i | \(0.568138\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.67206e9 | −0.592047 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.62395e10 | 1.24194 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.40692e9 | −0.106632 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.37922e9 | 0.103599 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.95646e8 | −0.0368983 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.67185e10 | 1.23354 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.83754e9 | 0.353763 | 0.176882 | − | 0.984232i | \(-0.443399\pi\) | ||||
0.176882 | + | 0.984232i | \(0.443399\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.40723e9 | 0.174481 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.53289e10 | 1.81969 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.99366e9 | −0.355601 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.65590e9 | 0.328639 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.10631e10 | 1.47373 | 0.736865 | − | 0.676040i | \(-0.236305\pi\) | ||||
0.736865 | + | 0.676040i | \(0.236305\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.34955e10 | −0.936001 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.65286e9 | −0.594902 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.20246e9 | −0.286417 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.43399e10 | −1.64449 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.90764e9 | 0.596630 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.32648e10 | 0.880810 | 0.440405 | − | 0.897799i | \(-0.354835\pi\) | ||||
0.440405 | + | 0.897799i | \(0.354835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.24665e10 | −0.820676 | −0.410338 | − | 0.911933i | \(-0.634589\pi\) | ||||
−0.410338 | + | 0.911933i | \(0.634589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.79220e9 | 0.443296 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.19594e9 | −0.336212 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.30263e9 | −0.276031 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.29367e9 | 0.209501 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.83660e10 | −1.15828 | −0.579141 | − | 0.815228i | \(-0.696612\pi\) | ||||
−0.579141 | + | 0.815228i | \(0.696612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.65247e9 | −0.290927 | −0.145463 | − | 0.989364i | \(-0.546467\pi\) | ||||
−0.145463 | + | 0.989364i | \(0.546467\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.22834e9 | 0.0761605 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.62501e9 | −0.407302 | −0.203651 | − | 0.979044i | \(-0.565281\pi\) | ||||
−0.203651 | + | 0.979044i | \(0.565281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.24995e9 | −0.381009 | −0.190505 | − | 0.981686i | \(-0.561012\pi\) | ||||
−0.190505 | + | 0.981686i | \(0.561012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.63297e9 | −0.521863 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.03442e10 | −1.81894 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.46124e9 | 0.562400 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.32487e9 | 0.313885 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.30459e10 | 1.34719 | 0.673593 | − | 0.739103i | \(-0.264750\pi\) | ||||
0.673593 | + | 0.739103i | \(0.264750\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.66158e10 | −0.963240 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.56527e10 | −0.899897 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.20437e10 | −0.686690 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.58176e10 | 1.45990 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.12905e9 | 0.231565 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.81648e10 | −1.56658 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.01575e10 | −1.66369 | −0.831847 | − | 0.555006i | \(-0.812716\pi\) | ||||
−0.831847 | + | 0.555006i | \(0.812716\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.25965e9 | −0.0689237 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.33465e10 | −0.724329 | −0.362165 | − | 0.932114i | \(-0.617962\pi\) | ||||
−0.362165 | + | 0.932114i | \(0.617962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.93560e10 | 1.04193 | 0.520965 | − | 0.853578i | \(-0.325572\pi\) | ||||
0.520965 | + | 0.853578i | \(0.325572\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.48607e9 | −0.399708 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.05481e9 | −0.161788 | −0.0808940 | − | 0.996723i | \(-0.525778\pi\) | ||||
−0.0808940 | + | 0.996723i | \(0.525778\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.77982e10 | −0.935019 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.24359e8 | −0.00648055 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.01660e10 | −0.525511 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.22100e9 | −0.165169 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.95376e9 | 0.150254 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.62601e10 | 1.82979 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.65091e10 | 0.826465 | 0.413233 | − | 0.910626i | \(-0.364400\pi\) | ||||
0.413233 | + | 0.910626i | \(0.364400\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.70939e9 | 0.0848947 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.79401e9 | 0.285472 | 0.142736 | − | 0.989761i | \(-0.454410\pi\) | ||||
0.142736 | + | 0.989761i | \(0.454410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.02986e10 | −0.992209 | −0.496104 | − | 0.868263i | \(-0.665237\pi\) | ||||
−0.496104 | + | 0.868263i | \(0.665237\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.84534e9 | 0.380461 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.71123e10 | −0.823334 | −0.411667 | − | 0.911334i | \(-0.635053\pi\) | ||||
−0.411667 | + | 0.911334i | \(0.635053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.64647e10 | 1.74067 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.52541e8 | −0.0403779 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.18952e9 | −0.243863 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.88722e8 | −0.0227867 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.71234e9 | −0.264265 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.81238e9 | −0.312709 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.55702e10 | −0.709182 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.28939e10 | −1.03469 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.19658e10 | 0.536625 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.34285e9 | 0.282266 | 0.141133 | − | 0.989991i | \(-0.454925\pi\) | ||||
0.141133 | + | 0.989991i | \(0.454925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.41671e9 | 0.150881 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.93974e10 | −0.850018 | −0.425009 | − | 0.905189i | \(-0.639729\pi\) | ||||
−0.425009 | + | 0.905189i | \(0.639729\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.35305e10 | 0.588389 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.01619e10 | 0.438530 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.63249e10 | −1.98391 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.42437e10 | −1.03038 | −0.515188 | − | 0.857077i | \(-0.672278\pi\) | ||||
−0.515188 | + | 0.857077i | \(0.672278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.14050e9 | 0.174640 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.54477e9 | 0.106523 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.11745e10 | 0.464227 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.14715e10 | 0.472979 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.27725e10 | 0.931872 | 0.465936 | − | 0.884818i | \(-0.345718\pi\) | ||||
0.465936 | + | 0.884818i | \(0.345718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.16684e10 | −0.473903 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.84288e9 | −0.275837 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.20852e9 | 0.288407 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.68538e10 | 1.06639 | 0.533196 | − | 0.845992i | \(-0.320991\pi\) | ||||
0.533196 | + | 0.845992i | \(0.320991\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.17333e10 | −0.462477 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.92886e10 | 1.53710 | 0.768552 | − | 0.639788i | \(-0.220978\pi\) | ||||
0.768552 | + | 0.639788i | \(0.220978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.29834e10 | 0.504193 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.70246e9 | −0.258359 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.61412e9 | −0.367862 | −0.183931 | − | 0.982939i | \(-0.558882\pi\) | ||||
−0.183931 | + | 0.982939i | \(0.558882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.75387e9 | −0.294501 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.45751e10 | −0.549516 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.03874e9 | 0.226007 | 0.113003 | − | 0.993595i | \(-0.463953\pi\) | ||||
0.113003 | + | 0.993595i | \(0.463953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.44600e10 | 0.908751 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.09070e9 | 0.0402266 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.87332e10 | −2.15040 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.56747e10 | 1.66014 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.55285e9 | −0.308616 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.57463e10 | −0.922293 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.51151e9 | 0.0893187 | 0.0446593 | − | 0.999002i | \(-0.485780\pi\) | ||||
0.0446593 | + | 0.999002i | \(0.485780\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.21251e9 | 0.148733 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.52174e9 | 0.298718 | 0.149359 | − | 0.988783i | \(-0.452279\pi\) | ||||
0.149359 | + | 0.988783i | \(0.452279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.74136e10 | −3.04217 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.26638e9 | 0.0783100 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.00947e10 | −0.346307 | −0.173153 | − | 0.984895i | \(-0.555396\pi\) | ||||
−0.173153 | + | 0.984895i | \(0.555396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.90411e10 | 0.648564 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.19686e9 | −0.0404762 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.91948e10 | −0.980322 | −0.490161 | − | 0.871632i | \(-0.663062\pi\) | ||||
−0.490161 | + | 0.871632i | \(0.663062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.98545e10 | 1.32877 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.76129e10 | −0.914117 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.97057e10 | 1.30516 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.49553e10 | −0.488132 | −0.244066 | − | 0.969759i | \(-0.578481\pi\) | ||||
−0.244066 | + | 0.969759i | \(0.578481\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.56240e9 | −0.0506372 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.38017e10 | −0.765996 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.03923e9 | 0.161039 | 0.0805196 | − | 0.996753i | \(-0.474342\pi\) | ||||
0.0805196 | + | 0.996753i | \(0.474342\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.75575e9 | −0.246119 |
(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.l.1.2 | yes | 3 | |
4.3 | odd | 2 | 384.8.a.j.1.2 | yes | 3 | ||
8.3 | odd | 2 | 384.8.a.k.1.2 | yes | 3 | ||
8.5 | even | 2 | 384.8.a.i.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.a.i.1.2 | ✓ | 3 | 8.5 | even | 2 | ||
384.8.a.j.1.2 | yes | 3 | 4.3 | odd | 2 | ||
384.8.a.k.1.2 | yes | 3 | 8.3 | odd | 2 | ||
384.8.a.l.1.2 | yes | 3 | 1.1 | even | 1 | trivial |