Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(197.773761087\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2070x^{2} - 13768x + 561570 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(45.8607\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −250.262 | −0.179073 | −0.0895366 | − | 0.995984i | \(-0.528539\pi\) | ||||
−0.0895366 | + | 0.995984i | \(0.528539\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1655.62 | −0.260627 | −0.130313 | − | 0.991473i | \(-0.541598\pi\) | ||||
−0.130313 | + | 0.991473i | \(0.541598\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −848.983 | −0.0174837 | −0.00874183 | − | 0.999962i | \(-0.502783\pi\) | ||||
−0.00874183 | + | 0.999962i | \(0.502783\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −69683.7 | −0.676684 | −0.338342 | − | 0.941023i | \(-0.609866\pi\) | ||||
−0.338342 | + | 0.941023i | \(0.609866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −20271.3 | −0.103388 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 282069. | 0.819098 | 0.409549 | − | 0.912288i | \(-0.365686\pi\) | ||||
0.409549 | + | 0.912288i | \(0.365686\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −470922. | −0.829006 | −0.414503 | − | 0.910048i | \(-0.636045\pi\) | ||||
−0.414503 | + | 0.910048i | \(0.636045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −134105. | −0.150473 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.41851e6 | 1.80207 | 0.901036 | − | 0.433745i | \(-0.142808\pi\) | ||||
0.901036 | + | 0.433745i | \(0.142808\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.89049e6 | −0.967933 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.90059e6 | 1.02409 | 0.512047 | − | 0.858958i | \(-0.328888\pi\) | ||||
0.512047 | + | 0.858958i | \(0.328888\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.99099e6 | −0.776164 | −0.388082 | − | 0.921625i | \(-0.626862\pi\) | ||||
−0.388082 | + | 0.921625i | \(0.626862\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −68767.7 | −0.0100942 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 414339. | 0.0466713 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.47494e6 | −0.480254 | −0.240127 | − | 0.970741i | \(-0.577189\pi\) | ||||
−0.240127 | + | 0.970741i | \(0.577189\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.64438e6 | −0.390684 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.25933e7 | 0.696004 | 0.348002 | − | 0.937494i | \(-0.386860\pi\) | ||||
0.348002 | + | 0.937494i | \(0.386860\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.12591e7 | −0.502222 | −0.251111 | − | 0.967958i | \(-0.580796\pi\) | ||||
−0.251111 | + | 0.967958i | \(0.580796\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.64197e6 | −0.0596911 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.89424e7 | 0.865155 | 0.432578 | − | 0.901597i | \(-0.357604\pi\) | ||||
0.432578 | + | 0.901597i | \(0.357604\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.76125e7 | −0.932074 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.28476e7 | 0.472907 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.61718e6 | 0.167420 | 0.0837098 | − | 0.996490i | \(-0.473323\pi\) | ||||
0.0837098 | + | 0.996490i | \(0.473323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 212469. | 0.00313085 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.81447e7 | −0.478627 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.53642e7 | 0.165073 | 0.0825364 | − | 0.996588i | \(-0.473698\pi\) | ||||
0.0825364 | + | 0.996588i | \(0.473698\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.89328e7 | 0.267551 | 0.133776 | − | 0.991012i | \(-0.457290\pi\) | ||||
0.133776 | + | 0.991012i | \(0.457290\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.08625e7 | −0.0868756 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.74392e7 | 0.121176 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.43864e8 | −0.872200 | −0.436100 | − | 0.899898i | \(-0.643641\pi\) | ||||
−0.436100 | + | 0.899898i | \(0.643641\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.95899e8 | 1.04043 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.80186e8 | −0.841506 | −0.420753 | − | 0.907175i | \(-0.638234\pi\) | ||||
−0.420753 | + | 0.907175i | \(0.638234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.57115e8 | 1.05968 | 0.529839 | − | 0.848098i | \(-0.322252\pi\) | ||||
0.529839 | + | 0.848098i | \(0.322252\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.53130e8 | −0.558836 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.40559e6 | 0.00455671 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.36452e8 | −0.394148 | −0.197074 | − | 0.980389i | \(-0.563144\pi\) | ||||
−0.197074 | + | 0.980389i | \(0.563144\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.41915e7 | −0.0559514 | −0.0279757 | − | 0.999609i | \(-0.508906\pi\) | ||||
−0.0279757 | + | 0.999609i | \(0.508906\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.05914e7 | −0.146679 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.15948e8 | 0.591260 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.66242e8 | −1.46347 | −0.731735 | − | 0.681589i | \(-0.761289\pi\) | ||||
−0.731735 | + | 0.681589i | \(0.761289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.15370e8 | 0.176362 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.23271e8 | −0.448118 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.17854e8 | 0.148453 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.24828e8 | −0.716618 | −0.358309 | − | 0.933603i | \(-0.616647\pi\) | ||||
−0.358309 | + | 0.933603i | \(0.616647\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.57018e6 | −0.00582788 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.63587e8 | 0.443288 | 0.221644 | − | 0.975128i | \(-0.428858\pi\) | ||||
0.221644 | + | 0.975128i | \(0.428858\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.18683e9 | −1.03901 | −0.519507 | − | 0.854466i | \(-0.673884\pi\) | ||||
−0.519507 | + | 0.854466i | \(0.673884\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.35615e7 | 0.0269457 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.61716e9 | −1.19269 | −0.596343 | − | 0.802730i | \(-0.703380\pi\) | ||||
−0.596343 | + | 0.802730i | \(0.703380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.78924e8 | 0.189264 | 0.0946318 | − | 0.995512i | \(-0.469833\pi\) | ||||
0.0946318 | + | 0.995512i | \(0.469833\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.43470e8 | −0.277275 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.83311e8 | 0.451940 | 0.225970 | − | 0.974134i | \(-0.427445\pi\) | ||||
0.225970 | + | 0.974134i | \(0.427445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.05261e8 | −0.322703 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.57195e8 | −0.225561 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.66999e8 | −0.213479 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.35723e9 | −0.999694 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.02006e9 | 0.401838 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.61913e8 | 0.352404 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.05194e9 | 0.699919 | 0.349960 | − | 0.936765i | \(-0.386195\pi\) | ||||
0.349960 | + | 0.936765i | \(0.386195\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.11988e8 | −0.289958 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.10603e9 | −0.328131 | −0.164065 | − | 0.986449i | \(-0.552461\pi\) | ||||
−0.164065 | + | 0.986449i | \(0.552461\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.79667e8 | 0.216061 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.33000e8 | −0.0344627 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.04415e9 | 0.253233 | 0.126617 | − | 0.991952i | \(-0.459588\pi\) | ||||
0.126617 | + | 0.991952i | \(0.459588\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.93771e9 | 0.667487 | 0.333743 | − | 0.942664i | \(-0.391688\pi\) | ||||
0.333743 | + | 0.942664i | \(0.391688\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.34433e9 | 0.499498 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.91603e7 | 0.0118309 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.76171e8 | −0.183388 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.04662e9 | −0.538133 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.75086e9 | −0.623437 | −0.311719 | − | 0.950174i | \(-0.600905\pi\) | ||||
−0.311719 | + | 0.950174i | \(0.600905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.48184e9 | 0.388487 | 0.194244 | − | 0.980953i | \(-0.437775\pi\) | ||||
0.194244 | + | 0.980953i | \(0.437775\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.85066e9 | 0.273033 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.98796e8 | 0.138990 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.65770e9 | −0.743175 | −0.371588 | − | 0.928398i | \(-0.621186\pi\) | ||||
−0.371588 | + | 0.928398i | \(0.621186\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.78991e8 | 0.0966597 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00412e9 | −0.469668 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.28827e9 | −0.697729 | −0.348865 | − | 0.937173i | \(-0.613433\pi\) | ||||
−0.348865 | + | 0.937173i | \(0.613433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.72100e7 | 0.00180760 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.43509e9 | −0.142776 | −0.0713882 | − | 0.997449i | \(-0.522743\pi\) | ||||
−0.0713882 | + | 0.997449i | \(0.522743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.74868e9 | −0.542098 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.08972e9 | −0.276335 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.06084e10 | −0.900416 | −0.450208 | − | 0.892924i | \(-0.648650\pi\) | ||||
−0.450208 | + | 0.892924i | \(0.648650\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.12994e9 | 0.252269 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.24450e9 | 0.0953048 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.84540e8 | 0.0279964 | 0.0139982 | − | 0.999902i | \(-0.495544\pi\) | ||||
0.0139982 | + | 0.999902i | \(0.495544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.54919e9 | −0.245797 | −0.122898 | − | 0.992419i | \(-0.539219\pi\) | ||||
−0.122898 | + | 0.992419i | \(0.539219\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.34356e9 | 0.154471 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.37017e9 | 0.0860007 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.39472e8 | −0.0143208 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.79863e8 | −0.0501576 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.80130e10 | 1.52304 | 0.761518 | − | 0.648144i | \(-0.224455\pi\) | ||||
0.761518 | + | 0.648144i | \(0.224455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.01773e10 | 0.527986 | 0.263993 | − | 0.964525i | \(-0.414960\pi\) | ||||
0.263993 | + | 0.964525i | \(0.414960\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.41258e9 | 0.0699610 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.40263e9 | −0.350177 | −0.175089 | − | 0.984553i | \(-0.556021\pi\) | ||||
−0.175089 | + | 0.984553i | \(0.556021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.14131e10 | 0.515899 | 0.257950 | − | 0.966158i | \(-0.416953\pi\) | ||||
0.257950 | + | 0.966158i | \(0.416953\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.16530e10 | −0.503565 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.45789e9 | −0.266906 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.15162e9 | −0.124636 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.58678e10 | 0.600690 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.99805e8 | 0.0144941 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.50794e10 | −0.523735 | −0.261868 | − | 0.965104i | \(-0.584338\pi\) | ||||
−0.261868 | + | 0.965104i | \(0.584338\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.45950e10 | −0.485844 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.81773e9 | 0.0899345 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.60756e9 | 0.202289 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.08263e10 | 0.611806 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.96556e10 | −0.554271 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.05027e10 | 0.284399 | 0.142200 | − | 0.989838i | \(-0.454583\pi\) | ||||
0.142200 | + | 0.989838i | \(0.454583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.24035e10 | −0.322644 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.86346e10 | −1.71564 | −0.857821 | − | 0.513948i | \(-0.828182\pi\) | ||||
−0.857821 | + | 0.513948i | \(0.828182\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.87491e10 | −1.41170 | −0.705848 | − | 0.708363i | \(-0.749434\pi\) | ||||
−0.705848 | + | 0.708363i | \(0.749434\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.13853e8 | 0.00263082 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.66986e10 | −0.815734 | −0.407867 | − | 0.913041i | \(-0.633727\pi\) | ||||
−0.407867 | + | 0.913041i | \(0.633727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.24319e9 | −0.154926 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.10526e10 | −0.227561 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.46017e10 | 0.487724 | 0.243862 | − | 0.969810i | \(-0.421586\pi\) | ||||
0.243862 | + | 0.969810i | \(0.421586\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.56409e10 | −1.44438 | −0.722188 | − | 0.691697i | \(-0.756863\pi\) | ||||
−0.722188 | + | 0.691697i | \(0.756863\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.41301e9 | 0.166909 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.28156e10 | 0.560975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.95951e9 | −0.0323036 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.92636e10 | 0.465367 | 0.232683 | − | 0.972553i | \(-0.425249\pi\) | ||||
0.232683 | + | 0.972553i | \(0.425249\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.05327e9 | −0.0315068 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.71790e9 | −0.0846849 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.61646e10 | −0.374123 | −0.187062 | − | 0.982348i | \(-0.559896\pi\) | ||||
−0.187062 | + | 0.982348i | \(0.559896\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.06440e9 | 0.125167 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.55918e10 | 0.341364 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.64847e9 | 0.0599114 | 0.0299557 | − | 0.999551i | \(-0.490463\pi\) | ||||
0.0299557 | + | 0.999551i | \(0.490463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.40682e9 | −0.0299804 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.01656e10 | −0.844935 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.15725e10 | −0.600527 | −0.300264 | − | 0.953856i | \(-0.597075\pi\) | ||||
−0.300264 | + | 0.953856i | \(0.597075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.43382e11 | 1.61485 | 0.807424 | − | 0.589971i | \(-0.200861\pi\) | ||||
0.807424 | + | 0.589971i | \(0.200861\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.34494e9 | 0.101823 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.60500e9 | 0.0169230 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.25340e10 | −0.740257 | −0.370128 | − | 0.928981i | \(-0.620686\pi\) | ||||
−0.370128 | + | 0.928981i | \(0.620686\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.61849e10 | −0.258721 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.62285e11 | −1.55275 | −0.776374 | − | 0.630272i | \(-0.782943\pi\) | ||||
−0.776374 | + | 0.630272i | \(0.782943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.79317e11 | −1.66182 | −0.830908 | − | 0.556410i | \(-0.812178\pi\) | ||||
−0.830908 | + | 0.556410i | \(0.812178\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.54618e9 | 0.0857093 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.08497e10 | −0.181397 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.90247e10 | −0.329078 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.06111e10 | −0.413740 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.30277e11 | −1.82535 | −0.912676 | − | 0.408684i | \(-0.865988\pi\) | ||||
−0.912676 | + | 0.408684i | \(0.865988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.84508e9 | −0.0295601 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.51185e8 | −0.00336473 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.68530e11 | −1.21943 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.86408e10 | 0.130893 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.75506e10 | 0.255932 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.24081e9 | −0.0479113 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.81856e11 | −1.81094 | −0.905471 | − | 0.424409i | \(-0.860482\pi\) | ||||
−0.905471 | + | 0.424409i | \(0.860482\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.61333e10 | −0.599875 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.33240e11 | 1.41378 | 0.706889 | − | 0.707325i | \(-0.250098\pi\) | ||||
0.706889 | + | 0.707325i | \(0.250098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.29142e11 | −1.93836 | −0.969179 | − | 0.246360i | \(-0.920766\pi\) | ||||
−0.969179 | + | 0.246360i | \(0.920766\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.71848e9 | 0.0155571 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.06182e10 | 0.504021 | 0.252011 | − | 0.967724i | \(-0.418908\pi\) | ||||
0.252011 | + | 0.967724i | \(0.418908\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.31154e9 | −0.0179049 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.30990e11 | −0.688597 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.32833e11 | −0.679037 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.31737e11 | 0.654985 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.25929e10 | 0.109271 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.79175e10 | −0.225483 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.07245e11 | 1.40689 | 0.703443 | − | 0.710752i | \(-0.251645\pi\) | ||||
0.703443 | + | 0.710752i | \(0.251645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.59211e10 | −0.160085 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.60038e10 | 0.156188 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.39132e11 | 0.587615 | 0.293807 | − | 0.955865i | \(-0.405078\pi\) | ||||
0.293807 | + | 0.955865i | \(0.405078\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.34482e10 | 0.260928 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.38829e9 | 0.0135702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.29082e11 | 0.503550 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.90262e10 | −0.186313 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.79900e11 | −1.03638 | −0.518192 | − | 0.855264i | \(-0.673395\pi\) | ||||
−0.518192 | + | 0.855264i | \(0.673395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.32395e11 | −1.56015 | −0.780075 | − | 0.625686i | \(-0.784819\pi\) | ||||
−0.780075 | + | 0.625686i | \(0.784819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.70328e10 | −0.130228 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.11287e11 | −0.381467 | −0.190734 | − | 0.981642i | \(-0.561087\pi\) | ||||
−0.190734 | + | 0.981642i | \(0.561087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.50937e10 | 0.150691 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.78269e10 | −0.123252 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.49311e10 | 0.0474423 | 0.0237212 | − | 0.999719i | \(-0.492449\pi\) | ||||
0.0237212 | + | 0.999719i | \(0.492449\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00920e11 | −0.312749 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.90935e11 | −0.577174 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.43462e10 | −0.189760 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.39582e10 | −0.270357 | −0.135178 | − | 0.990821i | \(-0.543161\pi\) | ||||
−0.135178 | + | 0.990821i | \(0.543161\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.26245e10 | 0.232001 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.59224e10 | −0.0436340 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00502e11 | −1.60629 | −0.803146 | − | 0.595783i | \(-0.796842\pi\) | ||||
−0.803146 | + | 0.595783i | \(0.796842\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.79150e10 | 0.203461 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.71808e11 | −0.692988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.20120e11 | −1.29487 | −0.647437 | − | 0.762119i | \(-0.724159\pi\) | ||||
−0.647437 | + | 0.762119i | \(0.724159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.66207e11 | 0.404099 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.99135e11 | 1.18529 | 0.592643 | − | 0.805465i | \(-0.298084\pi\) | ||||
0.592643 | + | 0.805465i | \(0.298084\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.51767e8 | −0.000815984 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.38710e10 | −0.167407 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.73874e11 | 0.385001 | 0.192500 | − | 0.981297i | \(-0.438340\pi\) | ||||
0.192500 | + | 0.981297i | \(0.438340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.82187e11 | 1.47607 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.95886e10 | −0.189446 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.41489e10 | 0.0705813 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.03254e11 | 0.814745 | 0.407373 | − | 0.913262i | \(-0.366445\pi\) | ||||
0.407373 | + | 0.913262i | \(0.366445\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.31530e10 | 0.124743 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.41251e11 | −0.659059 | −0.329529 | − | 0.944145i | \(-0.606890\pi\) | ||||
−0.329529 | + | 0.944145i | \(0.606890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.78107e11 | 0.525218 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.07730e10 | −0.0198970 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.64813e9 | 0.00839660 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.45414e11 | 0.433655 | 0.216828 | − | 0.976210i | \(-0.430429\pi\) | ||||
0.216828 | + | 0.976210i | \(0.430429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.45762e10 | 0.146204 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.54372e10 | −0.0430224 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.05422e9 | 0.0100194 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.37955e11 | 0.385374 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.19132e11 | 0.505833 | 0.252917 | − | 0.967488i | \(-0.418610\pi\) | ||||
0.252917 | + | 0.967488i | \(0.418610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.08208e12 | −1.67877 | −0.839386 | − | 0.543535i | \(-0.817085\pi\) | ||||
−0.839386 | + | 0.543535i | \(0.817085\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.89891e11 | 0.288385 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.33251e11 | −0.792832 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.79017e10 | −0.0697310 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.79199e9 | 0.00683058 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.02827e11 | −0.841482 | −0.420741 | − | 0.907181i | \(-0.638230\pi\) | ||||
−0.420741 | + | 0.907181i | \(0.638230\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.98033e11 | 0.544157 | 0.272078 | − | 0.962275i | \(-0.412289\pi\) | ||||
0.272078 | + | 0.962275i | \(0.412289\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.90699e10 | −0.105879 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.13893e12 | −1.49393 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.67851e11 | 0.215692 | 0.107846 | − | 0.994168i | \(-0.465605\pi\) | ||||
0.107846 | + | 0.994168i | \(0.465605\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46776e11 | −0.310691 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.78026e11 | 0.342980 | 0.171490 | − | 0.985186i | \(-0.445142\pi\) | ||||
0.171490 | + | 0.985186i | \(0.445142\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.16788e11 | 0.262068 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.03820e11 | −0.359942 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.66356e12 | 1.93165 | 0.965826 | − | 0.259191i | \(-0.0834560\pi\) | ||||
0.965826 | + | 0.259191i | \(0.0834560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.06915e10 | −0.0121687 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.01029e11 | 0.224293 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.88727e10 | −0.0315817 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.38333e11 | −0.684580 | −0.342290 | − | 0.939594i | \(-0.611203\pi\) | ||||
−0.342290 | + | 0.939594i | \(0.611203\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.49903e11 | 0.157636 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.76291e11 | 0.284913 | 0.142456 | − | 0.989801i | \(-0.454500\pi\) | ||||
0.142456 | + | 0.989801i | \(0.454500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.55833e11 | 0.157596 | 0.0787980 | − | 0.996891i | \(-0.474892\pi\) | ||||
0.0787980 | + | 0.996891i | \(0.474892\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.09025e10 | 0.0802460 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.11029e11 | −0.108022 | −0.0540108 | − | 0.998540i | \(-0.517201\pi\) | ||||
−0.0540108 | + | 0.998540i | \(0.517201\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.38184e11 | 0.227319 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.58273e11 | −0.429072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.55879e9 | 0.00878068 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.90275e11 | 0.802422 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.30983e10 | 0.0558065 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.41651e11 | 0.556915 | 0.278458 | − | 0.960449i | \(-0.410177\pi\) | ||||
0.278458 | + | 0.960449i | \(0.410177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.81514e11 | 0.324981 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.24334e11 | −0.271163 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.56371e11 | 0.128327 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.00844e11 | −0.403480 | −0.201740 | − | 0.979439i | \(-0.564660\pi\) | ||||
−0.201740 | + | 0.979439i | \(0.564660\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.09350e11 | −0.402834 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.02945e12 | −0.799353 | −0.399677 | − | 0.916656i | \(-0.630878\pi\) | ||||
−0.399677 | + | 0.916656i | \(0.630878\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.10024e12 | 0.838833 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.39401e9 | 0.00104362 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.98318e11 | 0.219319 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.93280e12 | 1.39552 | 0.697758 | − | 0.716333i | \(-0.254181\pi\) | ||||
0.697758 | + | 0.716333i | \(0.254181\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.16243e11 | −0.0824320 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.06855e11 | −0.422697 | −0.211348 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211348 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.16019e11 | −0.0793809 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.65643e11 | −0.312981 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.82186e12 | 1.86340 | 0.931698 | − | 0.363235i | \(-0.118328\pi\) | ||||
0.931698 | + | 0.363235i | \(0.118328\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.25684e11 | −0.276181 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.50267e11 | −0.159542 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.97019e11 | 0.186060 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.45716e10 | −0.0151261 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.59281e11 | −0.519855 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.19165e11 | 0.189778 | 0.0948888 | − | 0.995488i | \(-0.469750\pi\) | ||||
0.0948888 | + | 0.995488i | \(0.469750\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.03090e11 | 0.410916 | 0.205458 | − | 0.978666i | \(-0.434132\pi\) | ||||
0.205458 | + | 0.978666i | \(0.434132\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.53525e11 | 0.145648 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.12574e12 | −0.635754 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.04802e12 | 2.24746 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.00804e11 | 0.0550243 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.77546e11 | −0.470975 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.04714e11 | 0.213578 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.11477e10 | 0.0161637 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.19324e10 | 0.0162961 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.63274e11 | 0.132136 | 0.0660679 | − | 0.997815i | \(-0.478955\pi\) | ||||
0.0660679 | + | 0.997815i | \(0.478955\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.87485e11 | −0.141911 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.98043e10 | −0.0338920 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.43116e11 | −0.450425 | −0.225212 | − | 0.974310i | \(-0.572308\pi\) | ||||
−0.225212 | + | 0.974310i | \(0.572308\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.89828e11 | 0.0891837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.83687e12 | −0.848979 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.25913e11 | 0.102725 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.10984e11 | 0.0496525 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.73948e12 | 1.64613 | 0.823063 | − | 0.567950i | \(-0.192263\pi\) | ||||
0.823063 | + | 0.567950i | \(0.192263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.84576e11 | 0.339846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.93973e10 | −0.00826813 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.81433e11 | −0.160004 | −0.0800019 | − | 0.996795i | \(-0.525493\pi\) | ||||
−0.0800019 | + | 0.996795i | \(0.525493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.96033e11 | −0.0809304 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.12689e10 | −0.0289585 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.58954e12 | −1.43560 | −0.717800 | − | 0.696249i | \(-0.754851\pi\) | ||||
−0.717800 | + | 0.696249i | \(0.754851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.19723e12 | 1.25867 | 0.629334 | − | 0.777135i | \(-0.283328\pi\) | ||||
0.629334 | + | 0.777135i | \(0.283328\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.26906e12 | 0.879325 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.57217e12 | −1.74428 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.67840e12 | 0.630381 | 0.315191 | − | 0.949028i | \(-0.397932\pi\) | ||||
0.315191 | + | 0.949028i | \(0.397932\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.24357e11 | 0.304833 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00518e10 | 0.0145824 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.16482e9 | −0.00292711 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.14419e11 | 0.0403920 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.78170e12 | 1.66231 | 0.831153 | − | 0.556043i | \(-0.187681\pi\) | ||||
0.831153 | + | 0.556043i | \(0.187681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.87945e12 | 0.643445 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.99613e11 | −0.202175 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.42074e12 | 0.471811 | 0.235906 | − | 0.971776i | \(-0.424194\pi\) | ||||
0.235906 | + | 0.971776i | \(0.424194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.16872e11 | 0.0382284 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.24461e11 | 0.297854 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.72919e12 | −1.18357 | −0.591784 | − | 0.806096i | \(-0.701576\pi\) | ||||
−0.591784 | + | 0.806096i | \(0.701576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.32876e11 | 0.104075 | 0.0520375 | − | 0.998645i | \(-0.483428\pi\) | ||||
0.0520375 | + | 0.998645i | \(0.483428\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.43893e11 | −0.290733 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.89925e11 | 0.179018 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.38715e12 | 0.414739 | 0.207369 | − | 0.978263i | \(-0.433510\pi\) | ||||
0.207369 | + | 0.978263i | \(0.433510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.23089e11 | −0.154098 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.01681e12 | −0.585437 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.54790e12 | −0.442763 | −0.221382 | − | 0.975187i | \(-0.571057\pi\) | ||||
−0.221382 | + | 0.975187i | \(0.571057\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.55282e11 | −0.0719584 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.17696e12 | 0.326947 | 0.163473 | − | 0.986548i | \(-0.447730\pi\) | ||||
0.163473 | + | 0.986548i | \(0.447730\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.72922e12 | −0.473415 | −0.236708 | − | 0.971581i | \(-0.576068\pi\) | ||||
−0.236708 | + | 0.971581i | \(0.576068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.28529e12 | 0.346809 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.43417e12 | 0.381420 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.45164e12 | 0.904827 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.23842e10 | 0.00836815 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.54431e12 | −0.393376 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.73742e12 | −1.44074 | −0.720368 | − | 0.693592i | \(-0.756027\pi\) | ||||
−0.720368 | + | 0.693592i | \(0.756027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.22143e12 | −0.302379 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.13524e11 | −0.125337 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.62098e12 | 0.630720 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.18220e12 | −0.280502 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.57753e12 | 1.77283 | 0.886414 | − | 0.462894i | \(-0.153189\pi\) | ||||
0.886414 | + | 0.462894i | \(0.153189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.80446e12 | 1.10840 | 0.554199 | − | 0.832384i | \(-0.313025\pi\) | ||||
0.554199 | + | 0.832384i | \(0.313025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.28236e11 | 0.0519237 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.43505e12 | 0.321958 | 0.160979 | − | 0.986958i | \(-0.448535\pi\) | ||||
0.160979 | + | 0.986958i | \(0.448535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.30439e10 | −0.00288608 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.35213e11 | 0.116792 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.17024e12 | 1.32798 | 0.663991 | − | 0.747740i | \(-0.268861\pi\) | ||||
0.663991 | + | 0.747740i | \(0.268861\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.76798e11 | 0.0587594 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.68693e12 | 0.353226 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.01866e11 | 0.0416945 | 0.0208472 | − | 0.999783i | \(-0.493364\pi\) | ||||
0.0208472 | + | 0.999783i | \(0.493364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.37300e12 | −1.70598 | −0.852991 | − | 0.521925i | \(-0.825214\pi\) | ||||
−0.852991 | + | 0.521925i | \(0.825214\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.59211e12 | −0.320008 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.95121e11 | −0.0386908 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.43360e12 | 1.84549 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.50717e11 | 0.164198 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.45635e10 | −0.00467777 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.11671e12 | 1.71305 | 0.856525 | − | 0.516105i | \(-0.172619\pi\) | ||||
0.856525 | + | 0.516105i | \(0.172619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00469e12 | −0.186279 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.62986e12 | 1.57890 | 0.789450 | − | 0.613815i | \(-0.210366\pi\) | ||||
0.789450 | + | 0.613815i | \(0.210366\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.03448e12 | 0.186770 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.55940e12 | −0.990527 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.73461e12 | 0.480842 | 0.240421 | − | 0.970669i | \(-0.422715\pi\) | ||||
0.240421 | + | 0.970669i | \(0.422715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.61312e11 | −0.0453473 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.75867e12 | −0.815043 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.70161e11 | −0.113290 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.23661e12 | 1.20749 | 0.603746 | − | 0.797177i | \(-0.293674\pi\) | ||||
0.603746 | + | 0.797177i | \(0.293674\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.22209e9 | 0.00151890 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.35199e11 | −0.119529 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.55218e12 | 0.570095 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.97259e12 | −0.470964 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.35635e12 | −0.368561 | −0.184280 | − | 0.982874i | \(-0.558995\pi\) | ||||
−0.184280 | + | 0.982874i | \(0.558995\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.57827e12 | 0.398134 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.86699e11 | −0.0894466 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.67524e11 | −0.115533 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.84172e12 | −0.273725 | −0.136862 | − | 0.990590i | \(-0.543702\pi\) | ||||
−0.136862 | + | 0.990590i | \(0.543702\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.95264e11 | −0.131383 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.65225e12 | −1.39870 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.48056e10 | −0.00211860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.99274e12 | 0.281588 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.00065e12 | 0.139637 | 0.0698186 | − | 0.997560i | \(-0.477758\pi\) | ||||
0.0698186 | + | 0.997560i | \(0.477758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.96494e12 | 0.270795 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.12691e12 | −0.833910 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.37404e12 | −0.991253 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.46409e13 | 1.94385 | 0.971925 | − | 0.235291i | \(-0.0756044\pi\) | ||||
0.971925 | + | 0.235291i | \(0.0756044\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.17585e12 | −0.411369 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.30354e12 | 0.166785 | 0.0833925 | − | 0.996517i | \(-0.473424\pi\) | ||||
0.0833925 | + | 0.996517i | \(0.473424\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.62453e11 | 0.0963652 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.22138e11 | 0.0152492 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.15412e12 | 0.635704 | 0.317852 | − | 0.948140i | \(-0.397039\pi\) | ||||
0.317852 | + | 0.948140i | \(0.397039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.65806e12 | 0.323879 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.22504e12 | −0.990121 | −0.495060 | − | 0.868859i | \(-0.664854\pi\) | ||||
−0.495060 | + | 0.868859i | \(0.664854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.38700e11 | 0.111641 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.58720e11 | −0.0186505 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.67740e12 | 0.310846 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.09125e12 | 0.239898 | 0.119949 | − | 0.992780i | \(-0.461727\pi\) | ||||
0.119949 | + | 0.992780i | \(0.461727\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.37035e12 | 0.268680 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.21110e11 | −0.0695677 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.40301e13 | −1.55285 | −0.776427 | − | 0.630208i | \(-0.782970\pi\) | ||||
−0.776427 | + | 0.630208i | \(0.782970\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.66315e11 | −0.0181905 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.88984e11 | 0.0528523 | 0.0264262 | − | 0.999651i | \(-0.491587\pi\) | ||||
0.0264262 | + | 0.999651i | \(0.491587\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.61792e11 | −0.0493272 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.63150e11 | −0.0488928 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.07063e12 | −0.111702 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.51278e12 | 0.568463 | 0.284232 | − | 0.958756i | \(-0.408262\pi\) | ||||
0.284232 | + | 0.958756i | \(0.408262\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.11933e12 | −0.216000 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.93968e12 | −0.799826 | −0.399913 | − | 0.916553i | \(-0.630960\pi\) | ||||
−0.399913 | + | 0.916553i | \(0.630960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.54495e12 | 0.751275 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.34217e11 | 0.0722653 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.93045e12 | −0.576991 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.52975e11 | 0.0147126 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.07293e12 | 0.197087 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.41591e12 | 0.133083 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.12131e12 | 0.197114 | 0.0985569 | − | 0.995131i | \(-0.468577\pi\) | ||||
0.0985569 | + | 0.995131i | \(0.468577\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.76526e11 | 0.0345899 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.29686e12 | −0.117788 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.01615e12 | −0.181048 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.94952e11 | −0.0173092 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.56756e13 | 1.37613 | 0.688067 | − | 0.725647i | \(-0.258459\pi\) | ||||
0.688067 | + | 0.725647i | \(0.258459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.16376e12 | 0.708647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.68341e12 | −0.487824 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.18286e11 | −0.0185271 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00208e12 | 0.0841050 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.17737e12 | −0.346715 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.33817e13 | −1.09836 | −0.549178 | − | 0.835705i | \(-0.685059\pi\) | ||||
−0.549178 | + | 0.835705i | \(0.685059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.33572e12 | 0.595455 | 0.297727 | − | 0.954651i | \(-0.403771\pi\) | ||||
0.297727 | + | 0.954651i | \(0.403771\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.16139e13 | 0.932333 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.57372e12 | 0.124945 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.30216e12 | 0.416345 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.56940e11 | 0.0587874 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.64810e12 | 0.510685 | 0.255343 | − | 0.966851i | \(-0.417812\pi\) | ||||
0.255343 | + | 0.966851i | \(0.417812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.61148e12 | 0.350381 | 0.175191 | − | 0.984535i | \(-0.443946\pi\) | ||||
0.175191 | + | 0.984535i | \(0.443946\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.30005e11 | 0.00977050 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.64749e13 | −1.22475 | −0.612377 | − | 0.790566i | \(-0.709786\pi\) | ||||
−0.612377 | + | 0.790566i | \(0.709786\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.33872e13 | −1.71982 | −0.859910 | − | 0.510446i | \(-0.829480\pi\) | ||||
−0.859910 | + | 0.510446i | \(0.829480\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.87525e12 | −0.427388 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.06093e13 | −0.763460 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.59150e11 | 0.0255674 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.12098e12 | −0.149373 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.19129e12 | 0.222350 | 0.111175 | − | 0.993801i | \(-0.464539\pi\) | ||||
0.111175 | + | 0.993801i | \(0.464539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.07463e11 | 0.0487665 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.31451e13 | −0.896480 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.43868e12 | 0.0970753 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.90267e12 | 0.260547 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.45247e13 | −0.959450 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.32412e13 | −0.865453 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.01905e13 | −1.30580 | −0.652899 | − | 0.757445i | \(-0.726448\pi\) | ||||
−0.652899 | + | 0.757445i | \(0.726448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.73241e11 | 0.0494843 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.40886e13 | −0.892185 | −0.446093 | − | 0.894987i | \(-0.647185\pi\) | ||||
−0.446093 | + | 0.894987i | \(0.647185\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.11678e13 | −1.32650 | −0.663250 | − | 0.748398i | \(-0.730823\pi\) | ||||
−0.663250 | + | 0.748398i | \(0.730823\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.68882e12 | −0.104730 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.28437e12 | −0.447037 | −0.223519 | − | 0.974700i | \(-0.571754\pi\) | ||||
−0.223519 | + | 0.974700i | \(0.571754\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.65489e12 | 0.161240 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.16100e12 | −0.189993 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.15846e11 | 0.00689115 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.00250e13 | 0.590204 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.09950e12 | −0.238873 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.59256e12 | −0.0918459 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.59566e13 | −1.48166 | −0.740831 | − | 0.671692i | \(-0.765568\pi\) | ||||
−0.740831 | + | 0.671692i | \(0.765568\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.86525e13 | −1.05387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.85083e12 | −0.550911 | −0.275456 | − | 0.961314i | \(-0.588829\pi\) | ||||
−0.275456 | + | 0.961314i | \(0.588829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.71297e11 | 0.0426971 | 0.0213486 | − | 0.999772i | \(-0.493204\pi\) | ||||
0.0213486 | + | 0.999772i | \(0.493204\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.11451e11 | −0.0170665 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.94743e12 | 0.539579 | 0.269789 | − | 0.962919i | \(-0.413046\pi\) | ||||
0.269789 | + | 0.962919i | \(0.413046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.39723e12 | −0.182418 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.65460e10 | −0.00194263 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.36296e13 | −0.717219 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.62359e10 | −0.00501341 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.36510e13 | −0.704040 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.55672e13 | −0.794864 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.71271e12 | 0.137133 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.50990e12 | 0.0755708 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.88230e11 | 0.0440156 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.51839e13 | 0.744988 | 0.372494 | − | 0.928035i | \(-0.378503\pi\) | ||||
0.372494 | + | 0.928035i | \(0.378503\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.04160e12 | 0.147763 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.30119e13 | 0.625903 | 0.312951 | − | 0.949769i | \(-0.398682\pi\) | ||||
0.312951 | + | 0.949769i | \(0.398682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.05382e10 | 0.000978235 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.86505e11 | −0.0276616 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.83117e12 | 0.0855197 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.88036e13 | 1.33207 | 0.666034 | − | 0.745921i | \(-0.267990\pi\) | ||||
0.666034 | + | 0.745921i | \(0.267990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.28303e13 | −1.04555 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.25560e13 | 0.569434 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.03503e13 | 0.464854 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.78680e12 | −0.346338 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.00577e13 | −0.883510 | −0.441755 | − | 0.897136i | \(-0.645644\pi\) | ||||
−0.441755 | + | 0.897136i | \(0.645644\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.77126e13 | 0.772695 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.88924e13 | 0.816245 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.99309e10 | 0.00256448 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.18883e13 | 1.35146 | 0.675731 | − | 0.737149i | \(-0.263828\pi\) | ||||
0.675731 | + | 0.737149i | \(0.263828\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.66605e13 | −1.11911 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.39219e12 | −0.141035 | −0.0705175 | − | 0.997511i | \(-0.522465\pi\) | ||||
−0.0705175 | + | 0.997511i | \(0.522465\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.04569e13 | 1.25425 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.20197e11 | 0.00898189 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.55975e13 | −1.43828 | −0.719142 | − | 0.694863i | \(-0.755465\pi\) | ||||
−0.719142 | + | 0.694863i | \(0.755465\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.79167e13 | −0.717068 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.34007e12 | 0.290997 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.43100e13 | −0.954702 | −0.477351 | − | 0.878713i | \(-0.658403\pi\) | ||||
−0.477351 | + | 0.878713i | \(0.658403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.01061e12 | −0.272735 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.68235e11 | −0.0103374 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.72872e12 | −0.0659994 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.05116e13 | −0.397569 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.06102e13 | −0.397562 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.54698e12 | −0.0945482 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.53573e13 | 0.564801 | 0.282401 | − | 0.959297i | \(-0.408869\pi\) | ||||
0.282401 | + | 0.959297i | \(0.408869\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.07594e13 | −0.392042 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.16083e13 | −1.14108 | −0.570539 | − | 0.821271i | \(-0.693266\pi\) | ||||
−0.570539 | + | 0.821271i | \(0.693266\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.86373e12 | −0.173965 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.06707e13 | 0.378156 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.05660e13 | −0.371008 | −0.185504 | − | 0.982643i | \(-0.559392\pi\) | ||||
−0.185504 | + | 0.982643i | \(0.559392\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.35425e11 | 0.0255868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.83002e12 | 0.0630879 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.36692e13 | −1.49171 | −0.745856 | − | 0.666108i | \(-0.767959\pi\) | ||||
−0.745856 | + | 0.666108i | \(0.767959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.85260e12 | 0.0627074 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.88132e12 | −0.130182 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.72302e13 | −0.905040 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.20991e13 | 1.05721 | 0.528605 | − | 0.848868i | \(-0.322715\pi\) | ||||
0.528605 | + | 0.848868i | \(0.322715\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.48868e13 | 0.812266 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.85627e12 | −0.0923837 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.79644e13 | −1.21688 | −0.608441 | − | 0.793599i | \(-0.708205\pi\) | ||||
−0.608441 | + | 0.793599i | \(0.708205\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.90961e12 | −0.0924250 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.10.a.f.1.2 | yes | 4 | |
4.3 | odd | 2 | 384.10.a.b.1.2 | ✓ | 4 | ||
8.3 | odd | 2 | 384.10.a.g.1.3 | yes | 4 | ||
8.5 | even | 2 | 384.10.a.c.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.a.b.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
384.10.a.c.1.3 | yes | 4 | 8.5 | even | 2 | ||
384.10.a.f.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
384.10.a.g.1.3 | yes | 4 | 8.3 | odd | 2 |