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 | 1.3 | ||
Root | \(-25.0977\) 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 | ||||||||
\(5\) | −126.806 | −0.0907350 | −0.0453675 | − | 0.998970i | \(-0.514446\pi\) | ||||
−0.0453675 | + | 0.998970i | \(0.514446\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5939.66 | 0.935018 | 0.467509 | − | 0.883988i | \(-0.345151\pi\) | ||||
0.467509 | + | 0.883988i | \(0.345151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4237.38 | −0.0872630 | −0.0436315 | − | 0.999048i | \(-0.513893\pi\) | ||||
−0.0436315 | + | 0.999048i | \(0.513893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 136583. | 1.32633 | 0.663165 | − | 0.748473i | \(-0.269213\pi\) | ||||
0.663165 | + | 0.748473i | \(0.269213\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10271.3 | 0.0523859 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −230372. | −0.668976 | −0.334488 | − | 0.942400i | \(-0.608563\pi\) | ||||
−0.334488 | + | 0.942400i | \(0.608563\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −450474. | −0.793010 | −0.396505 | − | 0.918033i | \(-0.629777\pi\) | ||||
−0.396505 | + | 0.918033i | \(0.629777\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −481112. | −0.539833 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.33693e6 | 0.996167 | 0.498084 | − | 0.867129i | \(-0.334037\pi\) | ||||
0.498084 | + | 0.867129i | \(0.334037\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.93705e6 | −0.991767 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.08853e6 | −1.07344 | −0.536718 | − | 0.843761i | \(-0.680336\pi\) | ||||
−0.536718 | + | 0.843761i | \(0.680336\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.71901e6 | −0.917748 | −0.458874 | − | 0.888501i | \(-0.651747\pi\) | ||||
−0.458874 | + | 0.888501i | \(0.651747\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 343228. | 0.0503813 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −753184. | −0.0848389 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.93239e7 | 1.69507 | 0.847535 | − | 0.530739i | \(-0.178085\pi\) | ||||
0.847535 | + | 0.530739i | \(0.178085\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.10632e7 | −0.765757 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.33619e7 | −0.738485 | −0.369242 | − | 0.929333i | \(-0.620383\pi\) | ||||
−0.369242 | + | 0.929333i | \(0.620383\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.48837e6 | −0.200208 | −0.100104 | − | 0.994977i | \(-0.531918\pi\) | ||||
−0.100104 | + | 0.994977i | \(0.531918\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −831974. | −0.0302450 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.27952e7 | −0.382477 | −0.191238 | − | 0.981544i | \(-0.561250\pi\) | ||||
−0.191238 | + | 0.981544i | \(0.561250\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.07408e6 | −0.125741 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.86602e7 | 0.386233 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.11895e7 | 0.891127 | 0.445563 | − | 0.895250i | \(-0.353003\pi\) | ||||
0.445563 | + | 0.895250i | \(0.353003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 537325. | 0.00791781 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.64884e7 | 0.457845 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.93950e7 | 0.530700 | 0.265350 | − | 0.964152i | \(-0.414513\pi\) | ||||
0.265350 | + | 0.964152i | \(0.414513\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.72852e7 | 0.159842 | 0.0799210 | − | 0.996801i | \(-0.474533\pi\) | ||||
0.0799210 | + | 0.996801i | \(0.474533\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.89701e7 | 0.311673 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.73196e7 | −0.120345 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.72355e8 | −1.65120 | −0.825599 | − | 0.564257i | \(-0.809163\pi\) | ||||
−0.825599 | + | 0.564257i | \(0.809163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.08291e8 | −0.575137 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.24504e8 | 1.04848 | 0.524242 | − | 0.851569i | \(-0.324349\pi\) | ||||
0.524242 | + | 0.851569i | \(0.324349\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.69433e8 | −1.11045 | −0.555223 | − | 0.831702i | \(-0.687367\pi\) | ||||
−0.555223 | + | 0.831702i | \(0.687367\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.56901e8 | 0.572597 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.51686e7 | −0.0815925 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.14996e8 | −0.332172 | −0.166086 | − | 0.986111i | \(-0.553113\pi\) | ||||
−0.166086 | + | 0.986111i | \(0.553113\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.29829e8 | 1.45670 | 0.728351 | − | 0.685204i | \(-0.240287\pi\) | ||||
0.728351 | + | 0.685204i | \(0.240287\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.92126e7 | 0.0606995 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.31171e8 | 0.619749 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.35980e8 | 1.07446 | 0.537228 | − | 0.843437i | \(-0.319471\pi\) | ||||
0.537228 | + | 0.843437i | \(0.319471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.11257e8 | 1.24014 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.82240e8 | 0.529862 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.71228e7 | 0.0719538 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.48896e8 | −0.744221 | −0.372111 | − | 0.928188i | \(-0.621366\pi\) | ||||
−0.372111 | + | 0.928188i | \(0.621366\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.78014e7 | −0.0290877 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.08357e8 | 0.199233 | 0.0996164 | − | 0.995026i | \(-0.468238\pi\) | ||||
0.0996164 | + | 0.995026i | \(0.468238\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.16057e9 | 1.01603 | 0.508013 | − | 0.861349i | \(-0.330380\pi\) | ||||
0.508013 | + | 0.861349i | \(0.330380\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.10079e7 | 0.0489818 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.55331e8 | −0.483319 | −0.241659 | − | 0.970361i | \(-0.577692\pi\) | ||||
−0.241659 | + | 0.970361i | \(0.577692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.98216e8 | −0.202354 | −0.101177 | − | 0.994868i | \(-0.532261\pi\) | ||||
−0.101177 | + | 0.994868i | \(0.532261\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.56524e9 | −0.978650 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.44019e8 | −0.544663 | −0.272331 | − | 0.962204i | \(-0.587795\pi\) | ||||
−0.272331 | + | 0.962204i | \(0.587795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.69530e8 | −0.0903872 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.96122e8 | 0.442110 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.36833e9 | −0.625505 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.33999e9 | −0.992385 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.08232e9 | 0.426364 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.93297e8 | 0.180723 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.03041e9 | 0.692574 | 0.346287 | − | 0.938129i | \(-0.387442\pi\) | ||||
0.346287 | + | 0.938129i | \(0.387442\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.63558e8 | 0.115590 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.21820e9 | 0.361407 | 0.180704 | − | 0.983538i | \(-0.442163\pi\) | ||||
0.180704 | + | 0.983538i | \(0.442163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.67566e9 | −0.741479 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.73899e7 | 0.0174620 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.85728e9 | −1.17802 | −0.589008 | − | 0.808128i | \(-0.700481\pi\) | ||||
−0.589008 | + | 0.808128i | \(0.700481\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.29557e9 | −0.748798 | −0.374399 | − | 0.927268i | \(-0.622151\pi\) | ||||
−0.374399 | + | 0.927268i | \(0.622151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.03641e9 | 0.220823 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.78754e8 | −0.115740 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.18451e8 | 0.0973983 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.11001e8 | 0.0725963 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.03213e9 | 0.836400 | 0.418200 | − | 0.908355i | \(-0.362661\pi\) | ||||
0.418200 | + | 0.908355i | \(0.362661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.76425e9 | 0.432694 | 0.216347 | − | 0.976317i | \(-0.430586\pi\) | ||||
0.216347 | + | 0.976317i | \(0.430586\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.51147e9 | −0.222992 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.98399e8 | 0.0832718 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.19336e9 | −0.419469 | −0.209734 | − | 0.977758i | \(-0.567260\pi\) | ||||
−0.209734 | + | 0.977758i | \(0.567260\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.14635e9 | −0.514492 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.94088e9 | 0.931435 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.86760e9 | 0.429139 | 0.214569 | − | 0.976709i | \(-0.431165\pi\) | ||||
0.214569 | + | 0.976709i | \(0.431165\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.35233e7 | −0.00457135 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.96510e9 | −0.891931 | −0.445965 | − | 0.895050i | \(-0.647140\pi\) | ||||
−0.445965 | + | 0.895050i | \(0.647140\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.05044e9 | 0.759153 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.95556e9 | −0.264337 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.70609e9 | −0.823829 | −0.411914 | − | 0.911223i | \(-0.635140\pi\) | ||||
−0.411914 | + | 0.911223i | \(0.635140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.15054e10 | −0.927321 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00100e9 | −0.306400 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.67643e10 | 1.94857 | 0.974287 | − | 0.225312i | \(-0.0723401\pi\) | ||||
0.974287 | + | 0.225312i | \(0.0723401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.73116e10 | −1.19890 | −0.599450 | − | 0.800412i | \(-0.704614\pi\) | ||||
−0.599450 | + | 0.800412i | \(0.704614\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.40010e9 | −0.0922848 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.45039e9 | −0.153802 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.76176e8 | 0.0583769 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.15658e9 | −0.179944 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.60854e9 | 0.196192 | 0.0980959 | − | 0.995177i | \(-0.468725\pi\) | ||||
0.0980959 | + | 0.995177i | \(0.468725\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.86520e10 | −1.48644 | −0.743221 | − | 0.669046i | \(-0.766703\pi\) | ||||
−0.743221 | + | 0.669046i | \(0.766703\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.40288e9 | 0.0694810 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.52639e10 | −1.19510 | −0.597549 | − | 0.801833i | \(-0.703858\pi\) | ||||
−0.597549 | + | 0.801833i | \(0.703858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.39547e9 | −0.334293 | −0.167146 | − | 0.985932i | \(-0.553455\pi\) | ||||
−0.167146 | + | 0.985932i | \(0.553455\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.20608e10 | 0.953320 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.42845e10 | −1.00368 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.69437e9 | 0.0670064 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.77157e9 | 0.332056 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.90883e9 | 0.0692005 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.16676e9 | 0.283647 | 0.141824 | − | 0.989892i | \(-0.454703\pi\) | ||||
0.141824 | + | 0.989892i | \(0.454703\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.81848e10 | −0.605342 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.69153e8 | 0.0181659 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.80293e10 | −0.858111 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.18240e10 | 0.641116 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.14650e10 | −0.887283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.20049e10 | −1.67901 | −0.839507 | − | 0.543349i | \(-0.817156\pi\) | ||||
−0.839507 | + | 0.543349i | \(0.817156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.27090e10 | −0.330589 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.12021e10 | −0.529984 | −0.264992 | − | 0.964251i | \(-0.585369\pi\) | ||||
−0.264992 | + | 0.964251i | \(0.585369\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.34925e10 | 0.564508 | 0.282254 | − | 0.959340i | \(-0.408918\pi\) | ||||
0.282254 | + | 0.959340i | \(0.408918\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.03866e9 | 0.0471075 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.64418e10 | −0.810025 | −0.405012 | − | 0.914311i | \(-0.632733\pi\) | ||||
−0.405012 | + | 0.914311i | \(0.632733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.62250e9 | 0.0347040 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.31471e9 | 0.191779 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.03924e10 | −1.79201 | −0.896007 | − | 0.444039i | \(-0.853545\pi\) | ||||
−0.896007 | + | 0.444039i | \(0.853545\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.80041e10 | 0.725695 | 0.362848 | − | 0.931848i | \(-0.381805\pi\) | ||||
0.362848 | + | 0.931848i | \(0.381805\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.43424e8 | 0.0114091 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.15272e10 | −1.05179 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.10161e10 | −0.841028 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.45362e10 | 1.50337 | 0.751686 | − | 0.659522i | \(-0.229241\pi\) | ||||
0.751686 | + | 0.659522i | \(0.229241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.66506e9 | −0.0869286 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.36622e9 | −0.0350449 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.68326e10 | −0.526664 | −0.263332 | − | 0.964705i | \(-0.584821\pi\) | ||||
−0.263332 | + | 0.964705i | \(0.584821\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.14778e11 | 1.58492 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.68249e10 | −0.357812 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.98154e10 | 0.899810 | 0.449905 | − | 0.893077i | \(-0.351458\pi\) | ||||
0.449905 | + | 0.893077i | \(0.351458\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.49114e9 | −0.0808564 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.15144e10 | −0.620337 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.08188e10 | −0.708194 | −0.354097 | − | 0.935209i | \(-0.615212\pi\) | ||||
−0.354097 | + | 0.935209i | \(0.615212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.33650e9 | 0.0601028 | 0.0300514 | − | 0.999548i | \(-0.490433\pi\) | ||||
0.0300514 | + | 0.999548i | \(0.490433\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.57118e10 | −0.715997 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.20800e9 | 0.0865446 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.34420e11 | −1.37184 | −0.685922 | − | 0.727675i | \(-0.740601\pi\) | ||||
−0.685922 | + | 0.727675i | \(0.740601\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.09614e10 | −0.305916 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.92090e11 | −1.83791 | −0.918957 | − | 0.394357i | \(-0.870967\pi\) | ||||
−0.918957 | + | 0.394357i | \(0.870967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.72340e10 | 0.437739 | 0.218870 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218870 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.62695e9 | −0.0415425 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.93652e10 | −0.690497 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.55164e10 | −0.552471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.25605e10 | 0.429676 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.72252e10 | −0.136540 | −0.0682702 | − | 0.997667i | \(-0.521748\pi\) | ||||
−0.0682702 | + | 0.997667i | \(0.521748\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.26358e9 | −0.0481530 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.25192e9 | 0.0167938 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.82602e11 | 1.32125 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.66594e10 | −0.187198 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.68769e10 | −0.115027 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.19187e9 | −0.0145033 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.42172e10 | 0.605351 | 0.302676 | − | 0.953094i | \(-0.402120\pi\) | ||||
0.302676 | + | 0.953094i | \(0.402120\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.40064e10 | −0.586603 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.95356e10 | −0.482103 | −0.241051 | − | 0.970512i | \(-0.577492\pi\) | ||||
−0.241051 | + | 0.970512i | \(0.577492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.27784e10 | −0.369709 | −0.184855 | − | 0.982766i | \(-0.559181\pi\) | ||||
−0.184855 | + | 0.982766i | \(0.559181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.94164e9 | −0.0282796 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.48671e10 | −0.527653 | −0.263827 | − | 0.964570i | \(-0.584985\pi\) | ||||
−0.263827 | + | 0.964570i | \(0.584985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.73247e10 | 0.0936714 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.30818e10 | 0.279044 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.03777e11 | 0.530505 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.64568e11 | −1.31541 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.41555e10 | 0.116829 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.59988e10 | −0.357623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.21508e11 | 1.93010 | 0.965051 | − | 0.262063i | \(-0.0844028\pi\) | ||||
0.965051 | + | 0.262063i | \(0.0844028\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.26784e11 | 0.565024 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.45363e10 | 0.149821 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.95896e11 | −0.827355 | −0.413678 | − | 0.910423i | \(-0.635756\pi\) | ||||
−0.413678 | + | 0.910423i | \(0.635756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.64655e10 | 0.314461 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.99962e10 | 0.0800854 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.69825e11 | −1.05259 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.37320e10 | 0.0521851 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.00666e11 | −0.372736 | −0.186368 | − | 0.982480i | \(-0.559672\pi\) | ||||
−0.186368 | + | 0.982480i | \(0.559672\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.21109e11 | 0.436980 | 0.218490 | − | 0.975839i | \(-0.429887\pi\) | ||||
0.218490 | + | 0.975839i | \(0.429887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.25858e10 | −0.255252 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50575e11 | −0.516139 | −0.258069 | − | 0.966126i | \(-0.583086\pi\) | ||||
−0.258069 | + | 0.966126i | \(0.583086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.84685e10 | −0.0951342 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.10835e11 | 0.361135 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.85699e11 | −1.54327 | −0.771636 | − | 0.636065i | \(-0.780561\pi\) | ||||
−0.771636 | + | 0.636065i | \(0.780561\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.19761e11 | −0.371135 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.89539e11 | 0.572954 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.41657e10 | 0.100756 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.61310e11 | −0.464155 | −0.232078 | − | 0.972697i | \(-0.574552\pi\) | ||||
−0.232078 | + | 0.972697i | \(0.574552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.76675e10 | −0.246162 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.04048e11 | 0.833220 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.73064e11 | −0.462932 | −0.231466 | − | 0.972843i | \(-0.574352\pi\) | ||||
−0.231466 | + | 0.972843i | \(0.574352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.99571e10 | −0.104340 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.58424e11 | −1.42373 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.65005e11 | −1.65557 | −0.827787 | − | 0.561043i | \(-0.810400\pi\) | ||||
−0.827787 | + | 0.561043i | \(0.810400\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.64463e11 | −0.399858 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.90834e11 | 0.453171 | 0.226585 | − | 0.973991i | \(-0.427244\pi\) | ||||
0.226585 | + | 0.973991i | \(0.427244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.19153e9 | 0.00740330 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.94482e10 | −0.0667359 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.83430e11 | −1.29186 | −0.645930 | − | 0.763397i | \(-0.723530\pi\) | ||||
−0.645930 | + | 0.763397i | \(0.723530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.07991e11 | −0.666412 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.86740e10 | −0.208659 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.45822e10 | 0.0301396 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.15367e11 | −1.04126 | −0.520630 | − | 0.853782i | \(-0.674303\pi\) | ||||
−0.520630 | + | 0.853782i | \(0.674303\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.16729e11 | 0.428093 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.54840e11 | 1.84409 | 0.922043 | − | 0.387088i | \(-0.126519\pi\) | ||||
0.922043 | + | 0.387088i | \(0.126519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.44537e11 | −1.21724 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.45858e9 | −0.0100817 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.18829e10 | −0.147917 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.02451e12 | −1.81034 | −0.905168 | − | 0.425054i | \(-0.860255\pi\) | ||||
−0.905168 | + | 0.425054i | \(0.860255\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.93440e11 | 0.680127 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.93389e11 | 0.496214 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.98661e10 | −0.132174 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.66941e11 | 0.432318 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.45721e11 | 0.547978 | 0.273989 | − | 0.961733i | \(-0.411657\pi\) | ||||
0.273989 | + | 0.961733i | \(0.411657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.62812e10 | 0.0252590 | 0.0126295 | − | 0.999920i | \(-0.495980\pi\) | ||||
0.0126295 | + | 0.999920i | \(0.495980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.39490e10 | −0.127492 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.46242e11 | 0.663468 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.02668e11 | 0.149455 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.68791e10 | 0.0668223 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.54079e11 | −1.05261 | −0.526307 | − | 0.850295i | \(-0.676424\pi\) | ||||
−0.526307 | + | 0.850295i | \(0.676424\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.87173e11 | 0.802732 | 0.401366 | − | 0.915918i | \(-0.368535\pi\) | ||||
0.401366 | + | 0.915918i | \(0.368535\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.19945e10 | −0.0562329 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.02251e11 | −0.789971 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.07502e11 | 0.266643 | 0.133322 | − | 0.991073i | \(-0.457436\pi\) | ||||
0.133322 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.32911e10 | −0.0419135 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.76397e11 | 0.957783 | 0.478891 | − | 0.877874i | \(-0.341039\pi\) | ||||
0.478891 | + | 0.877874i | \(0.341039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.06461e10 | −0.0974908 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.07603e11 | −0.482896 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.20244e12 | −1.39623 | −0.698113 | − | 0.715988i | \(-0.745977\pi\) | ||||
−0.698113 | + | 0.715988i | \(0.745977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.66195e10 | 0.0644424 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.23904e11 | −0.249816 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.02872e11 | −0.112524 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.35408e11 | 0.788688 | 0.394344 | − | 0.918963i | \(-0.370972\pi\) | ||||
0.394344 | + | 0.918963i | \(0.370972\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.22429e11 | 0.128744 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.28508e12 | 1.32518 | 0.662590 | − | 0.748982i | \(-0.269457\pi\) | ||||
0.662590 | + | 0.748982i | \(0.269457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.47746e11 | 0.452811 | 0.226406 | − | 0.974033i | \(-0.427302\pi\) | ||||
0.226406 | + | 0.974033i | \(0.427302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.84703e10 | −0.0480770 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.21634e12 | −1.18340 | −0.591698 | − | 0.806160i | \(-0.701542\pi\) | ||||
−0.591698 | + | 0.806160i | \(0.701542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.61770e12 | −1.54390 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.58662e11 | 0.242181 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.90189e10 | 0.0174707 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.72589e11 | 0.786481 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.35854e11 | 0.297042 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.70420e12 | 1.47915 | 0.739574 | − | 0.673075i | \(-0.235027\pi\) | ||||
0.739574 | + | 0.673075i | \(0.235027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.63932e12 | 2.24822 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.43212e11 | −0.537764 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.22839e10 | 0.0675269 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.60755e11 | 0.210064 | 0.105032 | − | 0.994469i | \(-0.466505\pi\) | ||||
0.105032 | + | 0.994469i | \(0.466505\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.13276e11 | −0.247763 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.16626e12 | −0.905586 | −0.452793 | − | 0.891616i | \(-0.649572\pi\) | ||||
−0.452793 | + | 0.891616i | \(0.649572\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.41885e11 | 0.718103 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.52539e9 | 0.00263927 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.33348e12 | 0.980352 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.38683e11 | 0.172333 | 0.0861664 | − | 0.996281i | \(-0.472538\pi\) | ||||
0.0861664 | + | 0.996281i | \(0.472538\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.26173e11 | 0.514957 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.01016e12 | 0.703614 | 0.351807 | − | 0.936073i | \(-0.385567\pi\) | ||||
0.351807 | + | 0.936073i | \(0.385567\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.64209e10 | −0.0180774 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.52086e11 | −0.438297 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.36854e12 | 0.903710 | 0.451855 | − | 0.892091i | \(-0.350762\pi\) | ||||
0.451855 | + | 0.892091i | \(0.350762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.60034e12 | −1.03829 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.39400e11 | 0.152615 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.47168e11 | −0.0921891 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.42179e10 | 0.0333761 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.86193e11 | 0.475638 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.43050e12 | −1.44519 | −0.722596 | − | 0.691271i | \(-0.757051\pi\) | ||||
−0.722596 | + | 0.691271i | \(0.757051\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.95220e12 | −1.14095 | −0.570475 | − | 0.821315i | \(-0.693241\pi\) | ||||
−0.570475 | + | 0.821315i | \(0.693241\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.31936e11 | 0.535389 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.08713e12 | 0.613951 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.37806e10 | −0.00765098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.24081e11 | 0.176900 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.82501e12 | −0.979475 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.30999e10 | 0.0438539 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.16791e12 | −1.12501 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.15008e10 | 0.0109725 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.91282e12 | 1.46193 | 0.730964 | − | 0.682416i | \(-0.239071\pi\) | ||||
0.730964 | + | 0.682416i | \(0.239071\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.40224e12 | 0.692186 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.78156e10 | 0.0183606 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.98365e12 | −0.947377 | −0.473689 | − | 0.880692i | \(-0.657078\pi\) | ||||
−0.473689 | + | 0.880692i | \(0.657078\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.13408e11 | 0.0532807 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.84178e12 | 0.851246 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.83039e11 | −0.310587 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.98482e11 | 0.0887978 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.14140e12 | 1.38285 | 0.691425 | − | 0.722448i | \(-0.256983\pi\) | ||||
0.691425 | + | 0.722448i | \(0.256983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.13036e11 | −0.265542 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.90702e10 | −0.0337039 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.06824e12 | 0.448107 | 0.224054 | − | 0.974577i | \(-0.428071\pi\) | ||||
0.224054 | + | 0.974577i | \(0.428071\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.19707e11 | 0.0494200 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.55683e11 | 0.103891 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.48022e12 | 1.39188 | 0.695940 | − | 0.718100i | \(-0.254988\pi\) | ||||
0.695940 | + | 0.718100i | \(0.254988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.19984e11 | −0.244072 | −0.122036 | − | 0.992526i | \(-0.538942\pi\) | ||||
−0.122036 | + | 0.992526i | \(0.538942\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.92291e11 | −0.113271 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.58969e12 | −0.987966 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.08907e12 | 1.91138 | 0.955691 | − | 0.294372i | \(-0.0951105\pi\) | ||||
0.955691 | + | 0.294372i | \(0.0951105\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.32082e12 | 0.858197 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.74097e12 | 1.36204 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.16909e11 | −0.0777624 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.13634e11 | −0.0401149 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.10341e11 | −0.177414 | −0.0887071 | − | 0.996058i | \(-0.528274\pi\) | ||||
−0.0887071 | + | 0.996058i | \(0.528274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.12579e12 | 0.727783 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.04638e12 | 0.689990 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.15153e12 | 0.714498 | 0.357249 | − | 0.934009i | \(-0.383715\pi\) | ||||
0.357249 | + | 0.934009i | \(0.383715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.73513e11 | 0.0567552 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.99033e11 | 0.193004 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.47411e12 | 1.10261 | 0.551307 | − | 0.834303i | \(-0.314129\pi\) | ||||
0.551307 | + | 0.834303i | \(0.314129\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.52520e11 | 0.266544 | 0.133272 | − | 0.991079i | \(-0.457452\pi\) | ||||
0.133272 | + | 0.991079i | \(0.457452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.78692e12 | −0.550399 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.96725e11 | 0.0900441 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.73779e12 | 1.41653 | 0.708267 | − | 0.705945i | \(-0.249477\pi\) | ||||
0.708267 | + | 0.705945i | \(0.249477\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.96704e12 | 0.579477 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.74760e12 | −0.507291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.29889e11 | 0.208778 | 0.104389 | − | 0.994537i | \(-0.466711\pi\) | ||||
0.104389 | + | 0.994537i | \(0.466711\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.37244e11 | −0.0386862 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.10485e12 | −1.41808 | −0.709038 | − | 0.705170i | \(-0.750871\pi\) | ||||
−0.709038 | + | 0.705170i | \(0.750871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.41159e12 | −1.48155 | −0.740776 | − | 0.671752i | \(-0.765542\pi\) | ||||
−0.740776 | + | 0.671752i | \(0.765542\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.10497e11 | −0.191712 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.77750e12 | 1.00464 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.72074e12 | 0.975369 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.54615e11 | −0.0399529 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.45170e12 | −1.13396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.54599e12 | −0.639329 | −0.319665 | − | 0.947531i | \(-0.603570\pi\) | ||||
−0.319665 | + | 0.947531i | \(0.603570\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.61508e11 | −0.163764 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.57468e11 | −0.0628407 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.93034e11 | −0.166774 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.47297e12 | 0.349495 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.55558e12 | 0.597899 | 0.298950 | − | 0.954269i | \(-0.403364\pi\) | ||||
0.298950 | + | 0.954269i | \(0.403364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.94766e12 | −0.449328 | −0.224664 | − | 0.974436i | \(-0.572128\pi\) | ||||
−0.224664 | + | 0.974436i | \(0.572128\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.61014e10 | −0.0104881 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.82986e12 | 1.53229 | 0.766147 | − | 0.642665i | \(-0.222171\pi\) | ||||
0.766147 | + | 0.642665i | \(0.222171\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.09305e11 | −0.0463105 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.27037e12 | 0.495431 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.20283e12 | 1.55022 | 0.775111 | − | 0.631825i | \(-0.217694\pi\) | ||||
0.775111 | + | 0.631825i | \(0.217694\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.54475e11 | −0.0327923 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.76775e12 | −0.370149 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.37156e12 | 0.696381 | 0.348191 | − | 0.937424i | \(-0.386796\pi\) | ||||
0.348191 | + | 0.937424i | \(0.386796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.04657e12 | −1.02823 | −0.514115 | − | 0.857721i | \(-0.671879\pi\) | ||||
−0.514115 | + | 0.857721i | \(0.671879\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.54866e12 | 0.512273 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.39290e11 | 0.0672781 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.46607e12 | −1.06932 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.02240e12 | 0.969379 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.32441e10 | −0.0139483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.03136e12 | 0.757503 | 0.378751 | − | 0.925498i | \(-0.376354\pi\) | ||||
0.378751 | + | 0.925498i | \(0.376354\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.02943e12 | 0.190866 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.67581e12 | −0.855476 | −0.427738 | − | 0.903903i | \(-0.640689\pi\) | ||||
−0.427738 | + | 0.903903i | \(0.640689\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.85422e12 | −0.695861 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.71737e12 | 0.305986 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.04924e12 | −0.712001 | −0.356001 | − | 0.934486i | \(-0.615860\pi\) | ||||
−0.356001 | + | 0.934486i | \(0.615860\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.15933e11 | 0.106887 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.90289e12 | −0.325919 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.99162e12 | 1.18193 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.85336e12 | −1.31040 | −0.655200 | − | 0.755455i | \(-0.727416\pi\) | ||||
−0.655200 | + | 0.755455i | \(0.727416\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.65131e11 | −0.0271975 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.17899e11 | 0.0679421 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.07822e12 | 0.494028 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.95179e12 | 0.467668 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.77407e12 | 1.52878 | 0.764389 | − | 0.644756i | \(-0.223041\pi\) | ||||
0.764389 | + | 0.644756i | \(0.223041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.70494e12 | −1.34421 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.31423e11 | −0.0200364 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.23757e12 | 0.186286 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.08047e13 | −1.60585 | −0.802924 | − | 0.596082i | \(-0.796723\pi\) | ||||
−0.802924 | + | 0.596082i | \(0.796723\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.54492e11 | −0.110724 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.30897e12 | −0.914230 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.33895e10 | 0.0105016 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.32179e12 | 1.03462 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.39028e12 | −0.194009 | −0.0970047 | − | 0.995284i | \(-0.530926\pi\) | ||||
−0.0970047 | + | 0.995284i | \(0.530926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.89340e12 | 0.950003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.07834e12 | −0.418980 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.91967e12 | 1.06460 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.60854e12 | 0.877406 | 0.438703 | − | 0.898632i | \(-0.355438\pi\) | ||||
0.438703 | + | 0.898632i | \(0.355438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.03400e12 | 0.133934 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.06680e12 | −0.904180 | −0.452090 | − | 0.891972i | \(-0.649321\pi\) | ||||
−0.452090 | + | 0.891972i | \(0.649321\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.21174e10 | −0.00658703 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.15407e12 | 0.144089 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.31518e12 | −0.532230 | −0.266115 | − | 0.963941i | \(-0.585740\pi\) | ||||
−0.266115 | + | 0.963941i | \(0.585740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.98370e12 | 0.607253 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.46782e13 | −1.76694 | −0.883472 | − | 0.468484i | \(-0.844800\pi\) | ||||
−0.883472 | + | 0.468484i | \(0.844800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.38105e11 | −0.0758907 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.13231e12 | 0.485568 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.89244e12 | −0.451912 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.75994e12 | −1.00490 | −0.502448 | − | 0.864607i | \(-0.667567\pi\) | ||||
−0.502448 | + | 0.864607i | \(0.667567\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.65743e12 | −0.867972 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.50523e11 | −0.0392605 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.42430e13 | −1.57642 | −0.788209 | − | 0.615408i | \(-0.788991\pi\) | ||||
−0.788209 | + | 0.615408i | \(0.788991\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.58870e11 | 0.0501882 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.15114e13 | −1.24422 | −0.622109 | − | 0.782931i | \(-0.713724\pi\) | ||||
−0.622109 | + | 0.782931i | \(0.713724\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.77130e12 | −0.189205 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.91664e11 | 0.0202332 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.74652e12 | 0.703884 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.69503e12 | 0.277905 | 0.138952 | − | 0.990299i | \(-0.455627\pi\) | ||||
0.138952 | + | 0.990299i | \(0.455627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.98344e12 | 0.304070 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.36336e13 | 1.37342 | 0.686710 | − | 0.726931i | \(-0.259054\pi\) | ||||
0.686710 | + | 0.726931i | \(0.259054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.14094e12 | 0.910192 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.29698e12 | −0.915055 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.01920e12 | 0.585626 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.51309e11 | −0.0914939 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.17281e12 | 0.206583 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.04938e11 | 0.0380605 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.76393e12 | −0.907274 | −0.453637 | − | 0.891187i | \(-0.649874\pi\) | ||||
−0.453637 | + | 0.891187i | \(0.649874\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.65505e12 | −0.519505 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.60715e12 | −0.509270 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.36087e12 | 0.212003 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.25782e11 | 0.0466825 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.96680e12 | −0.874970 | −0.437485 | − | 0.899226i | \(-0.644131\pi\) | ||||
−0.437485 | + | 0.899226i | \(0.644131\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.94765e12 | 0.255868 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.17267e12 | 0.358152 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.14169e12 | 0.0969009 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.00695e12 | −0.0845137 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.92632e12 | 0.408876 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.77919e12 | −0.392271 | −0.196135 | − | 0.980577i | \(-0.562839\pi\) | ||||
−0.196135 | + | 0.980577i | \(0.562839\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.25488e13 | 1.01861 | 0.509307 | − | 0.860585i | \(-0.329902\pi\) | ||||
0.509307 | + | 0.860585i | \(0.329902\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.32257e11 | −0.0347004 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.90436e11 | −0.0389379 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.02190e12 | 0.158767 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.32265e12 | 0.413381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.77488e13 | −1.36340 | −0.681701 | − | 0.731631i | \(-0.738760\pi\) | ||||
−0.681701 | + | 0.731631i | \(0.738760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.59964e13 | −1.97521 | −0.987607 | − | 0.156947i | \(-0.949835\pi\) | ||||
−0.987607 | + | 0.156947i | \(0.949835\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.64848e11 | −0.0499666 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.89884e12 | 0.587203 | 0.293602 | − | 0.955928i | \(-0.405146\pi\) | ||||
0.293602 | + | 0.955928i | \(0.405146\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.75453e12 | −0.129023 | −0.0645113 | − | 0.997917i | \(-0.520549\pi\) | ||||
−0.0645113 | + | 0.997917i | \(0.520549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.08880e13 | 0.792035 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.16893e12 | 0.0841174 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.13683e12 | 0.0809294 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.50788e12 | 0.176621 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.22719e13 | 1.55177 | 0.775886 | − | 0.630873i | \(-0.217303\pi\) | ||||
0.775886 | + | 0.630873i | \(0.217303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.20896e12 | 0.152267 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.55593e13 | 1.06112 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.02084e12 | −0.0688818 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.38988e13 | −0.927898 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.82595e12 | −0.252729 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.58347e13 | 1.68857 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.05383e13 | −0.681555 | −0.340777 | − | 0.940144i | \(-0.610690\pi\) | ||||
−0.340777 | + | 0.940144i | \(0.610690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.74783e11 | 0.0239846 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.26793e13 | −0.802936 | −0.401468 | − | 0.915873i | \(-0.631500\pi\) | ||||
−0.401468 | + | 0.915873i | \(0.631500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.77348e13 | −1.11136 | −0.555682 | − | 0.831395i | \(-0.687543\pi\) | ||||
−0.555682 | + | 0.831395i | \(0.687543\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.42858e12 | 0.398658 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.02098e12 | 0.124026 | 0.0620131 | − | 0.998075i | \(-0.480248\pi\) | ||||
0.0620131 | + | 0.998075i | \(0.480248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.23079e12 | 0.0747501 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.30683e12 | 0.318969 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.87284e11 | 0.0289863 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.71991e13 | −2.19004 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.25740e12 | −0.248074 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.93001e12 | 0.168979 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.27496e12 | 0.472354 | 0.236177 | − | 0.971710i | \(-0.424105\pi\) | ||||
0.236177 | + | 0.971710i | \(0.424105\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.39524e12 | 0.0788316 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.74131e13 | −1.53309 | −0.766543 | − | 0.642193i | \(-0.778025\pi\) | ||||
−0.766543 | + | 0.642193i | \(0.778025\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.35680e12 | −0.296539 | −0.148270 | − | 0.988947i | \(-0.547370\pi\) | ||||
−0.148270 | + | 0.988947i | \(0.547370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.07350e11 | 0.0278012 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.91189e12 | 0.320679 | 0.160339 | − | 0.987062i | \(-0.448741\pi\) | ||||
0.160339 | + | 0.987062i | \(0.448741\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.20599e13 | 0.647569 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.82405e11 | −0.00969589 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.76389e12 | 0.303308 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.39387e12 | −0.176804 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.47907e13 | −0.762822 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.92938e13 | 0.985144 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.17927e13 | −0.596142 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.15941e12 | 0.108079 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.19521e12 | 0.108782 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.45625e13 | 0.714502 | 0.357251 | − | 0.934008i | \(-0.383714\pi\) | ||||
0.357251 | + | 0.934008i | \(0.383714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.36703e12 | 0.0664109 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.50127e12 | 0.457035 | 0.228517 | − | 0.973540i | \(-0.426612\pi\) | ||||
0.228517 | + | 0.973540i | \(0.426612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.66882e12 | −0.127116 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.77542e11 | 0.00837346 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.23568e12 | 0.337923 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.17748e13 | −1.00701 | −0.503506 | − | 0.863992i | \(-0.667957\pi\) | ||||
−0.503506 | + | 0.863992i | \(0.667957\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.63159e12 | −0.349500 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.06635e13 | 1.39064 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.74313e13 | −1.68112 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.61452e12 | 0.338675 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.48742e13 | −1.53615 | −0.768075 | − | 0.640360i | \(-0.778785\pi\) | ||||
−0.768075 | + | 0.640360i | \(0.778785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.28574e12 | 0.0997135 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.44238e12 | 0.278342 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.23785e11 | −0.00529682 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.31211e12 | −0.225133 | −0.112566 | − | 0.993644i | \(-0.535907\pi\) | ||||
−0.112566 | + | 0.993644i | \(0.535907\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.08505e12 | 0.213452 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.60648e11 | −0.0274673 | −0.0137337 | − | 0.999906i | \(-0.504372\pi\) | ||||
−0.0137337 | + | 0.999906i | \(0.504372\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.78639e13 | −0.735654 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00273e11 | 0.0163273 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.16022e11 | 0.0289302 | 0.0144651 | − | 0.999895i | \(-0.495395\pi\) | ||||
0.0144651 | + | 0.999895i | \(0.495395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.67999e13 | −1.47282 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.68423e12 | 0.304641 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.31789e13 | −1.30300 | −0.651500 | − | 0.758649i | \(-0.725860\pi\) | ||||
−0.651500 | + | 0.758649i | \(0.725860\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.57584e11 | −0.0178015 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.40330e12 | −0.0540812 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.88506e13 | −1.10147 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.17057e12 | −0.157739 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.29963e12 | −0.161106 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.63325e12 | 0.134872 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.96440e13 | −1.45800 | −0.729002 | − | 0.684511i | \(-0.760016\pi\) | ||||
−0.729002 | + | 0.684511i | \(0.760016\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.40593e12 | −0.306287 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.13178e13 | −1.85260 | −0.926300 | − | 0.376786i | \(-0.877029\pi\) | ||||
−0.926300 | + | 0.376786i | \(0.877029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.95746e13 | −0.700140 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.14300e13 | 0.759453 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.68486e12 | 0.0942750 | 0.0471375 | − | 0.998888i | \(-0.484990\pi\) | ||||
0.0471375 | + | 0.998888i | \(0.484990\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.69489e12 | −0.0937603 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.95660e12 | −0.0674514 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.79462e12 | −0.129622 | −0.0648109 | − | 0.997898i | \(-0.520644\pi\) | ||||
−0.0648109 | + | 0.997898i | \(0.520644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.20362e12 | 0.108437 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.15591e12 | 0.206474 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.00063e12 | −0.199440 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.48099e12 | −0.246393 | −0.123196 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123196 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.41422e13 | −1.11434 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.37790e11 | 0.0303320 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.91760e13 | 1.57625 | 0.788125 | − | 0.615515i | \(-0.211052\pi\) | ||||
0.788125 | + | 0.615515i | \(0.211052\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.02695e13 | −0.326217 |
(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.b.1.3 | ✓ | 4 | |
4.3 | odd | 2 | 384.10.a.f.1.3 | yes | 4 | ||
8.3 | odd | 2 | 384.10.a.c.1.2 | yes | 4 | ||
8.5 | even | 2 | 384.10.a.g.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.a.b.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
384.10.a.c.1.2 | yes | 4 | 8.3 | odd | 2 | ||
384.10.a.f.1.3 | yes | 4 | 4.3 | odd | 2 | ||
384.10.a.g.1.2 | yes | 4 | 8.5 | even | 2 |