Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,10,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.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: | \(13.9059675764\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.203942560.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 83x^{2} + 1440 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7.63546\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −44.4771 | −1.96563 | −0.982815 | − | 0.184592i | \(-0.940904\pi\) | ||||
−0.982815 | + | 0.184592i | \(0.940904\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1466.22 | 2.86370 | ||||||||
\(5\) | 1050.62 | 0.751764 | 0.375882 | − | 0.926668i | \(-0.377340\pi\) | ||||
0.375882 | + | 0.926668i | \(0.377340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6591.86 | 1.03769 | 0.518844 | − | 0.854869i | \(-0.326362\pi\) | ||||
0.518844 | + | 0.854869i | \(0.326362\pi\) | |||||||
\(8\) | −42440.8 | −3.66335 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −46728.6 | −1.47769 | ||||||||
\(11\) | −14465.9 | −0.297906 | −0.148953 | − | 0.988844i | \(-0.547590\pi\) | ||||
−0.148953 | + | 0.988844i | \(0.547590\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5003.49 | 0.0485879 | 0.0242940 | − | 0.999705i | \(-0.492266\pi\) | ||||
0.0242940 | + | 0.999705i | \(0.492266\pi\) | |||||||
\(14\) | −293187. | −2.03971 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.13694e6 | 4.33709 | ||||||||
\(17\) | 444500. | 1.29078 | 0.645389 | − | 0.763854i | \(-0.276695\pi\) | ||||
0.645389 | + | 0.763854i | \(0.276695\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −487431. | −0.858069 | −0.429035 | − | 0.903288i | \(-0.641146\pi\) | ||||
−0.429035 | + | 0.903288i | \(0.641146\pi\) | |||||||
\(20\) | 1.54044e6 | 2.15283 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 643402. | 0.585572 | ||||||||
\(23\) | 67304.5 | 0.0501498 | 0.0250749 | − | 0.999686i | \(-0.492018\pi\) | ||||
0.0250749 | + | 0.999686i | \(0.492018\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −849319. | −0.434852 | ||||||||
\(26\) | −222541. | −0.0955059 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.66510e6 | 2.97163 | ||||||||
\(29\) | 3.41813e6 | 0.897425 | 0.448712 | − | 0.893676i | \(-0.351883\pi\) | ||||
0.448712 | + | 0.893676i | \(0.351883\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.45923e6 | 0.672747 | 0.336374 | − | 0.941729i | \(-0.390800\pi\) | ||||
0.336374 | + | 0.941729i | \(0.390800\pi\) | |||||||
\(32\) | −2.88383e7 | −4.86177 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.97701e7 | −2.53719 | ||||||||
\(35\) | 6.92555e6 | 0.780097 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.94510e6 | −0.346059 | −0.173030 | − | 0.984917i | \(-0.555356\pi\) | ||||
−0.173030 | + | 0.984917i | \(0.555356\pi\) | |||||||
\(38\) | 2.16796e7 | 1.68665 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.45892e7 | −2.75397 | ||||||||
\(41\) | 1.76061e7 | 0.973052 | 0.486526 | − | 0.873666i | \(-0.338264\pi\) | ||||
0.486526 | + | 0.873666i | \(0.338264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.30231e7 | 1.47302 | 0.736512 | − | 0.676425i | \(-0.236472\pi\) | ||||
0.736512 | + | 0.676425i | \(0.236472\pi\) | |||||||
\(44\) | −2.12102e7 | −0.853113 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.99351e6 | −0.0985759 | ||||||||
\(47\) | 3.71271e7 | 1.10982 | 0.554908 | − | 0.831912i | \(-0.312753\pi\) | ||||
0.554908 | + | 0.831912i | \(0.312753\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.09907e6 | 0.0767978 | ||||||||
\(50\) | 3.77753e7 | 0.854757 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.33620e6 | 0.139141 | ||||||||
\(53\) | 7.86818e7 | 1.36972 | 0.684861 | − | 0.728673i | \(-0.259863\pi\) | ||||
0.684861 | + | 0.728673i | \(0.259863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.51982e7 | −0.223955 | ||||||||
\(56\) | −2.79764e8 | −3.80142 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.52029e8 | −1.76401 | ||||||||
\(59\) | −5.13054e7 | −0.551225 | −0.275613 | − | 0.961269i | \(-0.588881\pi\) | ||||
−0.275613 | + | 0.961269i | \(0.588881\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.92723e7 | −0.178217 | −0.0891085 | − | 0.996022i | \(-0.528402\pi\) | ||||
−0.0891085 | + | 0.996022i | \(0.528402\pi\) | |||||||
\(62\) | −1.53857e8 | −1.32237 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00529e8 | 5.21935 | ||||||||
\(65\) | 5.25678e6 | 0.0365266 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.14838e8 | 1.30249 | 0.651245 | − | 0.758867i | \(-0.274247\pi\) | ||||
0.651245 | + | 0.758867i | \(0.274247\pi\) | |||||||
\(68\) | 6.51733e8 | 3.69640 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.08029e8 | −1.53338 | ||||||||
\(71\) | −3.25802e8 | −1.52157 | −0.760784 | − | 0.649006i | \(-0.775185\pi\) | ||||
−0.760784 | + | 0.649006i | \(0.775185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.57548e8 | 0.649322 | 0.324661 | − | 0.945830i | \(-0.394750\pi\) | ||||
0.324661 | + | 0.945830i | \(0.394750\pi\) | |||||||
\(74\) | 1.75467e8 | 0.680225 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.14680e8 | −2.45726 | ||||||||
\(77\) | −9.53573e7 | −0.309133 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.58634e7 | 0.103593 | 0.0517964 | − | 0.998658i | \(-0.483505\pi\) | ||||
0.0517964 | + | 0.998658i | \(0.483505\pi\) | |||||||
\(80\) | 1.19450e9 | 3.26047 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.83069e8 | −1.91266 | ||||||||
\(83\) | −8.07984e6 | −0.0186875 | −0.00934375 | − | 0.999956i | \(-0.502974\pi\) | ||||
−0.00934375 | + | 0.999956i | \(0.502974\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.67001e8 | 0.970359 | ||||||||
\(86\) | −1.46877e9 | −2.89542 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.13945e8 | 1.09133 | ||||||||
\(89\) | −9.43654e8 | −1.59425 | −0.797127 | − | 0.603812i | \(-0.793648\pi\) | ||||
−0.797127 | + | 0.603812i | \(0.793648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.29823e7 | 0.0504191 | ||||||||
\(92\) | 9.86830e7 | 0.143614 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.65131e9 | −2.18149 | ||||||||
\(95\) | −5.12106e8 | −0.645065 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.67052e8 | 1.10912 | 0.554558 | − | 0.832145i | \(-0.312887\pi\) | ||||
0.554558 | + | 0.832145i | \(0.312887\pi\) | |||||||
\(98\) | −1.37838e8 | −0.150956 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.24529e9 | −1.24529 | ||||||||
\(101\) | 1.68398e9 | 1.61024 | 0.805121 | − | 0.593110i | \(-0.202100\pi\) | ||||
0.805121 | + | 0.593110i | \(0.202100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00611e8 | 0.0880805 | 0.0440403 | − | 0.999030i | \(-0.485977\pi\) | ||||
0.0440403 | + | 0.999030i | \(0.485977\pi\) | |||||||
\(104\) | −2.12352e8 | −0.177995 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.49954e9 | −2.69237 | ||||||||
\(107\) | −5.50494e8 | −0.406000 | −0.203000 | − | 0.979179i | \(-0.565069\pi\) | ||||
−0.203000 | + | 0.979179i | \(0.565069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.31023e9 | 0.889055 | 0.444527 | − | 0.895765i | \(-0.353372\pi\) | ||||
0.444527 | + | 0.895765i | \(0.353372\pi\) | |||||||
\(110\) | 6.75972e8 | 0.440212 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.49457e9 | 4.50055 | ||||||||
\(113\) | 7.75402e7 | 0.0447377 | 0.0223689 | − | 0.999750i | \(-0.492879\pi\) | ||||
0.0223689 | + | 0.999750i | \(0.492879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.07116e7 | 0.0377008 | ||||||||
\(116\) | 5.01172e9 | 2.56996 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.28192e9 | 1.08351 | ||||||||
\(119\) | 2.93008e9 | 1.33943 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.14869e9 | −0.911252 | ||||||||
\(122\) | 8.57176e8 | 0.350309 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.07198e9 | 1.92655 | ||||||||
\(125\) | −2.94431e9 | −1.07867 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.89287e9 | −0.645661 | −0.322830 | − | 0.946457i | \(-0.604634\pi\) | ||||
−0.322830 | + | 0.946457i | \(0.604634\pi\) | |||||||
\(128\) | −1.63923e10 | −5.39755 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.33806e8 | −0.0717978 | ||||||||
\(131\) | 4.62187e9 | 1.37119 | 0.685593 | − | 0.727985i | \(-0.259543\pi\) | ||||
0.685593 | + | 0.727985i | \(0.259543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.21308e9 | −0.890409 | ||||||||
\(134\) | −9.55538e9 | −2.56022 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.88649e10 | −4.72857 | ||||||||
\(137\) | 6.82694e9 | 1.65571 | 0.827854 | − | 0.560944i | \(-0.189562\pi\) | ||||
0.827854 | + | 0.560944i | \(0.189562\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.87668e9 | 1.10805 | 0.554023 | − | 0.832501i | \(-0.313092\pi\) | ||||
0.554023 | + | 0.832501i | \(0.313092\pi\) | |||||||
\(140\) | 1.01544e10 | 2.23397 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.44907e10 | 2.99084 | ||||||||
\(143\) | −7.23801e7 | −0.0144746 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.59117e9 | 0.674651 | ||||||||
\(146\) | −7.00728e9 | −1.27633 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.78437e9 | −0.991011 | ||||||||
\(149\) | −7.64937e9 | −1.27142 | −0.635708 | − | 0.771930i | \(-0.719292\pi\) | ||||
−0.635708 | + | 0.771930i | \(0.719292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.19589e9 | −0.656791 | −0.328396 | − | 0.944540i | \(-0.606508\pi\) | ||||
−0.328396 | + | 0.944540i | \(0.606508\pi\) | |||||||
\(152\) | 2.06870e10 | 3.14341 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.24122e9 | 0.607642 | ||||||||
\(155\) | 3.63434e9 | 0.505747 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.60479e8 | −0.0998938 | −0.0499469 | − | 0.998752i | \(-0.515905\pi\) | ||||
−0.0499469 | + | 0.998752i | \(0.515905\pi\) | |||||||
\(158\) | −1.59510e9 | −0.203625 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.02981e10 | −3.65490 | ||||||||
\(161\) | 4.43662e8 | 0.0520398 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.55113e9 | −0.837853 | −0.418926 | − | 0.908020i | \(-0.637593\pi\) | ||||
−0.418926 | + | 0.908020i | \(0.637593\pi\) | |||||||
\(164\) | 2.58143e10 | 2.78653 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.59368e8 | 0.0367327 | ||||||||
\(167\) | −8.05764e9 | −0.801648 | −0.400824 | − | 0.916155i | \(-0.631276\pi\) | ||||
−0.400824 | + | 0.916155i | \(0.631276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.05795e10 | −0.997639 | ||||||||
\(170\) | −2.07709e10 | −1.90737 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.84190e10 | 4.21830 | ||||||||
\(173\) | −4.12318e9 | −0.349965 | −0.174982 | − | 0.984572i | \(-0.555987\pi\) | ||||
−0.174982 | + | 0.984572i | \(0.555987\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.59860e9 | −0.451240 | ||||||||
\(176\) | −1.64469e10 | −1.29204 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.19710e10 | 3.13371 | ||||||||
\(179\) | −2.46170e10 | −1.79224 | −0.896120 | − | 0.443811i | \(-0.853626\pi\) | ||||
−0.896120 | + | 0.443811i | \(0.853626\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.17661e9 | −0.289248 | −0.144624 | − | 0.989487i | \(-0.546197\pi\) | ||||
−0.144624 | + | 0.989487i | \(0.546197\pi\) | |||||||
\(182\) | −1.46696e9 | −0.0991054 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.85646e9 | −0.183716 | ||||||||
\(185\) | −4.14481e9 | −0.260155 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.43009e9 | −0.384530 | ||||||||
\(188\) | 5.44364e10 | 3.17818 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.27770e10 | 1.26796 | ||||||||
\(191\) | −1.46430e10 | −0.796122 | −0.398061 | − | 0.917359i | \(-0.630317\pi\) | ||||
−0.398061 | + | 0.917359i | \(0.630317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.58666e10 | 0.823144 | 0.411572 | − | 0.911377i | \(-0.364980\pi\) | ||||
0.411572 | + | 0.911377i | \(0.364980\pi\) | |||||||
\(194\) | −4.30117e10 | −2.18011 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.54390e9 | 0.219926 | ||||||||
\(197\) | 4.01582e9 | 0.189966 | 0.0949832 | − | 0.995479i | \(-0.469720\pi\) | ||||
0.0949832 | + | 0.995479i | \(0.469720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.90309e10 | −1.76429 | −0.882144 | − | 0.470980i | \(-0.843901\pi\) | ||||
−0.882144 | + | 0.470980i | \(0.843901\pi\) | |||||||
\(200\) | 3.60458e10 | 1.59301 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.48987e10 | −3.16514 | ||||||||
\(203\) | 2.25319e10 | 0.931248 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.84973e10 | 0.731505 | ||||||||
\(206\) | −4.47491e9 | −0.173134 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.68869e9 | 0.210730 | ||||||||
\(209\) | 7.05114e9 | 0.255624 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.70099e10 | 0.938108 | 0.469054 | − | 0.883170i | \(-0.344595\pi\) | ||||
0.469054 | + | 0.883170i | \(0.344595\pi\) | |||||||
\(212\) | 1.15364e11 | 3.92248 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.44844e10 | 0.798046 | ||||||||
\(215\) | 3.46948e10 | 1.10737 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.28028e10 | 0.698102 | ||||||||
\(218\) | −5.82753e10 | −1.74755 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.22838e10 | −0.641340 | ||||||||
\(221\) | 2.22405e9 | 0.0627162 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.73036e10 | −1.55171 | −0.775854 | − | 0.630912i | \(-0.782681\pi\) | ||||
−0.775854 | + | 0.630912i | \(0.782681\pi\) | |||||||
\(224\) | −1.90098e11 | −5.04500 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.44877e9 | −0.0879379 | ||||||||
\(227\) | −3.50057e10 | −0.875029 | −0.437514 | − | 0.899211i | \(-0.644141\pi\) | ||||
−0.437514 | + | 0.899211i | \(0.644141\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.47530e10 | 1.55597 | 0.777984 | − | 0.628284i | \(-0.216243\pi\) | ||||
0.777984 | + | 0.628284i | \(0.216243\pi\) | |||||||
\(230\) | −3.14505e9 | −0.0741058 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.45068e11 | −3.28758 | ||||||||
\(233\) | 5.91061e10 | 1.31380 | 0.656902 | − | 0.753976i | \(-0.271866\pi\) | ||||
0.656902 | + | 0.753976i | \(0.271866\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.90066e10 | 0.834319 | ||||||||
\(236\) | −7.52248e10 | −1.57855 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.30322e11 | −2.63281 | ||||||||
\(239\) | 4.04702e10 | 0.802315 | 0.401158 | − | 0.916009i | \(-0.368608\pi\) | ||||
0.401158 | + | 0.916009i | \(0.368608\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.37089e9 | 0.0643677 | 0.0321839 | − | 0.999482i | \(-0.489754\pi\) | ||||
0.0321839 | + | 0.999482i | \(0.489754\pi\) | |||||||
\(242\) | 9.55674e10 | 1.79119 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.82573e10 | −0.510361 | ||||||||
\(245\) | 3.25595e9 | 0.0577338 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.43886e9 | −0.0416918 | ||||||||
\(248\) | −1.46813e11 | −2.46451 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.30954e11 | 2.12026 | ||||||||
\(251\) | 4.69295e10 | 0.746301 | 0.373151 | − | 0.927771i | \(-0.378277\pi\) | ||||
0.373151 | + | 0.927771i | \(0.378277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.73621e8 | −0.0149399 | ||||||||
\(254\) | 8.41895e10 | 1.26913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.70414e11 | 5.39023 | ||||||||
\(257\) | 1.74946e10 | 0.250152 | 0.125076 | − | 0.992147i | \(-0.460083\pi\) | ||||
0.125076 | + | 0.992147i | \(0.460083\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.60056e10 | −0.359102 | ||||||||
\(260\) | 7.70757e9 | 0.104601 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.05567e11 | −2.69525 | ||||||||
\(263\) | −1.00629e11 | −1.29695 | −0.648476 | − | 0.761235i | \(-0.724593\pi\) | ||||
−0.648476 | + | 0.761235i | \(0.724593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.26648e10 | 1.02971 | ||||||||
\(266\) | 1.42909e11 | 1.75021 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.14999e11 | 3.72995 | ||||||||
\(269\) | −2.18445e10 | −0.254365 | −0.127182 | − | 0.991879i | \(-0.540593\pi\) | ||||
−0.127182 | + | 0.991879i | \(0.540593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.19462e10 | 0.585049 | 0.292524 | − | 0.956258i | \(-0.405505\pi\) | ||||
0.292524 | + | 0.956258i | \(0.405505\pi\) | |||||||
\(272\) | 5.05371e11 | 5.59822 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.03643e11 | −3.25451 | ||||||||
\(275\) | 1.22862e10 | 0.129545 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.37704e9 | −0.0854932 | −0.0427466 | − | 0.999086i | \(-0.513611\pi\) | ||||
−0.0427466 | + | 0.999086i | \(0.513611\pi\) | |||||||
\(278\) | −2.16901e11 | −2.17801 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.93926e11 | −2.85777 | ||||||||
\(281\) | −8.16325e10 | −0.781061 | −0.390530 | − | 0.920590i | \(-0.627708\pi\) | ||||
−0.390530 | + | 0.920590i | \(0.627708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.11475e10 | −0.566683 | −0.283341 | − | 0.959019i | \(-0.591443\pi\) | ||||
−0.283341 | + | 0.959019i | \(0.591443\pi\) | |||||||
\(284\) | −4.77696e11 | −4.35732 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.21926e9 | 0.0284517 | ||||||||
\(287\) | 1.16057e11 | 1.00972 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.89921e10 | 0.666106 | ||||||||
\(290\) | −1.59725e11 | −1.32612 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.30999e11 | 1.85946 | ||||||||
\(293\) | −1.73459e11 | −1.37497 | −0.687486 | − | 0.726198i | \(-0.741286\pi\) | ||||
−0.687486 | + | 0.726198i | \(0.741286\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.39026e10 | −0.414391 | ||||||||
\(296\) | 1.67433e11 | 1.26774 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.40222e11 | 2.49913 | ||||||||
\(299\) | 3.36758e8 | 0.00243667 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.17684e11 | 1.52854 | ||||||||
\(302\) | 1.86621e11 | 1.29101 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.54182e11 | −3.72153 | ||||||||
\(305\) | −2.02479e10 | −0.133977 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.89397e11 | −1.21689 | −0.608443 | − | 0.793598i | \(-0.708205\pi\) | ||||
−0.608443 | + | 0.793598i | \(0.708205\pi\) | |||||||
\(308\) | −1.39814e11 | −0.885266 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.61645e11 | −0.994112 | ||||||||
\(311\) | −1.47676e11 | −0.895137 | −0.447569 | − | 0.894250i | \(-0.647710\pi\) | ||||
−0.447569 | + | 0.894250i | \(0.647710\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.64248e9 | 0.0273402 | 0.0136701 | − | 0.999907i | \(-0.495649\pi\) | ||||
0.0136701 | + | 0.999907i | \(0.495649\pi\) | |||||||
\(314\) | 3.38239e10 | 0.196354 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.25835e10 | 0.296659 | ||||||||
\(317\) | −1.76364e11 | −0.980943 | −0.490471 | − | 0.871457i | \(-0.663175\pi\) | ||||
−0.490471 | + | 0.871457i | \(0.663175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.94464e10 | −0.267348 | ||||||||
\(320\) | 7.35991e11 | 3.92372 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.97328e10 | −0.102291 | ||||||||
\(323\) | −2.16663e11 | −1.10758 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.24956e9 | −0.0211285 | ||||||||
\(326\) | 3.35853e11 | 1.64691 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.47217e11 | −3.56463 | ||||||||
\(329\) | 2.44737e11 | 1.15164 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.09857e11 | −1.41885 | −0.709423 | − | 0.704783i | \(-0.751044\pi\) | ||||
−0.709423 | + | 0.704783i | \(0.751044\pi\) | |||||||
\(332\) | −1.18468e10 | −0.0535155 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.58381e11 | 1.57574 | ||||||||
\(335\) | 2.25714e11 | 0.979165 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.13658e11 | 1.32471 | 0.662356 | − | 0.749189i | \(-0.269557\pi\) | ||||
0.662356 | + | 0.749189i | \(0.269557\pi\) | |||||||
\(338\) | 4.70544e11 | 1.96099 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.84724e11 | 2.77882 | ||||||||
\(341\) | −5.00409e10 | −0.200415 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.45577e11 | −0.957996 | ||||||||
\(344\) | −1.40153e12 | −5.39620 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.83387e11 | 0.687902 | ||||||||
\(347\) | 8.10841e10 | 0.300229 | 0.150115 | − | 0.988669i | \(-0.452036\pi\) | ||||
0.150115 | + | 0.988669i | \(0.452036\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.68777e11 | 0.969791 | 0.484896 | − | 0.874572i | \(-0.338858\pi\) | ||||
0.484896 | + | 0.874572i | \(0.338858\pi\) | |||||||
\(350\) | 2.49010e11 | 0.886972 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.17172e11 | 1.44835 | ||||||||
\(353\) | 3.92960e11 | 1.34698 | 0.673491 | − | 0.739195i | \(-0.264794\pi\) | ||||
0.673491 | + | 0.739195i | \(0.264794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.42295e11 | −1.14386 | ||||||||
\(356\) | −1.38360e12 | −4.56547 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.09489e12 | 3.52288 | ||||||||
\(359\) | −2.48781e11 | −0.790484 | −0.395242 | − | 0.918577i | \(-0.629339\pi\) | ||||
−0.395242 | + | 0.918577i | \(0.629339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50984e10 | −0.263718 | ||||||||
\(362\) | 1.85764e11 | 0.568555 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.83592e10 | 0.144385 | ||||||||
\(365\) | 1.65523e11 | 0.488136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.25248e11 | −0.935875 | −0.467937 | − | 0.883762i | \(-0.655003\pi\) | ||||
−0.467937 | + | 0.883762i | \(0.655003\pi\) | |||||||
\(368\) | 7.65214e10 | 0.217504 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.84349e11 | 0.511368 | ||||||||
\(371\) | 5.18660e11 | 1.42135 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.55232e11 | −0.950217 | −0.475108 | − | 0.879927i | \(-0.657591\pi\) | ||||
−0.475108 | + | 0.879927i | \(0.657591\pi\) | |||||||
\(374\) | 2.85992e11 | 0.755844 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.57571e12 | −4.06565 | ||||||||
\(377\) | 1.71026e10 | 0.0436040 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.17590e11 | −1.03962 | −0.519809 | − | 0.854283i | \(-0.673997\pi\) | ||||
−0.519809 | + | 0.854283i | \(0.673997\pi\) | |||||||
\(380\) | −7.50858e11 | −1.84727 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.51279e11 | 1.56488 | ||||||||
\(383\) | 8.39723e9 | 0.0199408 | 0.00997038 | − | 0.999950i | \(-0.496826\pi\) | ||||
0.00997038 | + | 0.999950i | \(0.496826\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00184e11 | −0.232395 | ||||||||
\(386\) | −7.05701e11 | −1.61800 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.41791e12 | 3.17618 | ||||||||
\(389\) | 4.47803e11 | 0.991549 | 0.495774 | − | 0.868451i | \(-0.334884\pi\) | ||||
0.495774 | + | 0.868451i | \(0.334884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.99168e10 | 0.0647322 | ||||||||
\(392\) | −1.31527e11 | −0.281337 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.78612e11 | −0.373404 | ||||||||
\(395\) | 3.76788e10 | 0.0778773 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.93449e11 | 1.80515 | 0.902573 | − | 0.430537i | \(-0.141676\pi\) | ||||
0.902573 | + | 0.430537i | \(0.141676\pi\) | |||||||
\(398\) | 1.73598e12 | 3.46794 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.65628e11 | −1.88599 | ||||||||
\(401\) | −2.21707e10 | −0.0428183 | −0.0214092 | − | 0.999771i | \(-0.506815\pi\) | ||||
−0.0214092 | + | 0.999771i | \(0.506815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.73082e10 | 0.0326874 | ||||||||
\(404\) | 2.46908e12 | 4.61126 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.00215e12 | −1.83049 | ||||||||
\(407\) | 5.70695e10 | 0.103093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.79724e11 | 0.847688 | 0.423844 | − | 0.905735i | \(-0.360680\pi\) | ||||
0.423844 | + | 0.905735i | \(0.360680\pi\) | |||||||
\(410\) | −8.22709e11 | −1.43787 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.47518e11 | 0.252236 | ||||||||
\(413\) | −3.38198e11 | −0.572000 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.48885e9 | −0.0140486 | ||||||||
\(416\) | −1.44292e11 | −0.236223 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.13614e11 | −0.502462 | ||||||||
\(419\) | −8.35323e11 | −1.32401 | −0.662005 | − | 0.749500i | \(-0.730294\pi\) | ||||
−0.662005 | + | 0.749500i | \(0.730294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.06281e11 | 0.320029 | 0.160014 | − | 0.987115i | \(-0.448846\pi\) | ||||
0.160014 | + | 0.987115i | \(0.448846\pi\) | |||||||
\(422\) | −1.20133e12 | −1.84397 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.33932e12 | −5.01778 | ||||||||
\(425\) | −3.77522e11 | −0.561297 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.27040e11 | −0.184934 | ||||||||
\(428\) | −8.07144e11 | −1.16266 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.54312e12 | −2.17667 | ||||||||
\(431\) | −3.46311e11 | −0.483414 | −0.241707 | − | 0.970349i | \(-0.577707\pi\) | ||||
−0.241707 | + | 0.970349i | \(0.577707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.41282e9 | −0.0101342 | −0.00506708 | − | 0.999987i | \(-0.501613\pi\) | ||||
−0.00506708 | + | 0.999987i | \(0.501613\pi\) | |||||||
\(434\) | −1.01420e12 | −1.37221 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.92108e12 | 2.54599 | ||||||||
\(437\) | −3.28063e10 | −0.0430320 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.59814e11 | 1.23338 | 0.616690 | − | 0.787206i | \(-0.288473\pi\) | ||||
0.616690 | + | 0.787206i | \(0.288473\pi\) | |||||||
\(440\) | 6.45024e11 | 0.820425 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.89194e10 | −0.123277 | ||||||||
\(443\) | −2.88512e11 | −0.355915 | −0.177958 | − | 0.984038i | \(-0.556949\pi\) | ||||
−0.177958 | + | 0.984038i | \(0.556949\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.91423e11 | −1.19850 | ||||||||
\(446\) | 2.54870e12 | 3.05008 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.61780e12 | 5.41606 | ||||||||
\(449\) | −1.00029e12 | −1.16150 | −0.580749 | − | 0.814083i | \(-0.697240\pi\) | ||||
−0.580749 | + | 0.814083i | \(0.697240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.54688e11 | −0.289878 | ||||||||
\(452\) | 1.13691e11 | 0.128116 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.55695e12 | 1.71998 | ||||||||
\(455\) | 3.46520e10 | 0.0379033 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.83855e11 | 0.304420 | 0.152210 | − | 0.988348i | \(-0.451361\pi\) | ||||
0.152210 | + | 0.988348i | \(0.451361\pi\) | |||||||
\(458\) | −2.88003e12 | −3.05846 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.03678e11 | 0.107964 | ||||||||
\(461\) | 6.45819e8 | 0.000665973 0 | 0.000332987 | − | 1.00000i | \(-0.499894\pi\) | ||||
0.000332987 | 1.00000i | \(0.499894\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.83071e11 | −0.488536 | −0.244268 | − | 0.969708i | \(-0.578548\pi\) | ||||
−0.244268 | + | 0.969708i | \(0.578548\pi\) | |||||||
\(464\) | 3.88622e12 | 3.89222 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.62887e12 | −2.58245 | ||||||||
\(467\) | 7.10128e11 | 0.690893 | 0.345447 | − | 0.938438i | \(-0.387727\pi\) | ||||
0.345447 | + | 0.938438i | \(0.387727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.41618e12 | 1.35158 | ||||||||
\(470\) | −1.73490e12 | −1.63996 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.17744e12 | 2.01933 | ||||||||
\(473\) | −4.77709e11 | −0.438822 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.13985e11 | 0.373133 | ||||||||
\(476\) | 4.29613e12 | 3.83572 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.80000e12 | −1.57706 | ||||||||
\(479\) | −1.54619e10 | −0.0134200 | −0.00671002 | − | 0.999977i | \(-0.502136\pi\) | ||||
−0.00671002 | + | 0.999977i | \(0.502136\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.97393e10 | −0.0168143 | ||||||||
\(482\) | −1.49928e11 | −0.126523 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.15044e12 | −2.60956 | ||||||||
\(485\) | 1.01601e12 | 0.833793 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.65405e11 | −0.455490 | −0.227745 | − | 0.973721i | \(-0.573135\pi\) | ||||
−0.227745 | + | 0.973721i | \(0.573135\pi\) | |||||||
\(488\) | 8.17932e11 | 0.652872 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.44815e11 | −0.113483 | ||||||||
\(491\) | 3.72733e11 | 0.289421 | 0.144711 | − | 0.989474i | \(-0.453775\pi\) | ||||
0.144711 | + | 0.989474i | \(0.453775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.51936e12 | 1.15838 | ||||||||
\(494\) | 1.08473e11 | 0.0819506 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.93295e12 | 2.91777 | ||||||||
\(497\) | −2.14764e12 | −1.57891 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.57615e11 | −0.258204 | −0.129102 | − | 0.991631i | \(-0.541209\pi\) | ||||
−0.129102 | + | 0.991631i | \(0.541209\pi\) | |||||||
\(500\) | −4.31699e12 | −3.08899 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.08729e12 | −1.46695 | ||||||||
\(503\) | 1.08145e12 | 0.753267 | 0.376633 | − | 0.926362i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926362i | \(0.377082\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.76923e12 | 1.21052 | ||||||||
\(506\) | 4.33039e10 | 0.0293663 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.77536e12 | −1.84898 | ||||||||
\(509\) | 6.97300e11 | 0.460458 | 0.230229 | − | 0.973137i | \(-0.426053\pi\) | ||||
0.230229 | + | 0.973137i | \(0.426053\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.03853e12 | 0.673794 | ||||||||
\(512\) | −8.08206e12 | −5.19765 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.78108e11 | −0.491706 | ||||||||
\(515\) | 1.05705e11 | 0.0662157 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.37078e11 | −0.330621 | ||||||||
\(518\) | 1.15665e12 | 0.705861 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.23102e11 | −0.133810 | ||||||||
\(521\) | 1.96135e12 | 1.16623 | 0.583116 | − | 0.812389i | \(-0.301833\pi\) | ||||
0.583116 | + | 0.812389i | \(0.301833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.03647e10 | −0.0352797 | −0.0176399 | − | 0.999844i | \(-0.505615\pi\) | ||||
−0.0176399 | + | 0.999844i | \(0.505615\pi\) | |||||||
\(524\) | 6.77665e12 | 3.92667 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.47570e12 | 2.54933 | ||||||||
\(527\) | 1.53763e12 | 0.868367 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.79662e12 | −0.997485 | ||||||||
\(530\) | −3.67669e12 | −2.02402 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.71107e12 | −2.54987 | ||||||||
\(533\) | 8.80920e10 | 0.0472785 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.78361e11 | −0.305216 | ||||||||
\(536\) | −9.11790e12 | −4.77148 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.71580e11 | 0.499987 | ||||||||
\(539\) | −4.48308e10 | −0.0228785 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.58437e12 | −0.795185 | −0.397592 | − | 0.917562i | \(-0.630154\pi\) | ||||
−0.397592 | + | 0.917562i | \(0.630154\pi\) | |||||||
\(542\) | −2.31042e12 | −1.14999 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.28186e13 | −6.27546 | ||||||||
\(545\) | 1.37656e12 | 0.668359 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.47236e12 | 0.703189 | 0.351595 | − | 0.936152i | \(-0.385640\pi\) | ||||
0.351595 | + | 0.936152i | \(0.385640\pi\) | |||||||
\(548\) | 1.00098e13 | 4.74146 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.46454e11 | −0.254637 | ||||||||
\(551\) | −1.66611e12 | −0.770052 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.36407e11 | 0.107497 | ||||||||
\(554\) | 3.72587e11 | 0.168048 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.15027e12 | 3.17311 | ||||||||
\(557\) | 1.23459e12 | 0.543470 | 0.271735 | − | 0.962372i | \(-0.412403\pi\) | ||||
0.271735 | + | 0.962372i | \(0.412403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.65231e11 | 0.0715711 | ||||||||
\(560\) | 7.87396e12 | 3.38335 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.63078e12 | 1.53528 | ||||||||
\(563\) | −3.22798e11 | −0.135407 | −0.0677037 | − | 0.997705i | \(-0.521567\pi\) | ||||
−0.0677037 | + | 0.997705i | \(0.521567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.14654e10 | 0.0336322 | ||||||||
\(566\) | 2.71967e12 | 1.11389 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.38273e13 | 5.57404 | ||||||||
\(569\) | 1.51796e12 | 0.607091 | 0.303546 | − | 0.952817i | \(-0.401830\pi\) | ||||
0.303546 | + | 0.952817i | \(0.401830\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.04069e11 | 0.237807 | 0.118903 | − | 0.992906i | \(-0.462062\pi\) | ||||
0.118903 | + | 0.992906i | \(0.462062\pi\) | |||||||
\(572\) | −1.06125e11 | −0.0414510 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.16188e12 | −1.98475 | ||||||||
\(575\) | −5.71630e10 | −0.0218077 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.16132e12 | −1.56293 | −0.781466 | − | 0.623948i | \(-0.785528\pi\) | ||||
−0.781466 | + | 0.623948i | \(0.785528\pi\) | |||||||
\(578\) | −3.51334e12 | −1.30932 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.26542e12 | 1.93200 | ||||||||
\(581\) | −5.32612e10 | −0.0193918 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.13820e12 | −0.408048 | ||||||||
\(584\) | −6.68646e12 | −2.37869 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.71498e12 | 2.70269 | ||||||||
\(587\) | −1.29792e12 | −0.451207 | −0.225604 | − | 0.974219i | \(-0.572435\pi\) | ||||
−0.225604 | + | 0.974219i | \(0.572435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.68614e12 | −0.577264 | ||||||||
\(590\) | 2.39743e12 | 0.814540 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.48536e12 | −1.50089 | ||||||||
\(593\) | −6.89642e11 | −0.229022 | −0.114511 | − | 0.993422i | \(-0.536530\pi\) | ||||
−0.114511 | + | 0.993422i | \(0.536530\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.07841e12 | 1.00693 | ||||||||
\(596\) | −1.12156e13 | −3.64096 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.49780e10 | −0.00478960 | ||||||||
\(599\) | 6.81664e11 | 0.216346 | 0.108173 | − | 0.994132i | \(-0.465500\pi\) | ||||
0.108173 | + | 0.994132i | \(0.465500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.73397e12 | −1.48010 | −0.740049 | − | 0.672553i | \(-0.765198\pi\) | ||||
−0.740049 | + | 0.672553i | \(0.765198\pi\) | |||||||
\(602\) | −9.68195e12 | −3.00454 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.15208e12 | −1.88086 | ||||||||
\(605\) | −2.25745e12 | −0.685046 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.38422e12 | −1.01183 | −0.505917 | − | 0.862582i | \(-0.668846\pi\) | ||||
−0.505917 | + | 0.862582i | \(0.668846\pi\) | |||||||
\(608\) | 1.40567e13 | 4.17173 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.00568e11 | 0.263349 | ||||||||
\(611\) | 1.85765e11 | 0.0539237 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.77900e12 | −0.794906 | −0.397453 | − | 0.917622i | \(-0.630106\pi\) | ||||
−0.397453 | + | 0.917622i | \(0.630106\pi\) | |||||||
\(614\) | 8.42382e12 | 2.39195 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.04704e12 | 1.13246 | ||||||||
\(617\) | −5.70613e12 | −1.58511 | −0.792554 | − | 0.609802i | \(-0.791249\pi\) | ||||
−0.792554 | + | 0.609802i | \(0.791249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.70022e12 | 1.56057 | 0.780285 | − | 0.625424i | \(-0.215074\pi\) | ||||
0.780285 | + | 0.625424i | \(0.215074\pi\) | |||||||
\(620\) | 5.32873e12 | 1.44831 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.56823e12 | 1.75951 | ||||||||
\(623\) | −6.22044e12 | −1.65434 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.43453e12 | −0.376053 | ||||||||
\(626\) | −2.06484e11 | −0.0537406 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.11503e12 | −0.286066 | ||||||||
\(629\) | −1.75360e12 | −0.446685 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.58053e11 | −0.190356 | −0.0951782 | − | 0.995460i | \(-0.530342\pi\) | ||||
−0.0951782 | + | 0.995460i | \(0.530342\pi\) | |||||||
\(632\) | −1.52207e12 | −0.379497 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.84417e12 | 1.92817 | ||||||||
\(635\) | −1.98869e12 | −0.485384 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.55062e10 | 0.00373144 | ||||||||
\(638\) | 2.19924e12 | 0.525507 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.72222e13 | −4.05768 | ||||||||
\(641\) | 3.07750e12 | 0.720007 | 0.360003 | − | 0.932951i | \(-0.382776\pi\) | ||||
0.360003 | + | 0.932951i | \(0.382776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.10425e12 | 0.485455 | 0.242727 | − | 0.970095i | \(-0.421958\pi\) | ||||
0.242727 | + | 0.970095i | \(0.421958\pi\) | |||||||
\(644\) | 6.50505e11 | 0.149027 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.63655e12 | 2.17709 | ||||||||
\(647\) | 1.41884e12 | 0.318319 | 0.159160 | − | 0.987253i | \(-0.449122\pi\) | ||||
0.159160 | + | 0.987253i | \(0.449122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.42180e11 | 0.164213 | ||||||||
\(650\) | 1.89008e11 | 0.0415309 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.10716e13 | −2.39936 | ||||||||
\(653\) | −3.40288e11 | −0.0732382 | −0.0366191 | − | 0.999329i | \(-0.511659\pi\) | ||||
−0.0366191 | + | 0.999329i | \(0.511659\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.85583e12 | 1.03081 | ||||||||
\(656\) | 2.00171e13 | 4.22022 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.08852e13 | −2.26371 | ||||||||
\(659\) | 4.62024e12 | 0.954290 | 0.477145 | − | 0.878825i | \(-0.341672\pi\) | ||||
0.477145 | + | 0.878825i | \(0.341672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.63497e12 | −0.944365 | −0.472183 | − | 0.881501i | \(-0.656534\pi\) | ||||
−0.472183 | + | 0.881501i | \(0.656534\pi\) | |||||||
\(662\) | 1.37815e13 | 2.78893 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.42915e11 | 0.0684589 | ||||||||
\(665\) | −3.37573e12 | −0.669377 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.30056e11 | 0.0450057 | ||||||||
\(668\) | −1.18142e13 | −2.29568 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.00391e13 | −1.92468 | ||||||||
\(671\) | 2.78791e11 | 0.0530918 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00517e13 | −1.88874 | −0.944370 | − | 0.328886i | \(-0.893327\pi\) | ||||
−0.944370 | + | 0.328886i | \(0.893327\pi\) | |||||||
\(674\) | −1.39506e13 | −2.60390 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.55118e13 | −2.85694 | ||||||||
\(677\) | 8.83179e12 | 1.61584 | 0.807922 | − | 0.589289i | \(-0.200592\pi\) | ||||
0.807922 | + | 0.589289i | \(0.200592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.37467e12 | 1.15092 | ||||||||
\(680\) | −1.98199e13 | −3.55477 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.22568e12 | 0.393942 | ||||||||
\(683\) | −1.10788e13 | −1.94805 | −0.974027 | − | 0.226430i | \(-0.927294\pi\) | ||||
−0.974027 | + | 0.226430i | \(0.927294\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.17253e12 | 1.24470 | ||||||||
\(686\) | 1.09226e13 | 1.88307 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.75454e13 | 6.38864 | ||||||||
\(689\) | 3.93684e11 | 0.0665520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.32931e11 | −0.105610 | −0.0528050 | − | 0.998605i | \(-0.516816\pi\) | ||||
−0.0528050 | + | 0.998605i | \(0.516816\pi\) | |||||||
\(692\) | −6.04547e12 | −1.00220 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.60639e12 | −0.590140 | ||||||||
\(695\) | 5.12355e12 | 0.832988 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.82591e12 | 1.25599 | ||||||||
\(698\) | −1.19545e13 | −1.90625 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.20875e12 | −1.29222 | ||||||||
\(701\) | 3.84382e12 | 0.601219 | 0.300609 | − | 0.953747i | \(-0.402810\pi\) | ||||
0.300609 | + | 0.953747i | \(0.402810\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.92297e12 | 0.296943 | ||||||||
\(704\) | −1.01338e13 | −1.55487 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.74777e13 | −2.64767 | ||||||||
\(707\) | 1.11006e13 | 1.67093 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.15935e12 | −0.915433 | −0.457716 | − | 0.889098i | \(-0.651333\pi\) | ||||
−0.457716 | + | 0.889098i | \(0.651333\pi\) | |||||||
\(710\) | 1.52243e13 | 2.24840 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.00494e13 | 5.84031 | ||||||||
\(713\) | 2.32822e11 | 0.0337381 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.60441e10 | −0.0108815 | ||||||||
\(716\) | −3.60938e13 | −5.13245 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.10651e13 | 1.55380 | ||||||||
\(719\) | 6.51194e12 | 0.908721 | 0.454361 | − | 0.890818i | \(-0.349868\pi\) | ||||
0.454361 | + | 0.890818i | \(0.349868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.63217e11 | 0.0914001 | ||||||||
\(722\) | 3.78493e12 | 0.518371 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.12381e12 | −0.828321 | ||||||||
\(725\) | −2.90309e12 | −0.390247 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.05785e12 | 0.273218 | 0.136609 | − | 0.990625i | \(-0.456380\pi\) | ||||
0.136609 | + | 0.990625i | \(0.456380\pi\) | |||||||
\(728\) | −1.39980e12 | −0.184703 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.36200e12 | −0.959496 | ||||||||
\(731\) | 1.46788e13 | 1.90135 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.96245e12 | 1.01878 | 0.509388 | − | 0.860537i | \(-0.329872\pi\) | ||||
0.509388 | + | 0.860537i | \(0.329872\pi\) | |||||||
\(734\) | 1.44661e13 | 1.83958 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.94095e12 | −0.243817 | ||||||||
\(737\) | −3.10783e12 | −0.388019 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.20258e12 | −0.518341 | −0.259171 | − | 0.965832i | \(-0.583449\pi\) | ||||
−0.259171 | + | 0.965832i | \(0.583449\pi\) | |||||||
\(740\) | −6.07719e12 | −0.745006 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.30685e13 | −2.79384 | ||||||||
\(743\) | −5.46810e12 | −0.658244 | −0.329122 | − | 0.944287i | \(-0.606753\pi\) | ||||
−0.329122 | + | 0.944287i | \(0.606753\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.03659e12 | −0.955804 | ||||||||
\(746\) | 1.57997e13 | 1.86777 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.42791e12 | −1.10118 | ||||||||
\(749\) | −3.62878e12 | −0.421302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.47523e12 | 0.857521 | 0.428760 | − | 0.903418i | \(-0.358950\pi\) | ||||
0.428760 | + | 0.903418i | \(0.358950\pi\) | |||||||
\(752\) | 4.22114e13 | 4.81338 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.60675e11 | −0.0857093 | ||||||||
\(755\) | −4.40829e12 | −0.493752 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.40395e12 | 0.155389 | 0.0776947 | − | 0.996977i | \(-0.475244\pi\) | ||||
0.0776947 | + | 0.996977i | \(0.475244\pi\) | |||||||
\(758\) | 1.85732e13 | 2.04350 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.17342e13 | 2.36310 | ||||||||
\(761\) | 7.95047e12 | 0.859334 | 0.429667 | − | 0.902987i | \(-0.358631\pi\) | ||||
0.429667 | + | 0.902987i | \(0.358631\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.63686e12 | 0.922562 | ||||||||
\(764\) | −2.14698e13 | −2.27986 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.73485e11 | −0.0391961 | ||||||||
\(767\) | −2.56706e11 | −0.0267829 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.95899e12 | −0.717592 | −0.358796 | − | 0.933416i | \(-0.616813\pi\) | ||||
−0.358796 | + | 0.933416i | \(0.616813\pi\) | |||||||
\(770\) | 4.45592e12 | 0.456803 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.32639e13 | 2.35724 | ||||||||
\(773\) | −1.22597e13 | −1.23501 | −0.617506 | − | 0.786566i | \(-0.711857\pi\) | ||||
−0.617506 | + | 0.786566i | \(0.711857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.93799e12 | −0.292545 | ||||||||
\(776\) | −4.10424e13 | −4.06308 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.99170e13 | −1.94902 | ||||||||
\(779\) | −8.58177e12 | −0.834945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.71302e12 | 0.453283 | ||||||||
\(782\) | −1.33062e12 | −0.127240 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.52346e12 | 0.333079 | ||||||||
\(785\) | −7.98975e11 | −0.0750965 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.19814e13 | 1.11332 | 0.556662 | − | 0.830739i | \(-0.312082\pi\) | ||||
0.556662 | + | 0.830739i | \(0.312082\pi\) | |||||||
\(788\) | 5.88807e12 | 0.544007 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.67585e12 | −0.153078 | ||||||||
\(791\) | 5.11135e11 | 0.0464238 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.64288e10 | −0.00865919 | ||||||||
\(794\) | −3.97380e13 | −3.54825 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.72277e13 | −5.05240 | ||||||||
\(797\) | 2.90159e12 | 0.254726 | 0.127363 | − | 0.991856i | \(-0.459349\pi\) | ||||
0.127363 | + | 0.991856i | \(0.459349\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.65030e13 | 1.43253 | ||||||||
\(800\) | 2.44929e13 | 2.11415 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.86089e11 | 0.0841650 | ||||||||
\(803\) | −2.27908e12 | −0.193437 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.66121e11 | 0.0391217 | ||||||||
\(806\) | −7.69821e11 | −0.0642513 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.14695e13 | −5.89888 | ||||||||
\(809\) | 1.25435e13 | 1.02956 | 0.514779 | − | 0.857323i | \(-0.327874\pi\) | ||||
0.514779 | + | 0.857323i | \(0.327874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.31788e13 | −1.06975 | −0.534874 | − | 0.844932i | \(-0.679641\pi\) | ||||
−0.534874 | + | 0.844932i | \(0.679641\pi\) | |||||||
\(812\) | 3.30366e13 | 2.66682 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.53829e12 | −0.202643 | ||||||||
\(815\) | −7.93338e12 | −0.629867 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.60965e13 | −1.26396 | ||||||||
\(818\) | −2.13367e13 | −1.66624 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.71211e13 | 2.09481 | ||||||||
\(821\) | −1.39450e13 | −1.07121 | −0.535606 | − | 0.844468i | \(-0.679917\pi\) | ||||
−0.535606 | + | 0.844468i | \(0.679917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.81146e13 | 1.37635 | 0.688177 | − | 0.725543i | \(-0.258411\pi\) | ||||
0.688177 | + | 0.725543i | \(0.258411\pi\) | |||||||
\(824\) | −4.27003e12 | −0.322670 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.50421e13 | 1.12434 | ||||||||
\(827\) | −9.15727e12 | −0.680756 | −0.340378 | − | 0.940289i | \(-0.610555\pi\) | ||||
−0.340378 | + | 0.940289i | \(0.610555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.41975e13 | 1.04404 | 0.522020 | − | 0.852933i | \(-0.325179\pi\) | ||||
0.522020 | + | 0.852933i | \(0.325179\pi\) | |||||||
\(830\) | 3.77560e11 | 0.0276143 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.50509e12 | 0.253597 | ||||||||
\(833\) | 1.37753e12 | 0.0991289 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.46553e12 | −0.602650 | ||||||||
\(836\) | 1.03385e13 | 0.732030 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.71528e13 | 2.60251 | ||||||||
\(839\) | −2.26357e13 | −1.57712 | −0.788561 | − | 0.614956i | \(-0.789174\pi\) | ||||
−0.788561 | + | 0.614956i | \(0.789174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.82351e12 | −0.194629 | ||||||||
\(842\) | −9.17478e12 | −0.629059 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.96024e13 | 2.68646 | ||||||||
\(845\) | −1.11150e13 | −0.749989 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.41638e13 | −0.945596 | ||||||||
\(848\) | 8.94567e13 | 5.94062 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.67911e13 | 1.10330 | ||||||||
\(851\) | −2.65523e11 | −0.0173548 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.75478e13 | −1.78163 | −0.890813 | − | 0.454370i | \(-0.849864\pi\) | ||||
−0.890813 | + | 0.454370i | \(0.849864\pi\) | |||||||
\(854\) | 5.65039e12 | 0.363511 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.33634e13 | 1.48732 | ||||||||
\(857\) | 1.19508e13 | 0.756801 | 0.378401 | − | 0.925642i | \(-0.376474\pi\) | ||||
0.378401 | + | 0.925642i | \(0.376474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.68633e13 | −1.05675 | −0.528377 | − | 0.849010i | \(-0.677199\pi\) | ||||
−0.528377 | + | 0.849010i | \(0.677199\pi\) | |||||||
\(860\) | 5.08700e13 | 3.17117 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.54029e13 | 0.950213 | ||||||||
\(863\) | 2.70257e13 | 1.65855 | 0.829275 | − | 0.558840i | \(-0.188753\pi\) | ||||
0.829275 | + | 0.558840i | \(0.188753\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.33190e12 | −0.263091 | ||||||||
\(866\) | 3.29701e11 | 0.0199200 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.34338e13 | 1.99916 | ||||||||
\(869\) | −5.18797e11 | −0.0308609 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.07494e12 | 0.0632853 | ||||||||
\(872\) | −5.56072e13 | −3.25692 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.45913e12 | 0.0845849 | ||||||||
\(875\) | −1.94085e13 | −1.11932 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.47392e13 | 0.841350 | 0.420675 | − | 0.907211i | \(-0.361793\pi\) | ||||
0.420675 | + | 0.907211i | \(0.361793\pi\) | |||||||
\(878\) | −4.26898e13 | −2.42437 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.72795e13 | −0.971312 | ||||||||
\(881\) | 2.25153e13 | 1.25918 | 0.629589 | − | 0.776928i | \(-0.283223\pi\) | ||||
0.629589 | + | 0.776928i | \(0.283223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.11103e13 | −1.16861 | −0.584307 | − | 0.811533i | \(-0.698634\pi\) | ||||
−0.584307 | + | 0.811533i | \(0.698634\pi\) | |||||||
\(884\) | 3.26094e12 | 0.179601 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.28322e13 | 0.699598 | ||||||||
\(887\) | −4.72702e12 | −0.256408 | −0.128204 | − | 0.991748i | \(-0.540921\pi\) | ||||
−0.128204 | + | 0.991748i | \(0.540921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.24775e13 | −0.669995 | ||||||||
\(890\) | 4.40956e13 | 2.35581 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.40195e13 | −4.44363 | ||||||||
\(893\) | −1.80969e13 | −0.952299 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.58631e13 | −1.34734 | ||||||||
\(896\) | −1.08056e14 | −5.60097 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.44902e13 | 2.28308 | ||||||||
\(899\) | 1.18241e13 | 0.603740 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.49740e13 | 1.76801 | ||||||||
\(902\) | 1.13278e13 | 0.569792 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.29087e12 | −0.163890 | ||||||||
\(905\) | −4.38804e12 | −0.217446 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.32865e13 | 0.651895 | 0.325948 | − | 0.945388i | \(-0.394317\pi\) | ||||
0.325948 | + | 0.945388i | \(0.394317\pi\) | |||||||
\(908\) | −5.13259e13 | −2.50582 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.54122e12 | −0.0745038 | ||||||||
\(911\) | 2.09108e13 | 1.00586 | 0.502930 | − | 0.864327i | \(-0.332255\pi\) | ||||
0.502930 | + | 0.864327i | \(0.332255\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.16882e11 | 0.00556711 | ||||||||
\(914\) | −1.26251e13 | −0.598378 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.49419e13 | 4.45583 | ||||||||
\(917\) | 3.04667e13 | 1.42286 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.12670e13 | −0.521060 | −0.260530 | − | 0.965466i | \(-0.583897\pi\) | ||||
−0.260530 | + | 0.965466i | \(0.583897\pi\) | |||||||
\(920\) | −3.00106e12 | −0.138111 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.87242e10 | −0.00130906 | ||||||||
\(923\) | −1.63015e12 | −0.0739298 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.35065e12 | 0.150484 | ||||||||
\(926\) | 2.14856e13 | 0.960281 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.85731e13 | −4.36307 | ||||||||
\(929\) | −2.48251e13 | −1.09350 | −0.546752 | − | 0.837294i | \(-0.684136\pi\) | ||||
−0.546752 | + | 0.837294i | \(0.684136\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.51058e12 | −0.0658978 | ||||||||
\(932\) | 8.66623e13 | 3.76235 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.15845e13 | −1.35804 | ||||||||
\(935\) | −6.75560e12 | −0.289076 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.05299e13 | 0.870081 | 0.435040 | − | 0.900411i | \(-0.356734\pi\) | ||||
0.435040 | + | 0.900411i | \(0.356734\pi\) | |||||||
\(938\) | −6.29878e13 | −2.65671 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.71921e13 | 2.38924 | ||||||||
\(941\) | 2.89837e13 | 1.20504 | 0.602519 | − | 0.798104i | \(-0.294164\pi\) | ||||
0.602519 | + | 0.798104i | \(0.294164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.18497e12 | 0.0487983 | ||||||||
\(944\) | −5.83313e13 | −2.39072 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.12471e13 | 0.862562 | ||||||||
\(947\) | 2.78208e13 | 1.12407 | 0.562036 | − | 0.827113i | \(-0.310018\pi\) | ||||
0.562036 | + | 0.827113i | \(0.310018\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.88290e11 | 0.0315492 | ||||||||
\(950\) | −1.84129e13 | −0.733441 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.24355e14 | −4.90679 | ||||||||
\(953\) | −2.85882e13 | −1.12271 | −0.561357 | − | 0.827573i | \(-0.689721\pi\) | ||||
−0.561357 | + | 0.827573i | \(0.689721\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.53842e13 | −0.598496 | ||||||||
\(956\) | 5.93381e13 | 2.29759 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.87702e11 | 0.0263788 | ||||||||
\(959\) | 4.50023e13 | 1.71811 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.44733e13 | −0.547411 | ||||||||
\(962\) | 8.77947e11 | 0.0330507 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.94246e12 | 0.184330 | ||||||||
\(965\) | 1.66698e13 | 0.618810 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.14935e13 | −1.89380 | −0.946898 | − | 0.321534i | \(-0.895802\pi\) | ||||
−0.946898 | + | 0.321534i | \(0.895802\pi\) | |||||||
\(968\) | 9.11919e13 | 3.33824 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.51890e13 | −1.63893 | ||||||||
\(971\) | 3.75474e13 | 1.35548 | 0.677740 | − | 0.735301i | \(-0.262959\pi\) | ||||
0.677740 | + | 0.735301i | \(0.262959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.21464e13 | 1.14981 | ||||||||
\(974\) | 2.51476e13 | 0.895325 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.19115e13 | −0.772944 | ||||||||
\(977\) | 3.25385e13 | 1.14254 | 0.571271 | − | 0.820762i | \(-0.306451\pi\) | ||||
0.571271 | + | 0.820762i | \(0.306451\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.36508e13 | 0.474937 | ||||||||
\(980\) | 4.77392e12 | 0.165332 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.65781e13 | −0.568895 | ||||||||
\(983\) | −5.63366e13 | −1.92442 | −0.962209 | − | 0.272310i | \(-0.912212\pi\) | ||||
−0.962209 | + | 0.272310i | \(0.912212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.21911e12 | 0.142810 | ||||||||
\(986\) | −6.75768e13 | −2.27694 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.57589e12 | −0.119393 | ||||||||
\(989\) | 2.22260e12 | 0.0738718 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.09674e13 | −0.690578 | −0.345289 | − | 0.938496i | \(-0.612219\pi\) | ||||
−0.345289 | + | 0.938496i | \(0.612219\pi\) | |||||||
\(992\) | −9.97583e13 | −3.27074 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.55210e13 | 3.10356 | ||||||||
\(995\) | −4.10067e13 | −1.32633 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.85780e13 | 1.55708 | 0.778541 | − | 0.627593i | \(-0.215960\pi\) | ||||
0.778541 | + | 0.627593i | \(0.215960\pi\) | |||||||
\(998\) | 1.59057e13 | 0.507533 | ||||||||
\(999\) | 0 | 0 |
(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 | 27.10.a.d.1.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 27.10.a.d.1.4 | yes | 4 | |
9.2 | odd | 6 | 81.10.c.j.28.1 | 8 | |||
9.4 | even | 3 | 81.10.c.j.55.4 | 8 | |||
9.5 | odd | 6 | 81.10.c.j.55.1 | 8 | |||
9.7 | even | 3 | 81.10.c.j.28.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.10.a.d.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
27.10.a.d.1.4 | yes | 4 | 3.2 | odd | 2 | inner | |
81.10.c.j.28.1 | 8 | 9.2 | odd | 6 | |||
81.10.c.j.28.4 | 8 | 9.7 | even | 3 | |||
81.10.c.j.55.1 | 8 | 9.5 | odd | 6 | |||
81.10.c.j.55.4 | 8 | 9.4 | even | 3 |