Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(193,384)]
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, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} - 1020 x^{14} + 7280 x^{13} + 388150 x^{12} - 2423904 x^{11} - 70542796 x^{10} + \cdots + 694045717832241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{108}\cdot 3^{28} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.10 | ||
Root | \(-8.47155 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.f.193.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 27.0000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 295.990i | − 1.05896i | −0.848321 | − | 0.529482i | \(-0.822386\pi\) | ||||
0.848321 | − | 0.529482i | \(-0.177614\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1208.55 | −1.33175 | −0.665873 | − | 0.746065i | \(-0.731941\pi\) | ||||
−0.665873 | + | 0.746065i | \(0.731941\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 8341.26i | − 1.88955i | −0.327727 | − | 0.944773i | \(-0.606283\pi\) | ||||
0.327727 | − | 0.944773i | \(-0.393717\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 9842.29i | − 1.24249i | −0.783615 | − | 0.621247i | \(-0.786626\pi\) | ||||
0.783615 | − | 0.621247i | \(-0.213374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7991.72 | 0.611394 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9080.24 | 0.448256 | 0.224128 | − | 0.974560i | \(-0.428047\pi\) | ||||
0.224128 | + | 0.974560i | \(0.428047\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 23035.9i | − 0.770490i | −0.922814 | − | 0.385245i | \(-0.874117\pi\) | ||||
0.922814 | − | 0.385245i | \(-0.125883\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 32630.9i | − 0.768884i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 92905.1 | 1.59218 | 0.796090 | − | 0.605178i | \(-0.206898\pi\) | ||||
0.796090 | + | 0.605178i | \(0.206898\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9484.89 | −0.121407 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 19683.0i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 38163.5i | 0.290573i | 0.989390 | + | 0.145287i | \(0.0464104\pi\) | ||||
−0.989390 | + | 0.145287i | \(0.953590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 78442.9 | 0.472920 | 0.236460 | − | 0.971641i | \(-0.424013\pi\) | ||||
0.236460 | + | 0.971641i | \(0.424013\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 225214. | 1.09093 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 357719.i | 1.41027i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 539121.i | − 1.74977i | −0.484334 | − | 0.874883i | \(-0.660938\pi\) | ||||
0.484334 | − | 0.874883i | \(-0.339062\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 265742. | 0.717355 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −872572. | −1.97723 | −0.988616 | − | 0.150460i | \(-0.951924\pi\) | ||||
−0.988616 | + | 0.150460i | \(0.951924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 548781.i | 1.05259i | 0.850302 | + | 0.526296i | \(0.176419\pi\) | ||||
−0.850302 | + | 0.526296i | \(0.823581\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 215776.i | 0.352988i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −59537.2 | −0.0836462 | −0.0418231 | − | 0.999125i | \(-0.513317\pi\) | ||||
−0.0418231 | + | 0.999125i | \(0.513317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 637052. | 0.773550 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 245167.i | 0.258801i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.43192e6i | − 1.32115i | −0.750758 | − | 0.660577i | \(-0.770312\pi\) | ||||
0.750758 | − | 0.660577i | \(-0.229688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.46893e6 | −2.00096 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 621968. | 0.444842 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 404986.i | − 0.256719i | −0.991728 | − | 0.128359i | \(-0.959029\pi\) | ||||
0.991728 | − | 0.128359i | \(-0.0409711\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.46875e6i | − 0.828501i | −0.910163 | − | 0.414251i | \(-0.864044\pi\) | ||||
0.910163 | − | 0.414251i | \(-0.135956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 881033. | 0.443916 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.91322e6 | −1.31576 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 586820.i | − 0.238365i | −0.992872 | − | 0.119183i | \(-0.961973\pi\) | ||||
0.992872 | − | 0.119183i | \(-0.0380274\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.50844e6i | 0.919245i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.70658e6 | −1.22905 | −0.614525 | − | 0.788897i | \(-0.710652\pi\) | ||||
−0.614525 | + | 0.788897i | \(0.710652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.57329e6 | 0.473346 | 0.236673 | − | 0.971589i | \(-0.423943\pi\) | ||||
0.236673 | + | 0.971589i | \(0.423943\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 256092.i | − 0.0700941i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00808e7i | 2.51640i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.58995e6 | 1.73198 | 0.865992 | − | 0.500058i | \(-0.166688\pi\) | ||||
0.865992 | + | 0.500058i | \(0.166688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.50373e6i | 1.05654i | 0.849078 | + | 0.528268i | \(0.177158\pi\) | ||||
−0.849078 | + | 0.528268i | \(0.822842\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.68766e6i | − 0.474687i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.03041e6 | −0.167762 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.90039e6 | −0.436106 | −0.218053 | − | 0.975937i | \(-0.569971\pi\) | ||||
−0.218053 | + | 0.975937i | \(0.569971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18949e7i | 1.65469i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.11796e6i | 0.273041i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.81838e6 | −0.815922 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.32490e6 | −1.03739 | −0.518696 | − | 0.854959i | \(-0.673582\pi\) | ||||
−0.518696 | + | 0.854959i | \(0.673582\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.08078e6i | 0.629848i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.16540e6i | 0.595437i | 0.954654 | + | 0.297719i | \(0.0962257\pi\) | ||||
−0.954654 | + | 0.297719i | \(0.903774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.55521e7 | 1.40236 | 0.701179 | − | 0.712986i | \(-0.252658\pi\) | ||||
0.701179 | + | 0.712986i | \(0.252658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.65840e6 | −0.814222 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.89410e6i | − 0.701874i | −0.936399 | − | 0.350937i | \(-0.885863\pi\) | ||||
0.936399 | − | 0.350937i | \(-0.114137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.19219e7i | − 1.62139i | −0.585472 | − | 0.810693i | \(-0.699091\pi\) | ||||
0.585472 | − | 0.810693i | \(-0.300909\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.45563e7 | 1.01023 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.22685e7 | 1.45183 | 0.725915 | − | 0.687784i | \(-0.241416\pi\) | ||||
0.725915 | + | 0.687784i | \(0.241416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.74989e7i | − 1.68606i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.17503e6i | 0.414165i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.09739e7 | −0.596964 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00895e7 | −2.57038 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.35594e7i | − 1.14156i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.03168e7i | − 0.930400i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.31332e6 | 0.273492 | 0.136746 | − | 0.990606i | \(-0.456336\pi\) | ||||
0.136746 | + | 0.990606i | \(0.456336\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.48171e7 | −0.607714 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.73606e6i | − 0.0674707i | −0.999431 | − | 0.0337354i | \(-0.989260\pi\) | ||||
0.999431 | − | 0.0337354i | \(-0.0107403\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.78400e7i | 1.02610i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.82596e6 | −0.203798 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.01382e7 | −1.00137 | −0.500686 | − | 0.865629i | \(-0.666919\pi\) | ||||
−0.500686 | + | 0.865629i | \(0.666919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.65011e6i | − 0.0836975i | −0.999124 | − | 0.0418488i | \(-0.986675\pi\) | ||||
0.999124 | − | 0.0418488i | \(-0.0133248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 1.60751e6i | − 0.0482932i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.20971e7 | −2.34775 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.12960e7 | 0.307707 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.72004e7i | 0.446609i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 4.54803e7i | − 1.12634i | −0.826340 | − | 0.563172i | \(-0.809581\pi\) | ||||
0.826340 | − | 0.563172i | \(-0.190419\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.25623e7 | −1.24238 | −0.621191 | − | 0.783659i | \(-0.713351\pi\) | ||||
−0.621191 | + | 0.783659i | \(0.713351\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.61950e6 | −0.149419 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.32183e7i | − 0.500806i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.91709e7i | − 0.395360i | −0.980267 | − | 0.197680i | \(-0.936659\pi\) | ||||
0.980267 | − | 0.197680i | \(-0.0633407\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.86619e7 | 0.762769 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.12281e8 | −2.12038 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.93967e7i | 0.893390i | 0.894686 | + | 0.446695i | \(0.147399\pi\) | ||||
−0.894686 | + | 0.446695i | \(0.852601\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 6.66610e7i | − 1.15526i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.03440e8 | 1.71862 | 0.859311 | − | 0.511453i | \(-0.170893\pi\) | ||||
0.859311 | + | 0.511453i | \(0.170893\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.41222e7 | −0.543793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.67931e7i | 0.256830i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.80500e7i | 0.705557i | 0.935707 | + | 0.352778i | \(0.114763\pi\) | ||||
−0.935707 | + | 0.352778i | \(0.885237\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.14630e7 | 0.161683 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.09346e7 | 0.148217 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.17664e6i | − 0.0153341i | −0.999971 | − | 0.00766705i | \(-0.997559\pi\) | ||||
0.999971 | − | 0.00766705i | \(-0.00244052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.72784e7i | 0.843336i | 0.906750 | + | 0.421668i | \(0.138555\pi\) | ||||
−0.906750 | + | 0.421668i | \(0.861445\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.96562e7 | 0.478336 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.59574e8 | −1.85294 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 7.57407e7i | − 0.847000i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.37879e7i | 0.256295i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.22053e7 | −0.438279 | −0.219139 | − | 0.975694i | \(-0.570325\pi\) | ||||
−0.219139 | + | 0.975694i | \(0.570325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.72792e8 | −1.73011 | −0.865056 | − | 0.501675i | \(-0.832717\pi\) | ||||
−0.865056 | + | 0.501675i | \(0.832717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 7.86568e7i | − 0.759653i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.37361e7i | 0.407575i | 0.979015 | + | 0.203788i | \(0.0653252\pi\) | ||||
−0.979015 | + | 0.203788i | \(0.934675\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.18697e7 | 0.646487 | 0.323243 | − | 0.946316i | \(-0.395227\pi\) | ||||
0.323243 | + | 0.946316i | \(0.395227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.58441e7 | 0.137620 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.61225e7i | − 0.386970i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.58272e8i | 2.09382i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.77278e7 | −0.530727 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.92148e8 | −1.45588 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.42645e8i | 1.04537i | 0.852527 | + | 0.522684i | \(0.175069\pi\) | ||||
−0.852527 | + | 0.522684i | \(0.824931\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.00078e8i | − 0.709593i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.62434e8 | 1.11466 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.48022e7 | −0.629810 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.24788e7i | 0.273286i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 8.93704e7i | − 0.556956i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.29773e7 | 0.501063 | 0.250531 | − | 0.968108i | \(-0.419395\pi\) | ||||
0.250531 | + | 0.968108i | \(0.419395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.91448e6 | 0.0404689 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.22220e8i | 0.693507i | 0.937956 | + | 0.346753i | \(0.112716\pi\) | ||||
−0.937956 | + | 0.346753i | \(0.887284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.21931e8i | 0.670948i | 0.942049 | + | 0.335474i | \(0.108896\pi\) | ||||
−0.942049 | + | 0.335474i | \(0.891104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.72183e8 | −1.45284 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.74651e8 | −0.904536 | −0.452268 | − | 0.891882i | \(-0.649385\pi\) | ||||
−0.452268 | + | 0.891882i | \(0.649385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.76224e7i | 0.0885784i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.04929e8i | 0.999962i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.65760e7 | −0.173302 | −0.0866510 | − | 0.996239i | \(-0.527616\pi\) | ||||
−0.0866510 | + | 0.996239i | \(0.527616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.08643e8 | −0.499970 | −0.249985 | − | 0.968250i | \(-0.580426\pi\) | ||||
−0.249985 | + | 0.968250i | \(0.580426\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.88561e8i | − 0.819162i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.26726e8 | −0.957329 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.48601e8 | −0.609991 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.03642e8i | 0.413691i | 0.978374 | + | 0.206846i | \(0.0663198\pi\) | ||||
−0.978374 | + | 0.206846i | \(0.933680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 7.74946e8i | − 3.00850i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.25668e7 | 0.274061 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.53253e8 | 0.563175 | 0.281587 | − | 0.959536i | \(-0.409139\pi\) | ||||
0.281587 | + | 0.959536i | \(0.409139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.51555e8i | 2.33025i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2.78212e7i | − 0.0968577i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.84479e8 | −0.625320 | −0.312660 | − | 0.949865i | \(-0.601220\pi\) | ||||
−0.312660 | + | 0.949865i | \(0.601220\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.23834e8 | −1.39906 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 7.83106e7i | − 0.251786i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.76958e8i | 0.554291i | 0.960828 | + | 0.277145i | \(0.0893884\pi\) | ||||
−0.960828 | + | 0.277145i | \(0.910612\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.88497e8 | −0.880540 | −0.440270 | − | 0.897865i | \(-0.645117\pi\) | ||||
−0.440270 | + | 0.897865i | \(0.645117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.21163e8 | −0.955335 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.91159e7i | 0.229403i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.63159e7i | 0.159203i | 0.996827 | + | 0.0796016i | \(0.0253648\pi\) | ||||
−0.996827 | + | 0.0796016i | \(0.974635\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.71849e7 | −0.157640 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.01509e8 | 1.34836 | 0.674181 | − | 0.738566i | \(-0.264497\pi\) | ||||
0.674181 | + | 0.738566i | \(0.264497\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.60409e8i | − 1.73205i | −0.500001 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500001 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.84096e8i | − 0.471073i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.05455e9 | 2.63317 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.27888e8 | −0.799066 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2.51772e8i | − 0.598939i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.05344e8i | 0.476920i | 0.971152 | + | 0.238460i | \(0.0766426\pi\) | ||||
−0.971152 | + | 0.238460i | \(0.923357\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.19872e8 | −0.271856 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.64181e8 | −0.363643 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 9.14399e8i | − 1.97827i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 6.63230e8i | − 1.40179i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.66466e8 | −0.343776 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.34735e8 | −0.877354 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.35013e8i | 0.463562i | 0.972768 | + | 0.231781i | \(0.0744552\pi\) | ||||
−0.972768 | + | 0.231781i | \(0.925545\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.19907e8i | 0.809651i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.80142e7 | −0.165917 | −0.0829586 | − | 0.996553i | \(-0.526437\pi\) | ||||
−0.0829586 | + | 0.996553i | \(0.526437\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.77867e8 | 1.61817 | 0.809084 | − | 0.587693i | \(-0.199964\pi\) | ||||
0.809084 | + | 0.587693i | \(0.199964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.60777e8i | − 0.470091i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.52195e8i | 1.32624i | 0.748512 | + | 0.663121i | \(0.230769\pi\) | ||||
−0.748512 | + | 0.663121i | \(0.769231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.18332e8 | 0.549051 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.40141e8 | 0.405227 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.09171e8i | − 0.345377i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.33530e7i | 0.150847i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.91893e8 | 0.936107 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.19538e7 | 0.111396 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.61554e8i | 0.851125i | 0.904929 | + | 0.425562i | \(0.139924\pi\) | ||||
−0.904929 | + | 0.425562i | \(0.860076\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.93019e8i | 0.583256i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.73693e8 | −0.252420 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.50757e8 | −0.356902 | −0.178451 | − | 0.983949i | \(-0.557109\pi\) | ||||
−0.178451 | + | 0.983949i | \(0.557109\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.01249e8i | 0.838215i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 6.54313e8i | − 0.893604i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.25384e8 | 0.301574 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.42472e8 | 0.973449 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 7.58059e8i | − 0.973979i | −0.873408 | − | 0.486990i | \(-0.838095\pi\) | ||||
0.873408 | − | 0.486990i | \(-0.161905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.46508e8i | 0.562264i | 0.959669 | + | 0.281132i | \(0.0907098\pi\) | ||||
−0.959669 | + | 0.281132i | \(0.909290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.93726e8 | −0.239118 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.29035e8 | −0.156134 | −0.0780668 | − | 0.996948i | \(-0.524875\pi\) | ||||
−0.0780668 | + | 0.996948i | \(0.524875\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.09711e9i | 1.30152i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2.96296e8i | − 0.344657i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.14531e8 | 0.472854 | 0.236427 | − | 0.971649i | \(-0.424024\pi\) | ||||
0.236427 | + | 0.971649i | \(0.424024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.63221e8 | 0.406346 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.35242e9i | − 1.48401i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.65678e8i | − 0.501257i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.12231e9 | −1.18517 | −0.592584 | − | 0.805508i | \(-0.701892\pi\) | ||||
−0.592584 | + | 0.805508i | \(0.701892\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.36105e8 | 0.659077 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.73055e9i | 1.75944i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.16853e8i | 0.615461i | 0.951474 | + | 0.307731i | \(0.0995696\pi\) | ||||
−0.951474 | + | 0.307731i | \(0.900430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.48553e8 | 0.537166 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.75616e8 | 0.361035 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.45320e8i | 0.325825i | 0.986640 | + | 0.162913i | \(0.0520889\pi\) | ||||
−0.986640 | + | 0.162913i | \(0.947911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.70460e8i | 0.157901i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.34038e9 | −1.21908 | −0.609541 | − | 0.792755i | \(-0.708646\pi\) | ||||
−0.609541 | + | 0.792755i | \(0.708646\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.98382e9 | 2.66477 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.00062e8i | − 0.350864i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.09565e8i | 0.697314i | 0.937250 | + | 0.348657i | \(0.113362\pi\) | ||||
−0.937250 | + | 0.348657i | \(0.886638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.43601e8 | 0.713704 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.68736e7 | 0.0389542 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.24655e9i | − 1.83411i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.77379e9i | 1.42277i | 0.702801 | + | 0.711387i | \(0.251933\pi\) | ||||
−0.702801 | + | 0.711387i | \(0.748067\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.51680e8 | −0.592418 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.24387e9 | 0.963315 | 0.481658 | − | 0.876360i | \(-0.340035\pi\) | ||||
0.481658 | + | 0.876360i | \(0.340035\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 7.72058e8i | − 0.587601i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.57301e8i | − 0.117663i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.49695e9 | −3.30626 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.54473e8 | −0.472999 | −0.236499 | − | 0.971632i | \(-0.576000\pi\) | ||||
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 8.13731e8i | − 0.578142i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.89446e8i | 0.341884i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.62905e9 | 1.11883 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.15531e7 | 0.0483228 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1.61210e8i | − 0.107064i | −0.998566 | − | 0.0535320i | \(-0.982952\pi\) | ||||
0.998566 | − | 0.0535320i | \(-0.0170479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.92687e9i | − 1.25853i | −0.777190 | − | 0.629266i | \(-0.783356\pi\) | ||||
0.777190 | − | 0.629266i | \(-0.216644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.34026e7 | 0.0278821 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.61251e7 | −0.0544212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.77506e9i | 1.10335i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.21662e9i | − 1.35547i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.61070e8 | 0.337557 | 0.168778 | − | 0.985654i | \(-0.446018\pi\) | ||||
0.168778 | + | 0.985654i | \(0.446018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.63369e9 | 1.55904 | 0.779519 | − | 0.626378i | \(-0.215463\pi\) | ||||
0.779519 | + | 0.626378i | \(0.215463\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.04992e8i | 0.177655i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2.14015e9i | − 1.22676i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.02903e9 | 1.70874 | 0.854372 | − | 0.519662i | \(-0.173942\pi\) | ||||
0.854372 | + | 0.519662i | \(0.173942\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.64411e8 | −0.257850 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.23887e9i | − 1.22353i | −0.791038 | − | 0.611767i | \(-0.790459\pi\) | ||||
0.791038 | − | 0.611767i | \(-0.209541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.58487e8i | 0.461821i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.22797e9 | 0.650295 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.86974e9 | 0.974807 | 0.487403 | − | 0.873177i | \(-0.337944\pi\) | ||||
0.487403 | + | 0.873177i | \(0.337944\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.27835e9i | 3.73607i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.41918e9i | − 0.717290i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.52077e9 | 1.75226 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.45091e9 | 1.20121 | 0.600607 | − | 0.799545i | \(-0.294926\pi\) | ||||
0.600607 | + | 0.799545i | \(0.294926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.78726e8i | − 0.0862669i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 3.52974e9i | − 1.67799i | −0.544139 | − | 0.838995i | \(-0.683144\pi\) | ||||
0.544139 | − | 0.838995i | \(-0.316856\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.30367e9 | −0.610427 | −0.305214 | − | 0.952284i | \(-0.598728\pi\) | ||||
−0.305214 | + | 0.952284i | \(0.598728\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.26894e8 | 0.289140 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.11104e9i | 1.41350i | 0.707463 | + | 0.706751i | \(0.249840\pi\) | ||||
−0.707463 | + | 0.706751i | \(0.750160\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.09201e8i | 0.317442i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.17613e8 | 0.228261 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.57753e9 | 1.98892 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.18493e8i | 0.0935425i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.04387e9i | 0.440385i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.91637e8 | −0.0796718 | −0.0398359 | − | 0.999206i | \(-0.512684\pi\) | ||||
−0.0398359 | + | 0.999206i | \(0.512684\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.30618e9 | −2.17408 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3.03157e9i | − 1.22420i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.76007e9i | 1.09856i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.25790e9 | −0.885837 | −0.442918 | − | 0.896562i | \(-0.646057\pi\) | ||||
−0.442918 | + | 0.896562i | \(0.646057\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.33371e9 | −0.515799 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.90733e8i | 0.0727176i | 0.999339 | + | 0.0363588i | \(0.0115759\pi\) | ||||
−0.999339 | + | 0.0363588i | \(0.988424\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.46534e8i | 0.130251i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.79985e9 | 0.666987 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.47960e9 | 1.63678 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.86435e9i | 1.39227i | 0.717909 | + | 0.696137i | \(0.245100\pi\) | ||||
−0.717909 | + | 0.696137i | \(0.754900\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.79288e9i | 0.992247i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.43474e8 | −0.295518 | −0.147759 | − | 0.989023i | \(-0.547206\pi\) | ||||
−0.147759 | + | 0.989023i | \(0.547206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.82489e9 | 0.630547 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9.21299e8i | − 0.313959i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 3.07188e9i | − 1.03250i | −0.856436 | − | 0.516252i | \(-0.827327\pi\) | ||||
0.856436 | − | 0.516252i | \(-0.172673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.90140e9 | −0.630377 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.53415e8 | −0.148281 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.60326e9i | − 1.48505i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.96616e8i | 0.158053i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.29735e9 | −0.407353 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.10240e9 | 0.961092 | 0.480546 | − | 0.876969i | \(-0.340438\pi\) | ||||
0.480546 | + | 0.876969i | \(0.340438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.05170e9i | − 0.627131i | −0.949567 | − | 0.313566i | \(-0.898476\pi\) | ||||
0.949567 | − | 0.313566i | \(-0.101524\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.09500e8i | 0.0933476i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.12281e8 | 0.211989 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.22653e9 | 1.53504 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.95235e8i | 0.0855729i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.58811e9i | 2.45670i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.63256e9 | −0.743260 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.17693e7 | 0.00885315 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.31381e9i | − 1.46166i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.25941e9i | 0.613487i | 0.951792 | + | 0.306743i | \(0.0992394\pi\) | ||||
−0.951792 | + | 0.306743i | \(0.900761\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.81652e9 | −0.486900 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.48867e9 | −1.71699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.29294e9i | 1.90523i | 0.304180 | + | 0.952615i | \(0.401618\pi\) | ||||
−0.304180 | + | 0.952615i | \(0.598382\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.07072e9i | 0.276167i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.79129e8 | 0.223884 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.17284e9 | −2.30656 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 4.30850e9i | − 1.06980i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.49041e9i | 0.365436i | 0.983165 | + | 0.182718i | \(0.0584895\pi\) | ||||
−0.983165 | + | 0.182718i | \(0.941510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.40127e9 | 1.30784 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.04500e9 | 0.489016 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 4.98977e9i | − 1.17842i | −0.807979 | − | 0.589212i | \(-0.799438\pi\) | ||||
0.807979 | − | 0.589212i | \(-0.200562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 6.59124e9i | − 1.53744i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.42273e8 | −0.147972 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.02061e9 | −1.14252 | −0.571260 | − | 0.820769i | \(-0.693545\pi\) | ||||
−0.571260 | + | 0.820769i | \(0.693545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.27701e8i | 0.0511846i | 0.999672 | + | 0.0255923i | \(0.00814717\pi\) | ||||
−0.999672 | + | 0.0255923i | \(0.991853\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.13954e9i | − 0.253040i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.81194e8 | −0.193301 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.73674e9 | 1.02651 | 0.513256 | − | 0.858235i | \(-0.328439\pi\) | ||||
0.513256 | + | 0.858235i | \(0.328439\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4.66540e9i | − 0.998881i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.65154e9i | − 1.40704i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.19440e10 | −2.49638 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.12373e9 | 0.438586 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.02047e9i | 0.412306i | 0.978520 | + | 0.206153i | \(0.0660944\pi\) | ||||
−0.978520 | + | 0.206153i | \(0.933906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.80700e9i | − 0.364380i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18087e9 | −0.235314 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.44514e9 | −1.26923 | −0.634616 | − | 0.772828i | \(-0.718842\pi\) | ||||
−0.634616 | + | 0.772828i | \(0.718842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.24817e9i | 0.632164i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.94048e9i | 0.373249i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.73444e9 | 1.09018 | 0.545088 | − | 0.838379i | \(-0.316496\pi\) | ||||
0.545088 | + | 0.838379i | \(0.316496\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.98830e9 | 0.937328 | 0.468664 | − | 0.883377i | \(-0.344736\pi\) | ||||
0.468664 | + | 0.883377i | \(0.344736\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.27792e8i | 0.0794551i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.48260e10i | 2.72194i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.01757e9 | 0.729127 | 0.364563 | − | 0.931179i | \(-0.381218\pi\) | ||||
0.364563 | + | 0.931179i | \(0.381218\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.24531e9 | 0.223417 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.85983e8i | 0.103930i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.59669e9i | − 0.981341i | −0.871345 | − | 0.490670i | \(-0.836752\pi\) | ||||
0.871345 | − | 0.490670i | \(-0.163248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.97335e9 | −1.20887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.49818e9 | −1.28516 | −0.642581 | − | 0.766218i | \(-0.722136\pi\) | ||||
−0.642581 | + | 0.766218i | \(0.722136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.06598e10i | 1.80647i | 0.429148 | + | 0.903234i | \(0.358814\pi\) | ||||
−0.429148 | + | 0.903234i | \(0.641186\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 1.82865e9i | − 0.306415i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.50527e9 | 0.580783 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.75456e9 | −1.10667 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 5.18800e9i | − 0.840550i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 4.89535e9i | − 0.784344i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.72314e9 | 1.38220 | 0.691099 | − | 0.722761i | \(-0.257127\pi\) | ||||
0.691099 | + | 0.722761i | \(0.257127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.85142e9 | −0.603543 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.86868e9i | − 0.289619i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.27005e9i | − 0.961132i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.70210e9 | 0.409684 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.26338e9 | −1.08927 | −0.544635 | − | 0.838673i | \(-0.683332\pi\) | ||||
−0.544635 | + | 0.838673i | \(0.683332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.78860e9i | 0.710347i | 0.934800 | + | 0.355173i | \(0.115578\pi\) | ||||
−0.934800 | + | 0.355173i | \(0.884422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.38571e9i | 0.643548i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.10498e10 | 1.60394 | 0.801971 | − | 0.597363i | \(-0.203785\pi\) | ||||
0.801971 | + | 0.597363i | \(0.203785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.37809e9 | −0.485082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.55966e9i | − 0.363621i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 8.16878e9i | − 1.14805i | −0.818837 | − | 0.574026i | \(-0.805381\pi\) | ||||
0.818837 | − | 0.574026i | \(-0.194619\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.13856e8 | −0.0714491 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.14693e9 | −0.157782 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6.84404e9i | − 0.931566i | −0.884899 | − | 0.465783i | \(-0.845773\pi\) | ||||
0.884899 | − | 0.465783i | \(-0.154227\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.19963e9i | 0.161563i | 0.996732 | + | 0.0807816i | \(0.0257416\pi\) | ||||
−0.996732 | + | 0.0807816i | \(0.974258\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.41300e9 | 0.321559 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.24035e9 | 1.08660 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.54558e9i | 0.462645i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.24039e9i | 0.289289i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.22512e10 | −1.56549 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.16862e9 | −0.780072 | −0.390036 | − | 0.920800i | \(-0.627538\pi\) | ||||
−0.390036 | + | 0.920800i | \(0.627538\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.86691e8i | 0.0233647i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.01999e9i | − 0.745651i | −0.927901 | − | 0.372826i | \(-0.878389\pi\) | ||||
0.927901 | − | 0.372826i | \(-0.121611\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.12696e10 | 1.38154 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.29993e9 | −0.400396 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.27889e10i | − 1.53590i | −0.640511 | − | 0.767949i | \(-0.721278\pi\) | ||||
0.640511 | − | 0.767949i | \(-0.278722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.92059e9i | 1.06042i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.29213e9 | −0.387372 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.40934e10 | −1.64153 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.77755e9i | 0.320250i | 0.987097 | + | 0.160125i | \(0.0511898\pi\) | ||||
−0.987097 | + | 0.160125i | \(0.948810\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 7.34893e9i | − 0.838799i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.84406e8 | −0.0886327 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.92316e9 | −0.886306 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 4.71558e9i | − 0.522234i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 7.94638e9i | − 0.871277i | −0.900122 | − | 0.435639i | \(-0.856523\pi\) | ||||
0.900122 | − | 0.435639i | \(-0.143477\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.24191e10 | −1.34818 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.75805e8 | −0.0511407 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 7.45119e9i | − 0.792972i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.68125e10i | 1.77162i | 0.464049 | + | 0.885810i | \(0.346396\pi\) | ||||
−0.464049 | + | 0.885810i | \(0.653604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.53307e9 | −0.577328 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.28775e9 | 0.752974 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.42999e10i | 2.48618i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 9.87552e8i | − 0.100056i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.38427e9 | 0.540227 | 0.270113 | − | 0.962829i | \(-0.412939\pi\) | ||||
0.270113 | + | 0.962829i | \(0.412939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.87955e10 | −1.86758 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.93337e9i | − 0.288658i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.61977e8i | − 0.0352775i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.83636e9 | −0.756387 | −0.378193 | − | 0.925727i | \(-0.623455\pi\) | ||||
−0.378193 | + | 0.925727i | \(0.623455\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.98307e9i | 0.471830i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.28847e10i | − 1.20840i | −0.796833 | − | 0.604200i | \(-0.793493\pi\) | ||||
0.796833 | − | 0.604200i | \(-0.206507\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.09114e9 | 0.472943 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.89482e9 | −0.450402 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.03527e10i | − 0.943624i | −0.881699 | − | 0.471812i | \(-0.843600\pi\) | ||||
0.881699 | − | 0.471812i | \(-0.156400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 6.12159e9i | − 0.552714i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.03056e9 | −0.807707 | −0.403854 | − | 0.914824i | \(-0.632330\pi\) | ||||
−0.403854 | + | 0.914824i | \(0.632330\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.34617e10 | −1.19276 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.01222e9i | − 0.352179i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.07490e10i | 0.934718i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.27926e10 | −1.10209 | −0.551046 | − | 0.834475i | \(-0.685771\pi\) | ||||
−0.551046 | + | 0.834475i | \(0.685771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.79832e9 | −0.238845 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.55579e10i | 1.31564i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.64139e9i | − 0.137524i | −0.997633 | − | 0.0687618i | \(-0.978095\pi\) | ||||
0.997633 | − | 0.0687618i | \(-0.0219048\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.09235e10 | 1.73696 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.25169e10 | 1.02956 | 0.514778 | − | 0.857323i | \(-0.327874\pi\) | ||||
0.514778 | + | 0.857323i | \(0.327874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.64938e10i | 2.15928i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.95930e9i | 0.158229i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.98599e9 | −0.318972 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.05617e10 | 0.837511 | 0.418756 | − | 0.908099i | \(-0.362466\pi\) | ||||
0.418756 | + | 0.908099i | \(0.362466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.13783e9i | 0.325149i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.85897e10i | 1.44759i | 0.690016 | + | 0.723794i | \(0.257603\pi\) | ||||
−0.690016 | + | 0.723794i | \(0.742397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.44022e8 | −0.0574156 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.75920e10 | −1.34537 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.01004e10i | 1.52344i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.09176e10i | 2.32235i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.51172e8 | 0.0559208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.67438e9 | −0.418672 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.81123e9i | 0.351840i | 0.984404 | + | 0.175920i | \(0.0562899\pi\) | ||||
−0.984404 | + | 0.175920i | \(0.943710\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 4.98094e9i | − 0.361029i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.69126e10 | −1.93347 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.44559e10 | −1.02941 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.14435e10i | − 0.807746i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.86151e10i | − 1.30245i | −0.758883 | − | 0.651226i | \(-0.774255\pi\) | ||||
0.758883 | − | 0.651226i | \(-0.225745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.40613e8 | −0.0374949 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.11439e9 | 0.145369 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.31232e10i | − 0.894409i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.32339e10i | 2.24541i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.77787e9 | −0.320020 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.02158e10 | −0.678345 | −0.339172 | − | 0.940724i | \(-0.610147\pi\) | ||||
−0.339172 | + | 0.940724i | \(0.610147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00546e10i | 1.32020i | 0.751177 | + | 0.660100i | \(0.229486\pi\) | ||||
−0.751177 | + | 0.660100i | \(0.770514\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.78942e9i | − 0.508380i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.46209e10 | 0.946069 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.26417e10 | 0.811011 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 8.67139e9i | − 0.551563i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.79346e10i | 1.13107i | 0.824724 | + | 0.565536i | \(0.191331\pi\) | ||||
−0.824724 | + | 0.565536i | \(0.808669\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.24280e10 | 0.777144 | 0.388572 | − | 0.921418i | \(-0.372968\pi\) | ||||
0.388572 | + | 0.921418i | \(0.372968\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.13613e9 | −0.132446 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.13534e10i | − 1.31280i | −0.754414 | − | 0.656399i | \(-0.772079\pi\) | ||||
0.754414 | − | 0.656399i | \(-0.227921\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 3.18974e10i | − 1.94453i | −0.233881 | − | 0.972265i | \(-0.575143\pi\) | ||||
0.233881 | − | 0.972265i | \(-0.424857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.52053e9 | −0.0919160 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.78458e9 | 0.346748 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3.06171e10i | − 1.81996i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.54399e9i | − 0.0910135i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.89333e10 | 1.10677 | 0.553386 | − | 0.832925i | \(-0.313335\pi\) | ||||
0.553386 | + | 0.832925i | \(0.313335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.57934e10 | 0.915567 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.35407e10i | 0.778477i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00998e10i | 0.575857i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.05356e10 | 3.42310 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.78310e10 | 0.999999 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 5.00871e10i | − 2.78594i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.46867e10i | − 0.810220i | −0.914268 | − | 0.405110i | \(-0.867233\pi\) | ||||
0.914268 | − | 0.405110i | \(-0.132767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.97060e9 | 0.271974 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.66249e9 | −0.361579 | −0.180790 | − | 0.983522i | \(-0.557865\pi\) | ||||
−0.180790 | + | 0.983522i | \(0.557865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.11084e10i | − 0.597966i | −0.954258 | − | 0.298983i | \(-0.903353\pi\) | ||||
0.954258 | − | 0.298983i | \(-0.0966474\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.84728e10i | 1.52026i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.57309e10 | −0.833134 | −0.416567 | − | 0.909105i | \(-0.636767\pi\) | ||||
−0.416567 | + | 0.909105i | \(0.636767\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.42223e10 | 0.747160 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 8.85297e9i | − 0.461341i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6.33097e10i | − 3.27266i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.77565e9 | −0.296167 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.79785e9 | 0.345797 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.45538e10i | 1.23906i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.22672e10i | − 1.11472i | −0.830270 | − | 0.557362i | \(-0.811814\pi\) | ||||
0.830270 | − | 0.557362i | \(-0.188186\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.54429e9 | −0.275350 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.20896e10 | −1.08836 | −0.544180 | − | 0.838968i | \(-0.683159\pi\) | ||||
−0.544180 | + | 0.838968i | \(0.683159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.65630e10i | 1.29842i | 0.760610 | + | 0.649210i | \(0.224900\pi\) | ||||
−0.760610 | + | 0.649210i | \(0.775100\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 3.23653e9i | − 0.156956i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.12167e10 | −1.98308 | −0.991540 | − | 0.129801i | \(-0.958566\pi\) | ||||
−0.991540 | + | 0.129801i | \(0.958566\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.62997e9 | −0.364222 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 4.43289e9i | − 0.209949i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.37149e9i | 0.0644485i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.48274e8 | −0.0162383 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.46888e10 | 1.14216 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.99366e9i | 0.137418i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.30022e10i | − 0.592216i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.79072e10 | 0.809321 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.99137e10 | 0.893063 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.16876e10i | − 0.965132i | −0.875860 | − | 0.482566i | \(-0.839705\pi\) | ||||
0.875860 | − | 0.482566i | \(-0.160295\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 4.49457e9i | − 0.198479i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.46518e10 | 0.642062 | 0.321031 | − | 0.947069i | \(-0.395971\pi\) | ||||
0.321031 | + | 0.947069i | \(0.395971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.59081e10 | 1.99637 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.17378e10i | − 0.506541i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.09812e9i | 0.0898539i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.27067e9 | 0.394010 | 0.197005 | − | 0.980403i | \(-0.436879\pi\) | ||||
0.197005 | + | 0.980403i | \(0.436879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.34535e9 | −0.267638 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.64813e10i | 1.52709i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.11350e9i | 0.212433i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.13375e10 | −0.467452 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.16010e10 | −1.29314 | −0.646570 | − | 0.762855i | \(-0.723797\pi\) | ||||
−0.646570 | + | 0.762855i | \(0.723797\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.46750e10i | − 0.596012i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.37638e9i | − 0.0957923i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.24185e10 | −0.896943 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.72794e9 | 0.267174 | 0.133587 | − | 0.991037i | \(-0.457351\pi\) | ||||
0.133587 | + | 0.991037i | \(0.457351\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.37024e10i | 0.934250i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.67548e9i | 0.300291i | 0.988664 | + | 0.150145i | \(0.0479742\pi\) | ||||
−0.988664 | + | 0.150145i | \(0.952026\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.10664e10 | −3.14811 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.04097e9 | 0.271407 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.29327e10i | − 0.877464i | −0.898618 | − | 0.438732i | \(-0.855428\pi\) | ||||
0.898618 | − | 0.438732i | \(-0.144572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.54848e10i | − 0.588130i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.03093e10 | −0.765706 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.11486e10 | 1.54003 | 0.770016 | − | 0.638025i | \(-0.220248\pi\) | ||||
0.770016 | + | 0.638025i | \(0.220248\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.24923e10i | 0.464122i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.59496e9i | 0.316995i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.64235e10 | 1.33357 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.13593e10 | −0.776346 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.48380e9i | 0.233958i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.11448e10i | 1.83213i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.35579e9 | 0.0837807 | 0.0418903 | − | 0.999122i | \(-0.486662\pi\) | ||||
0.0418903 | + | 0.999122i | \(0.486662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.64762e9 | 0.199403 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.53180e9i | 0.228963i | 0.993425 | + | 0.114482i | \(0.0365207\pi\) | ||||
−0.993425 | + | 0.114482i | \(0.963479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.20280e9i | 0.111464i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.52053e9 | −0.0870915 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.56047e10 | 0.878394 | 0.439197 | − | 0.898391i | \(-0.355263\pi\) | ||||
0.439197 | + | 0.898391i | \(0.355263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.41929e10i | 0.824042i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.59811e10i | 0.540462i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.64231e10 | 0.887252 | 0.443626 | − | 0.896212i | \(-0.353692\pi\) | ||||
0.443626 | + | 0.896212i | \(0.353692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.29454e10 | 0.431608 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.94275e9i | 0.0643143i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.09846e10i | 1.67591i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.41414e10 | 1.44075 | 0.720375 | − | 0.693585i | \(-0.243970\pi\) | ||||
0.720375 | + | 0.693585i | \(0.243970\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.51619e10 | −0.491397 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 2.12727e10i | − 0.684607i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.85869e10i | − 1.23312i | −0.787306 | − | 0.616562i | \(-0.788525\pi\) | ||||
0.787306 | − | 0.616562i | \(-0.211475\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.06115e10 | −0.336743 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.8.d.f.193.10 | yes | 16 | |
4.3 | odd | 2 | inner | 384.8.d.f.193.2 | ✓ | 16 | |
8.3 | odd | 2 | inner | 384.8.d.f.193.15 | yes | 16 | |
8.5 | even | 2 | inner | 384.8.d.f.193.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.f.193.2 | ✓ | 16 | 4.3 | odd | 2 | inner | |
384.8.d.f.193.7 | yes | 16 | 8.5 | even | 2 | inner | |
384.8.d.f.193.10 | yes | 16 | 1.1 | even | 1 | trivial | |
384.8.d.f.193.15 | yes | 16 | 8.3 | odd | 2 | inner |