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: | \(1\) |
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 | \(-0.630664\pi\) | ||||
−0.399062 | + | 0.916924i | \(0.630664\pi\) | |||||||
\(6\) | 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 | \(-0.441840\pi\) | ||||
0.181700 | + | 0.983354i | \(0.441840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2959.89 | 0.373657 | 0.186829 | − | 0.982393i | \(-0.440179\pi\) | ||||
0.186829 | + | 0.982393i | \(0.440179\pi\) | |||||||
\(14\) | 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 | \(-0.458651\pi\) | ||||
0.129536 | + | 0.991575i | \(0.458651\pi\) | |||||||
\(20\) | 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 | \(-0.469438\pi\) | ||||
0.0958645 | + | 0.995394i | \(0.469438\pi\) | |||||||
\(30\) | 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 | \(-0.279168\pi\) | ||||
0.639435 | + | 0.768845i | \(0.279168\pi\) | |||||||
\(38\) | 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 | \(-0.678834\pi\) | ||||
−0.532731 | + | 0.846285i | \(0.678834\pi\) | |||||||
\(44\) | 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 | \(-0.616063\pi\) | ||||
−0.356598 | + | 0.934258i | \(0.616063\pi\) | |||||||
\(54\) | 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 | \(-0.635459\pi\) | ||||
−0.412830 | + | 0.910808i | \(0.635459\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.68711e6 | −0.951677 | −0.475838 | − | 0.879533i | \(-0.657855\pi\) | ||||
−0.475838 | + | 0.879533i | \(0.657855\pi\) | |||||||
\(62\) | 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 | \(-0.570937\pi\) | ||||
−0.221016 | + | 0.975270i | \(0.570937\pi\) | |||||||
\(68\) | 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 | \(-0.199706\pi\) | ||||
0.809559 | + | 0.587038i | \(0.199706\pi\) | |||||||
\(84\) | 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 | \(-0.572670\pi\) | ||||
−0.226321 | + | 0.974053i | \(0.572670\pi\) | |||||||
\(102\) | 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 | \(-0.346800\pi\) | ||||
0.462924 | + | 0.886398i | \(0.346800\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.64178e6 | 0.121429 | 0.0607144 | − | 0.998155i | \(-0.480662\pi\) | ||||
0.0607144 | + | 0.998155i | \(0.480662\pi\) | |||||||
\(110\) | 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 | \(-0.700768\pi\) | ||||
−0.589735 | + | 0.807597i | \(0.700768\pi\) | |||||||
\(132\) | 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 | \(-0.859617\pi\) | ||||
−0.904315 | + | 0.426867i | \(0.859617\pi\) | |||||||
\(140\) | 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 | \(-0.718686\pi\) | ||||
−0.634237 | + | 0.773139i | \(0.718686\pi\) | |||||||
\(150\) | 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 | \(-0.781133\pi\) | ||||
−0.772777 | + | 0.634678i | \(0.781133\pi\) | |||||||
\(158\) | 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 | \(-0.432450\pi\) | ||||
0.210626 | + | 0.977567i | \(0.432450\pi\) | |||||||
\(164\) | 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 | \(-0.300796\pi\) | ||||
0.585760 | + | 0.810484i | \(0.300796\pi\) | |||||||
\(174\) | 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 | \(-0.495456\pi\) | ||||
0.0142751 | + | 0.999898i | \(0.495456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.36384e7 | −0.672358 | −0.336179 | − | 0.941798i | \(-0.609135\pi\) | ||||
−0.336179 | + | 0.941798i | \(0.609135\pi\) | |||||||
\(182\) | 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 | \(-0.813054\pi\) | ||||
−0.832435 | + | 0.554122i | \(0.813054\pi\) | |||||||
\(198\) | 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 | \(-0.271632\pi\) | ||||
0.657456 | + | 0.753493i | \(0.271632\pi\) | |||||||
\(212\) | 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 | \(-0.731114\pi\) | ||||
−0.663932 | + | 0.747793i | \(0.731114\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.47626e8 | −1.36261 | −0.681306 | − | 0.731998i | \(-0.738588\pi\) | ||||
−0.681306 | + | 0.731998i | \(0.738588\pi\) | |||||||
\(230\) | 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 | \(-0.503955\pi\) | ||||
−0.0124240 | + | 0.999923i | \(0.503955\pi\) | |||||||
\(252\) | 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 | \(-0.672839\pi\) | ||||
−0.516697 | + | 0.856168i | \(0.672839\pi\) | |||||||
\(270\) | 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 | \(-0.350730\pi\) | ||||
0.451947 | + | 0.892045i | \(0.350730\pi\) | |||||||
\(278\) | 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 | \(-0.564270\pi\) | ||||
−0.200541 | + | 0.979685i | \(0.564270\pi\) | |||||||
\(284\) | 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 | \(-0.523424\pi\) | ||||
−0.0735210 | + | 0.997294i | \(0.523424\pi\) | |||||||
\(294\) | 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 | \(-0.548327\pi\) | ||||
−0.151243 | + | 0.988497i | \(0.548327\pi\) | |||||||
\(308\) | 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 | \(-0.342124\pi\) | ||||
0.475895 | + | 0.879502i | \(0.342124\pi\) | |||||||
\(318\) | 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 | \(-0.486037\pi\) | ||||
0.0438531 | + | 0.999038i | \(0.486037\pi\) | |||||||
\(332\) | 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 | \(-0.311065\pi\) | ||||
0.559314 | + | 0.828956i | \(0.311065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.54583e8 | 0.824282 | 0.412141 | − | 0.911120i | \(-0.364781\pi\) | ||||
0.412141 | + | 0.911120i | \(0.364781\pi\) | |||||||
\(350\) | 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 | \(-0.572449\pi\) | ||||
−0.225645 | + | 0.974210i | \(0.572449\pi\) | |||||||
\(374\) | 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 | \(-0.782554\pi\) | ||||
−0.775603 | + | 0.631221i | \(0.782554\pi\) | |||||||
\(380\) | 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 | \(-0.623235\pi\) | ||||
−0.377555 | + | 0.925987i | \(0.623235\pi\) | |||||||
\(390\) | 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 | \(-0.213512\pi\) | ||||
0.783344 | + | 0.621588i | \(0.213512\pi\) | |||||||
\(398\) | 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 | \(-0.311765\pi\) | ||||
0.557488 | + | 0.830185i | \(0.311765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.42077e9 | −0.927976 | −0.463988 | − | 0.885842i | \(-0.653582\pi\) | ||||
−0.463988 | + | 0.885842i | \(0.653582\pi\) | |||||||
\(422\) | 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 | \(-0.274964\pi\) | ||||
0.649534 | + | 0.760333i | \(0.274964\pi\) | |||||||
\(444\) | 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 | \(-0.0991339\pi\) | ||||
0.951894 | + | 0.306428i | \(0.0991339\pi\) | |||||||
\(462\) | 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 | \(-0.216227\pi\) | ||||
0.778014 | + | 0.628247i | \(0.216227\pi\) | |||||||
\(468\) | 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 | \(-0.506348\pi\) | ||||
−0.0199416 | + | 0.999801i | \(0.506348\pi\) | |||||||
\(492\) | 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 | \(-0.823514\pi\) | ||||
−0.850192 | + | 0.526473i | \(0.823514\pi\) | |||||||
\(500\) | 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 | \(-0.701073\pi\) | ||||
−0.590509 | + | 0.807031i | \(0.701073\pi\) | |||||||
\(510\) | 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 | \(-0.393082\pi\) | ||||
0.329611 | + | 0.944117i | \(0.393082\pi\) | |||||||
\(524\) | 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 | \(-0.263862\pi\) | ||||
0.675653 | + | 0.737220i | \(0.263862\pi\) | |||||||
\(542\) | 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 | \(-0.673719\pi\) | ||||
−0.519062 | + | 0.854737i | \(0.673719\pi\) | |||||||
\(548\) | 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 | \(-0.628833\pi\) | ||||
−0.393779 | + | 0.919205i | \(0.628833\pi\) | |||||||
\(558\) | 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 | \(-0.137192\pi\) | ||||
0.908548 | + | 0.417781i | \(0.137192\pi\) | |||||||
\(564\) | 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 | \(-0.769787\pi\) | ||||
−0.749668 | + | 0.661814i | \(0.769787\pi\) | |||||||
\(572\) | 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 | \(-0.894498\pi\) | ||||
−0.945574 | + | 0.325408i | \(0.894498\pi\) | |||||||
\(588\) | 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 | \(-0.283114\pi\) | ||||
0.629855 | + | 0.776713i | \(0.283114\pi\) | |||||||
\(614\) | 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 | \(-0.742392\pi\) | ||||
−0.690006 | + | 0.723804i | \(0.742392\pi\) | |||||||
\(620\) | 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 | \(-0.452644\pi\) | ||||
0.148226 | + | 0.988954i | \(0.452644\pi\) | |||||||
\(644\) | 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 | \(-0.520694\pi\) | ||||
−0.0649654 | + | 0.997888i | \(0.520694\pi\) | |||||||
\(654\) | 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 | \(-0.720958\pi\) | ||||
−0.639740 | + | 0.768592i | \(0.720958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.20065e10 | 1.61700 | 0.808501 | − | 0.588495i | \(-0.200279\pi\) | ||||
0.808501 | + | 0.588495i | \(0.200279\pi\) | |||||||
\(662\) | 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 | \(-0.414627\pi\) | ||||
0.265004 | + | 0.964247i | \(0.414627\pi\) | |||||||
\(678\) | 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 | \(-0.932782\pi\) | ||||
−0.977786 | + | 0.209607i | \(0.932782\pi\) | |||||||
\(684\) | 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 | \(-0.776706\pi\) | ||||
−0.763875 | + | 0.645364i | \(0.776706\pi\) | |||||||
\(692\) | 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 | \(-0.571606\pi\) | ||||
−0.223065 | + | 0.974804i | \(0.571606\pi\) | |||||||
\(702\) | 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 | \(-0.818761\pi\) | ||||
−0.842236 | + | 0.539109i | \(0.818761\pi\) | |||||||
\(710\) | 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 | \(-0.652776\pi\) | ||||
−0.461743 | + | 0.887014i | \(0.652776\pi\) | |||||||
\(734\) | 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 | \(-0.558713\pi\) | ||||
−0.183408 | + | 0.983037i | \(0.558713\pi\) | |||||||
\(740\) | 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 | \(-0.827685\pi\) | ||||
−0.857018 | + | 0.515287i | \(0.827685\pi\) | |||||||
\(758\) | 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 | \(-0.431862\pi\) | ||||
0.212431 | + | 0.977176i | \(0.431862\pi\) | |||||||
\(774\) | 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 | \(-0.556601\pi\) | ||||
−0.176882 | + | 0.984232i | \(0.556601\pi\) | |||||||
\(788\) | 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 | \(-0.763695\pi\) | ||||
−0.736865 | + | 0.676040i | \(0.763695\pi\) | |||||||
\(798\) | 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 | \(-0.365411\pi\) | ||||
0.410338 | + | 0.911933i | \(0.365411\pi\) | |||||||
\(812\) | 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 | \(-0.303388\pi\) | ||||
0.579141 | + | 0.815228i | \(0.303388\pi\) | |||||||
\(822\) | 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 | \(-0.434719\pi\) | ||||
0.203651 | + | 0.979044i | \(0.434719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.24995e9 | 0.381009 | 0.190505 | − | 0.981686i | \(-0.438988\pi\) | ||||
0.190505 | + | 0.981686i | \(0.438988\pi\) | |||||||
\(830\) | 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 | \(-0.187284\pi\) | ||||
0.831847 | + | 0.555006i | \(0.187284\pi\) | |||||||
\(854\) | 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 | \(-0.674428\pi\) | ||||
−0.520965 | + | 0.853578i | \(0.674428\pi\) | |||||||
\(860\) | 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 | \(-0.635600\pi\) | ||||
−0.413233 | + | 0.910626i | \(0.635600\pi\) | |||||||
\(878\) | 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 | \(-0.334763\pi\) | ||||
0.496104 | + | 0.868263i | \(0.334763\pi\) | |||||||
\(884\) | 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 | \(-0.545075\pi\) | ||||
−0.141133 | + | 0.989991i | \(0.545075\pi\) | |||||||
\(908\) | 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 | \(-0.779022\pi\) | ||||
−0.768552 | + | 0.639788i | \(0.779022\pi\) | |||||||
\(942\) | 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 | \(-0.441118\pi\) | ||||
0.183931 | + | 0.982939i | \(0.441118\pi\) | |||||||
\(948\) | 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 | \(-0.547721\pi\) | ||||
−0.149359 | + | 0.988783i | \(0.547721\pi\) | |||||||
\(972\) | 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 | \(-0.525658\pi\) | ||||
−0.0805196 | + | 0.996753i | \(0.525658\pi\) | |||||||
\(998\) | 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.i.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 384.8.a.k.1.2 | yes | 3 | ||
8.3 | odd | 2 | 384.8.a.j.1.2 | yes | 3 | ||
8.5 | even | 2 | 384.8.a.l.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.a.i.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
384.8.a.j.1.2 | yes | 3 | 8.3 | odd | 2 | ||
384.8.a.k.1.2 | yes | 3 | 4.3 | odd | 2 | ||
384.8.a.l.1.2 | yes | 3 | 8.5 | even | 2 |