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 | 193.8 | ||
Root | \(-8.25013 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.f.193.9 |
$q$-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 | ||||||||
\(5\) | 484.521i | 1.73348i | 0.498765 | + | 0.866738i | \(0.333787\pi\) | ||||
−0.498765 | + | 0.866738i | \(0.666213\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 826.966 | 0.911264 | 0.455632 | − | 0.890168i | \(-0.349413\pi\) | ||||
0.455632 | + | 0.890168i | \(0.349413\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4559.22i | 1.03280i | 0.856348 | + | 0.516400i | \(0.172728\pi\) | ||||
−0.856348 | + | 0.516400i | \(0.827272\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3071.92i | − 0.387801i | −0.981021 | − | 0.193900i | \(-0.937886\pi\) | ||||
0.981021 | − | 0.193900i | \(-0.0621138\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13082.1 | 1.00082 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21664.0 | 1.06947 | 0.534733 | − | 0.845021i | \(-0.320412\pi\) | ||||
0.534733 | + | 0.845021i | \(0.320412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 58806.6i | − 1.96693i | −0.181106 | − | 0.983464i | \(-0.557968\pi\) | ||||
0.181106 | − | 0.983464i | \(-0.442032\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 22328.1i | − 0.526119i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18663.3 | 0.319846 | 0.159923 | − | 0.987130i | \(-0.448875\pi\) | ||||
0.159923 | + | 0.987130i | \(0.448875\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −156636. | −2.00494 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 210373.i | − 1.60176i | −0.598824 | − | 0.800880i | \(-0.704365\pi\) | ||||
0.598824 | − | 0.800880i | \(-0.295635\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 98739.9 | 0.595288 | 0.297644 | − | 0.954677i | \(-0.403799\pi\) | ||||
0.297644 | + | 0.954677i | \(0.403799\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 123099. | 0.596287 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 400682.i | 1.57965i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 549811.i | − 1.78446i | −0.451579 | − | 0.892231i | \(-0.649139\pi\) | ||||
0.451579 | − | 0.892231i | \(-0.350861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −82941.9 | −0.223897 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 559912. | 1.26875 | 0.634375 | − | 0.773025i | \(-0.281257\pi\) | ||||
0.634375 | + | 0.773025i | \(0.281257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 503917.i | 0.966538i | 0.875472 | + | 0.483269i | \(0.160551\pi\) | ||||
−0.875472 | + | 0.483269i | \(0.839449\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 353216.i | − 0.577825i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 970883. | 1.36403 | 0.682016 | − | 0.731337i | \(-0.261103\pi\) | ||||
0.682016 | + | 0.731337i | \(0.261103\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −139671. | −0.169597 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 584927.i | − 0.617456i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.49503e6i | − 1.37938i | −0.724106 | − | 0.689689i | \(-0.757747\pi\) | ||||
0.724106 | − | 0.689689i | \(-0.242253\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.20904e6 | −1.79033 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.58778e6 | −1.13561 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 415361.i | − 0.263296i | −0.991297 | − | 0.131648i | \(-0.957973\pi\) | ||||
0.991297 | − | 0.131648i | \(-0.0420268\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.20016e6i | 1.24108i | 0.784175 | + | 0.620540i | \(0.213087\pi\) | ||||
−0.784175 | + | 0.620540i | \(0.786913\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −602858. | −0.303755 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.48841e6 | 0.672243 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.95346e6i | 0.793492i | 0.917928 | + | 0.396746i | \(0.129861\pi\) | ||||
−0.917928 | + | 0.396746i | \(0.870139\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 503909.i | − 0.184663i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.29191e6 | −0.428377 | −0.214189 | − | 0.976792i | \(-0.568711\pi\) | ||||
−0.214189 | + | 0.976792i | \(0.568711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.21010e6 | 0.965803 | 0.482902 | − | 0.875675i | \(-0.339583\pi\) | ||||
0.482902 | + | 0.875675i | \(0.339583\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.22916e6i | 1.15755i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.77032e6i | 0.941153i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.91140e6 | 0.436171 | 0.218086 | − | 0.975930i | \(-0.430019\pi\) | ||||
0.218086 | + | 0.975930i | \(0.430019\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.28696e6i | 0.439021i | 0.975610 | + | 0.219511i | \(0.0704461\pi\) | ||||
−0.975610 | + | 0.219511i | \(0.929554\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.04966e7i | 1.85389i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.68008e6 | −0.924777 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.17696e6 | −0.477691 | −0.238845 | − | 0.971058i | \(-0.576769\pi\) | ||||
−0.238845 | + | 0.971058i | \(0.576769\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.54037e6i | − 0.353389i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2.66598e6i | − 0.343690i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.84930e7 | 3.40962 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.37459e6 | 0.264172 | 0.132086 | − | 0.991238i | \(-0.457832\pi\) | ||||
0.132086 | + | 0.991238i | \(0.457832\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 3.32367e6i | − 0.344267i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.11158e6i | 0.493663i | 0.969058 | + | 0.246831i | \(0.0793894\pi\) | ||||
−0.969058 | + | 0.246831i | \(0.920611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.05378e7 | −0.950214 | −0.475107 | − | 0.879928i | \(-0.657591\pi\) | ||||
−0.475107 | + | 0.879928i | \(0.657591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.08184e7 | 0.912014 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.18570e6i | 0.488142i | 0.969757 | + | 0.244071i | \(0.0784830\pi\) | ||||
−0.969757 | + | 0.244071i | \(0.921517\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.62679e6i | 0.712014i | 0.934483 | + | 0.356007i | \(0.115862\pi\) | ||||
−0.934483 | + | 0.356007i | \(0.884138\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.48449e7 | −1.03026 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.35874e7 | 1.53782 | 0.768911 | − | 0.639356i | \(-0.220799\pi\) | ||||
0.768911 | + | 0.639356i | \(0.220799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.04275e6i | 0.554445i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.23943e6i | 0.129267i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.79154e7 | 0.974566 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.29931e6 | −0.0666749 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.51176e7i | − 0.732513i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 3.80400e7i | − 1.74203i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.70889e7 | −1.17349 | −0.586744 | − | 0.809773i | \(-0.699590\pi\) | ||||
−0.586744 | + | 0.809773i | \(0.699590\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.36057e7 | 0.558031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 3.97308e7i | − 1.54411i | −0.635557 | − | 0.772054i | \(-0.719230\pi\) | ||||
0.635557 | − | 0.772054i | \(-0.280770\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.86310e7i | − 1.79239i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.53683e6 | −0.333607 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −739485. | −0.0245701 | −0.0122851 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122851 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3.11339e7i | − 0.983290i | −0.870796 | − | 0.491645i | \(-0.836396\pi\) | ||||
0.870796 | − | 0.491645i | \(-0.163604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.62139e7i | − 0.787524i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.40056e7 | 0.400520 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.01930e8 | 2.77661 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.77111e6i | 0.0979170i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.52064e6i | − 0.0871907i | −0.999049 | − | 0.0435954i | \(-0.986119\pi\) | ||||
0.999049 | − | 0.0435954i | \(-0.0138812\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.10851e7 | 0.262012 | 0.131006 | − | 0.991382i | \(-0.458179\pi\) | ||||
0.131006 | + | 0.991382i | \(0.458179\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.57930e7 | −0.356488 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.78416e7i | 1.03192i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.41227e6i | − 0.0291252i | −0.999894 | − | 0.0145626i | \(-0.995364\pi\) | ||||
0.999894 | − | 0.0145626i | \(-0.00463559\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.03657e7 | −0.796384 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.54339e7 | 0.291464 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2.04722e7i | − 0.370262i | −0.982714 | − | 0.185131i | \(-0.940729\pi\) | ||||
0.982714 | − | 0.185131i | \(-0.0592709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.96440e7i | 1.03365i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.31414e7 | 1.04907 | 0.524537 | − | 0.851388i | \(-0.324238\pi\) | ||||
0.524537 | + | 0.851388i | \(0.324238\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.33118e7 | 0.849611 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.28700e7i | 0.655642i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.19687e7i | 0.616261i | 0.951344 | + | 0.308130i | \(0.0997033\pi\) | ||||
−0.951344 | + | 0.308130i | \(0.900297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.29532e8 | −1.82703 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.12147e7 | −0.152014 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 5.08183e7i | − 0.662270i | −0.943583 | − | 0.331135i | \(-0.892569\pi\) | ||||
0.943583 | − | 0.331135i | \(-0.107431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 9.81793e7i | − 1.23068i | −0.788262 | − | 0.615340i | \(-0.789019\pi\) | ||||
0.788262 | − | 0.615340i | \(-0.210981\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.94043e7 | 0.716538 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.66395e8 | 3.09332 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.87708e7i | 1.10454i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.62772e7i | 0.175373i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.63430e7 | 0.585090 | 0.292545 | − | 0.956252i | \(-0.405498\pi\) | ||||
0.292545 | + | 0.956252i | \(0.405498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.05504e7 | 0.305891 | 0.152945 | − | 0.988235i | \(-0.451124\pi\) | ||||
0.152945 | + | 0.988235i | \(0.451124\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 4.01871e7i | − 0.388120i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.98819e8i | 1.85279i | 0.376549 | + | 0.926397i | \(0.377111\pi\) | ||||
−0.376549 | + | 0.926397i | \(0.622889\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.71467e8 | 1.54240 | 0.771198 | − | 0.636595i | \(-0.219658\pi\) | ||||
0.771198 | + | 0.636595i | \(0.219658\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.27434e7 | 0.458123 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.73972e8i | − 1.45963i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.71289e8i | 2.19935i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.36055e7 | −0.106615 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.68112e8 | 2.03144 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.89713e7i | − 0.212315i | −0.994349 | − | 0.106157i | \(-0.966145\pi\) | ||||
0.994349 | − | 0.106157i | \(-0.0338547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.48814e7i | 0.247324i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.44158e8 | −1.67547 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.16546e7 | 0.542465 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 8.66727e7i | − 0.557607i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 6.65500e7i | − 0.414739i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.79957e8 | 1.69054 | 0.845269 | − | 0.534342i | \(-0.179440\pi\) | ||||
0.845269 | + | 0.534342i | \(0.179440\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.14187e8 | 0.668312 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.01491e8i | 1.71074i | 0.518016 | + | 0.855371i | \(0.326671\pi\) | ||||
−0.518016 | + | 0.855371i | \(0.673329\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2.34566e8i | − 1.29075i | −0.763867 | − | 0.645374i | \(-0.776702\pi\) | ||||
0.763867 | − | 0.645374i | \(-0.223298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.01799e8 | 0.543375 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.88761e8 | −0.977610 | −0.488805 | − | 0.872393i | \(-0.662567\pi\) | ||||
−0.488805 | + | 0.872393i | \(0.662567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.70413e8i | 2.36452i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 5.16078e7i | − 0.251823i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.96557e8 | −1.87894 | −0.939470 | − | 0.342630i | \(-0.888682\pi\) | ||||
−0.939470 | + | 0.342630i | \(0.888682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.31086e7 | 0.336441 | 0.168221 | − | 0.985749i | \(-0.446198\pi\) | ||||
0.168221 | + | 0.985749i | \(0.446198\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.43489e7i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 6.76733e7i | − 0.293993i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.80649e8 | −0.762776 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.17480e7 | 0.253469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.10096e8i | 1.63692i | 0.574563 | + | 0.818460i | \(0.305172\pi\) | ||||
−0.574563 | + | 0.818460i | \(0.694828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.50900e7i | 0.330337i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.83409e8 | 1.07034 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.73230e8 | 0.636588 | 0.318294 | − | 0.947992i | \(-0.396890\pi\) | ||||
0.318294 | + | 0.947992i | \(0.396890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.54675e8i | − 1.62612i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.53362e8i | 0.533920i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.15032e8 | −1.74578 | −0.872890 | − | 0.487917i | \(-0.837757\pi\) | ||||
−0.872890 | + | 0.487917i | \(0.837757\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.24371e8 | 2.39112 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.57779e7i | 0.275795i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5.15831e8i | − 1.61575i | −0.589354 | − | 0.807875i | \(-0.700618\pi\) | ||||
0.589354 | − | 0.807875i | \(-0.299382\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.18405e6 | 0.0219269 | 0.0109634 | − | 0.999940i | \(-0.496510\pi\) | ||||
0.0109634 | + | 0.999940i | \(0.496510\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.85901e7 | −0.204029 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 7.14136e8i | − 2.07070i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.72429e8i | − 1.05284i | −0.850223 | − | 0.526422i | \(-0.823533\pi\) | ||||
0.850223 | − | 0.526422i | \(-0.176467\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.19814e7 | −0.198429 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.30771e8 | 0.620453 | 0.310227 | − | 0.950663i | \(-0.399595\pi\) | ||||
0.310227 | + | 0.950663i | \(0.399595\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.05188e7i | 0.158722i | 0.996846 | + | 0.0793612i | \(0.0252880\pi\) | ||||
−0.996846 | + | 0.0793612i | \(0.974712\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 7.69311e8i | − 1.96854i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.63028e8 | 1.15617 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.89888e7 | 0.143756 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 6.41139e7i | − 0.152520i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.55981e7i | 0.198805i | 0.995047 | + | 0.0994025i | \(0.0316931\pi\) | ||||
−0.995047 | + | 0.0994025i | \(0.968307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.01251e8 | 0.456417 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.97391e7 | −0.198762 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5.73322e7i | − 0.124036i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.16722e8i | 0.880772i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.38013e8 | 0.285016 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.06602e9 | −2.15138 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.47809e8i | 1.47505i | 0.675320 | + | 0.737525i | \(0.264005\pi\) | ||||
−0.675320 | + | 0.737525i | \(0.735995\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.84522e8i | 0.548606i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.83221e7 | −0.166498 | −0.0832488 | − | 0.996529i | \(-0.526530\pi\) | ||||
−0.0832488 | + | 0.996529i | \(0.526530\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.79088e8 | −0.514441 | −0.257220 | − | 0.966353i | \(-0.582807\pi\) | ||||
−0.257220 | + | 0.966353i | \(0.582807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.92097e8i | − 0.526551i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.42763e8i | − 0.428030i | −0.976830 | − | 0.214015i | \(-0.931346\pi\) | ||||
0.976830 | − | 0.214015i | \(-0.0686542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.59138e8 | 1.65430 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.67014e8 | 0.281829 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.27398e9i | − 2.10356i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.81172e8i | 0.777515i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.59923e8 | 0.411082 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.02887e8 | 1.24299 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.87662e8i | 1.19383i | 0.802305 | + | 0.596914i | \(0.203607\pi\) | ||||
−0.802305 | + | 0.596914i | \(0.796393\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00812e8i | 0.594821i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.46492e8 | −1.37550 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.60075e7 | 0.0370163 | 0.0185082 | − | 0.999829i | \(-0.494108\pi\) | ||||
0.0185082 | + | 0.999829i | \(0.494108\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 6.36860e8i | − 0.887862i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.50177e8i | 0.614813i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.96545e8 | −1.06581 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.44154e8 | 0.320109 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.99682e8i | 1.02746i | 0.857952 | + | 0.513729i | \(0.171736\pi\) | ||||
−0.857952 | + | 0.513729i | \(0.828264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.02045e9i | 1.28500i | 0.766286 | + | 0.642500i | \(0.222103\pi\) | ||||
−0.766286 | + | 0.642500i | \(0.777897\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.04647e7 | 0.0746323 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.29119e8 | 0.156236 | 0.0781178 | − | 0.996944i | \(-0.475109\pi\) | ||||
0.0781178 | + | 0.996944i | \(0.475109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6.25955e8i | − 0.742581i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.83715e8i | − 0.562666i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.61953e9 | 1.84738 | 0.923692 | − | 0.383136i | \(-0.125156\pi\) | ||||
0.923692 | + | 0.383136i | \(0.125156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.56434e9 | −2.86880 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.50812e7i | 0.0384948i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.55536e9i | 1.67420i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.58446e9 | −1.67321 | −0.836606 | − | 0.547805i | \(-0.815464\pi\) | ||||
−0.836606 | + | 0.547805i | \(0.815464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.08176e8 | −0.422917 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.23633e9i | − 1.25698i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.59891e8i | 0.259305i | 0.991559 | + | 0.129653i | \(0.0413862\pi\) | ||||
−0.991559 | + | 0.129653i | \(0.958614\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.02708e9 | −1.00576 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.46250e8 | −0.621164 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.18982e9i | 1.12265i | 0.827597 | + | 0.561323i | \(0.189707\pi\) | ||||
−0.827597 | + | 0.561323i | \(0.810293\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.31401e8i | 0.677514i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.10325e8 | 0.555092 | 0.277546 | − | 0.960712i | \(-0.410479\pi\) | ||||
0.277546 | + | 0.960712i | \(0.410479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.82680e9 | −1.63147 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.67355e8i | − 0.322179i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.28519e8i | − 0.541371i | −0.962668 | − | 0.270685i | \(-0.912750\pi\) | ||||
0.962668 | − | 0.270685i | \(-0.0872503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.04321e8 | 0.342064 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.07273e9 | −0.891491 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.26114e8i | 0.756092i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.99778e9i | − 1.60243i | −0.598374 | − | 0.801217i | \(-0.704186\pi\) | ||||
0.598374 | − | 0.801217i | \(-0.295814\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.31304e9 | −1.03484 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.23030e7 | −0.0482507 | −0.0241254 | − | 0.999709i | \(-0.507680\pi\) | ||||
−0.0241254 | + | 0.999709i | \(0.507680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3.03321e8i | − 0.230853i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.57494e8i | 0.192608i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.50671e9 | 1.84299 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.65740e9 | 1.19783 | 0.598914 | − | 0.800813i | \(-0.295599\pi\) | ||||
0.598914 | + | 0.800813i | \(0.295599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.99661e7i | 0.0141856i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.43489e8i | − 0.239932i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.10808e9 | −0.761032 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.40615e8 | −0.567703 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.44718e8i | 0.361762i | 0.983505 | + | 0.180881i | \(0.0578949\pi\) | ||||
−0.983505 | + | 0.180881i | \(0.942105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.75919e9i | − 1.14901i | −0.818500 | − | 0.574507i | \(-0.805194\pi\) | ||||
0.818500 | − | 0.574507i | \(-0.194806\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.07774e8 | −0.454677 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.39335e9 | −2.14421 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.81946e9i | 1.13095i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3.78150e8i | − 0.231241i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.38357e8 | −0.384055 | −0.192027 | − | 0.981390i | \(-0.561506\pi\) | ||||
−0.192027 | + | 0.981390i | \(0.561506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.18840e9 | 0.703486 | 0.351743 | − | 0.936097i | \(-0.385589\pi\) | ||||
0.351743 | + | 0.936097i | \(0.385589\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.75212e9i | − 1.60308i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.09752e9i | − 0.629113i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.11390e8 | 0.401312 | 0.200656 | − | 0.979662i | \(-0.435693\pi\) | ||||
0.200656 | + | 0.979662i | \(0.435693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.01820e8 | 0.0565324 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1.92825e9i | − 1.05378i | −0.849934 | − | 0.526890i | \(-0.823358\pi\) | ||||
0.849934 | − | 0.526890i | \(-0.176642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.53930e9i | − 0.828065i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.50574e7 | −0.0503396 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.20494e9 | −1.14957 | −0.574784 | − | 0.818305i | \(-0.694914\pi\) | ||||
−0.574784 | + | 0.818305i | \(0.694914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.55276e9i | 1.31036i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 2.99298e8i | − 0.151273i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.23086e9 | 0.612591 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.84830e9 | −1.39598 | −0.697989 | − | 0.716109i | \(-0.745921\pi\) | ||||
−0.697989 | + | 0.716109i | \(0.745921\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.26412e8i | 0.205819i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.27737e9i | − 0.607242i | −0.952793 | − | 0.303621i | \(-0.901804\pi\) | ||||
0.952793 | − | 0.303621i | \(-0.0981957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.68144e7 | −0.0406498 | −0.0203249 | − | 0.999793i | \(-0.506470\pi\) | ||||
−0.0203249 | + | 0.999793i | \(0.506470\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.29172e9 | 0.595777 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2.98319e9i | − 1.35541i | −0.735332 | − | 0.677707i | \(-0.762974\pi\) | ||||
0.735332 | − | 0.677707i | \(-0.237026\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.61544e9i | 0.723081i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.81313e7 | −0.0168155 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.29747e9 | −0.998240 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.21120e9i | 3.94356i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.08987e9i | 0.459792i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.69279e9 | 1.11951 | 0.559756 | − | 0.828658i | \(-0.310895\pi\) | ||||
0.559756 | + | 0.828658i | \(0.310895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.68898e9 | −0.692016 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.16715e8i | − 0.168277i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.15054e9i | 0.457936i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.99374e9 | −0.782199 | −0.391100 | − | 0.920348i | \(-0.627905\pi\) | ||||
−0.391100 | + | 0.920348i | \(0.627905\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.52751e8 | −0.213771 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.20091e9i | 0.839106i | 0.907731 | + | 0.419553i | \(0.137813\pi\) | ||||
−0.907731 | + | 0.419553i | \(0.862187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.55752e9i | − 1.71303i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.61039e9 | 0.596777 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.06836e9 | −0.390365 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.86309e9i | 0.671248i | 0.941996 | + | 0.335624i | \(0.108947\pi\) | ||||
−0.941996 | + | 0.335624i | \(0.891053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1.70482e9i | − 0.605683i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.27812e9 | −0.447800 | −0.223900 | − | 0.974612i | \(-0.571879\pi\) | ||||
−0.223900 | + | 0.974612i | \(0.571879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.47667e9 | −0.855752 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.43942e9i | − 0.490523i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.98340e9i | 1.00277i | 0.865226 | + | 0.501383i | \(0.167175\pi\) | ||||
−0.865226 | + | 0.501383i | \(0.832825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.65464e9 | 0.880102 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.15749e9 | 0.378535 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 5.10580e9i | − 1.64717i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.42647e9i | 1.40877i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.13316e9 | 0.355798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.31306e9 | 1.33614 | 0.668072 | − | 0.744097i | \(-0.267120\pi\) | ||||
0.668072 | + | 0.744097i | \(0.267120\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.68806e9i | − 0.515979i | −0.966148 | − | 0.257989i | \(-0.916940\pi\) | ||||
0.966148 | − | 0.257989i | \(-0.0830599\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.49737e9i | 1.05483i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.13910e9 | 0.636640 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.05651e9 | −0.897699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.02798e8i | 0.0877652i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.72001e9i | − 0.492022i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.99710e9 | −0.846182 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.37210e9 | −0.382362 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 6.36789e8i | − 0.175160i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.61857e9i | 1.25406i | 0.778997 | + | 0.627028i | \(0.215729\pi\) | ||||
−0.778997 | + | 0.627028i | \(0.784271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.65084e9 | −0.710533 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.66438e9 | −1.23426 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5.23901e9i | − 1.36865i | −0.729176 | − | 0.684327i | \(-0.760096\pi\) | ||||
0.729176 | − | 0.684327i | \(-0.239904\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.60392e9i | − 0.413694i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.23713e10 | −3.15055 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.58066e9 | 0.397467 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 7.19266e9i | − 1.78593i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.07267e9i | 0.508203i | 0.967178 | + | 0.254101i | \(0.0817797\pi\) | ||||
−0.967178 | + | 0.254101i | \(0.918220\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.54799e9 | 0.374824 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.66681e9 | 0.637708 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.56961e9i | − 0.370692i | −0.982673 | − | 0.185346i | \(-0.940659\pi\) | ||||
0.982673 | − | 0.185346i | \(-0.0593405\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.14286e10i | 2.66578i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.39484e8 | 0.101252 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.78553e9 | 1.08902 | 0.544512 | − | 0.838753i | \(-0.316715\pi\) | ||||
0.544512 | + | 0.838753i | \(0.316715\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.06103e9i | 1.58724i | 0.608416 | + | 0.793618i | \(0.291805\pi\) | ||||
−0.608416 | + | 0.793618i | \(0.708195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.52126e9i | − 0.337802i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.92333e9 | −0.641270 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.94695e9 | 1.72221 | 0.861103 | − | 0.508431i | \(-0.169774\pi\) | ||||
0.861103 | + | 0.508431i | \(0.169774\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 8.24862e8i | − 0.176606i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.89124e9i | 0.400064i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.81615e9 | 1.42462 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.08505e9 | −0.224081 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.79237e8i | 0.0773886i | 0.999251 | + | 0.0386943i | \(0.0123199\pi\) | ||||
−0.999251 | + | 0.0386943i | \(0.987680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5.80656e9i | − 1.17089i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.36813e9 | 1.06971 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.12403e9 | 1.20600 | 0.602998 | − | 0.797742i | \(-0.293973\pi\) | ||||
0.602998 | + | 0.797742i | \(0.293973\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.68037e9i | 1.68939i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.62962e9i | − 0.890503i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.63280e9 | −0.310412 | −0.155206 | − | 0.987882i | \(-0.549604\pi\) | ||||
−0.155206 | + | 0.987882i | \(0.549604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.80391e8 | 0.0338965 | 0.0169482 | − | 0.999856i | \(-0.494605\pi\) | ||||
0.0169482 | + | 0.999856i | \(0.494605\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.42407e9i | − 0.264497i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 6.29541e8i | − 0.115579i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.34640e9 | −0.607320 | −0.303660 | − | 0.952780i | \(-0.598209\pi\) | ||||
−0.303660 | + | 0.952780i | \(0.598209\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.69723e9 | −0.842716 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.98248e9i | − 0.528973i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.73850e9i | − 1.00621i | −0.864227 | − | 0.503103i | \(-0.832192\pi\) | ||||
0.864227 | − | 0.503103i | \(-0.167808\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.32481e9 | 1.26979 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.70937e9 | −0.464377 | −0.232188 | − | 0.972671i | \(-0.574589\pi\) | ||||
−0.232188 | + | 0.972671i | \(0.574589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.14429e9i | 1.38018i | 0.723723 | + | 0.690090i | \(0.242429\pi\) | ||||
−0.723723 | + | 0.690090i | \(0.757571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.67349e8i | 0.0615543i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.62724e9 | −0.435303 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.19404e9 | 1.01483 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7.23902e9i | − 1.17285i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.19111e10i | − 1.90842i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.96870e9 | 0.470397 | 0.235198 | − | 0.971947i | \(-0.424426\pi\) | ||||
0.235198 | + | 0.971947i | \(0.424426\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.82226e8 | −0.122580 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.31251e10i | − 2.03421i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.29057e8i | 0.0657699i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.41799e8 | 0.142792 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.66582e9 | 0.399787 | 0.199893 | − | 0.979818i | \(-0.435940\pi\) | ||||
0.199893 | + | 0.979818i | \(0.435940\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.27436e10i | 1.89040i | 0.326490 | + | 0.945201i | \(0.394134\pi\) | ||||
−0.326490 | + | 0.945201i | \(0.605866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.59227e9i | 0.967333i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.37698e9 | −0.635345 | −0.317672 | − | 0.948201i | \(-0.602901\pi\) | ||||
−0.317672 | + | 0.948201i | \(0.602901\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.89372e9 | 0.271932 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.20467e9i | − 0.313192i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.10731e9i | 0.436705i | 0.975870 | + | 0.218353i | \(0.0700683\pi\) | ||||
−0.975870 | + | 0.218353i | \(0.929932\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.92504e10 | 2.67667 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.34016e9 | −0.321934 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.99805e9i | − 0.271962i | −0.990711 | − | 0.135981i | \(-0.956581\pi\) | ||||
0.990711 | − | 0.135981i | \(-0.0434186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.24765e9i | − 0.841417i | −0.907196 | − | 0.420709i | \(-0.861781\pi\) | ||||
0.907196 | − | 0.420709i | \(-0.138219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.79685e9 | −0.239450 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.35628e10 | 3.10706 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.92626e9i | − 0.512316i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 7.55885e9i | − 0.976032i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.00310e10 | −1.28179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.67358e9 | 0.338096 | 0.169048 | − | 0.985608i | \(-0.445931\pi\) | ||||
0.169048 | + | 0.985608i | \(0.445931\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.08306e9i | − 0.385850i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 9.95715e9i | − 1.23332i | −0.787231 | − | 0.616658i | \(-0.788486\pi\) | ||||
0.787231 | − | 0.616658i | \(-0.211514\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.96370e9 | 0.240731 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.14027e9 | 0.987697 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 7.62355e9i | − 0.915555i | −0.889067 | − | 0.457778i | \(-0.848646\pi\) | ||||
0.889067 | − | 0.457778i | \(-0.151354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 3.58296e8i | − 0.0425917i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.33329e9 | −0.745214 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.59260e9 | −0.534923 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.62210e9i | 0.417625i | 0.977956 | + | 0.208813i | \(0.0669599\pi\) | ||||
−0.977956 | + | 0.208813i | \(0.933040\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.74856e9i | − 0.313718i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.50850e10 | 1.70451 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.21299e10 | 1.35688 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.09654e9i | 0.564424i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.00062e10i | − 1.09712i | −0.836111 | − | 0.548560i | \(-0.815176\pi\) | ||||
0.836111 | − | 0.548560i | \(-0.184824\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.23325e10 | −3.50991 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.27012e10 | 1.36515 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.22710e9i | 0.449857i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.02466e10i | − 1.07974i | −0.841748 | − | 0.539871i | \(-0.818473\pi\) | ||||
0.841748 | − | 0.539871i | \(-0.181527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.39341e9 | −0.145390 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.84281e9 | 0.190400 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.78599e9i | 0.694292i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.07070e10i | 1.08481i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.71442e9 | 0.974689 | 0.487344 | − | 0.873210i | \(-0.337966\pi\) | ||||
0.487344 | + | 0.873210i | \(0.337966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.71443e9 | −0.865896 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.97393e9i | − 0.194244i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.29519e10i | 3.21143i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.01862e10 | 0.983201 | 0.491600 | − | 0.870821i | \(-0.336412\pi\) | ||||
0.491600 | + | 0.870821i | \(0.336412\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.09168e10i | 1.03368i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.49661e10i | 1.40360i | 0.712374 | + | 0.701800i | \(0.247620\pi\) | ||||
−0.712374 | + | 0.701800i | \(0.752380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.82718e9 | −0.169737 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.90625e9 | −0.819518 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.66094e10i | 1.51390i | 0.653471 | + | 0.756952i | \(0.273312\pi\) | ||||
−0.653471 | + | 0.756952i | \(0.726688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.87753e9i | 0.440389i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.30569e9 | −0.385107 | −0.192554 | − | 0.981286i | \(-0.561677\pi\) | ||||
−0.192554 | + | 0.981286i | \(0.561677\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.70583e9 | 0.151143 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.66720e9i | − 0.146340i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.11537e9i | 0.444826i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.44644e9 | −0.813820 | −0.406910 | − | 0.913468i | \(-0.633394\pi\) | ||||
−0.406910 | + | 0.913468i | \(0.633394\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.10726e10 | 0.945076 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.37097e9i | 0.454191i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.38829e9i | − 0.116318i | −0.998307 | − | 0.0581589i | \(-0.981477\pi\) | ||||
0.998307 | − | 0.0581589i | \(-0.0185230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.29743e9 | 0.190720 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.38138e10 | 1.13623 | 0.568117 | − | 0.822948i | \(-0.307672\pi\) | ||||
0.568117 | + | 0.822948i | \(0.307672\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.96102e9i | 0.648833i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 7.65206e9i | − 0.617964i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.27596e9 | −0.102106 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.94935e10 | 1.54578 | 0.772889 | − | 0.634541i | \(-0.218811\pi\) | ||||
0.772889 | + | 0.634541i | \(0.218811\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 4.67722e9i | − 0.367534i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.67350e10i | 1.30316i | 0.758580 | + | 0.651580i | \(0.225894\pi\) | ||||
−0.758580 | + | 0.651580i | \(0.774106\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.54662e10 | −1.19351 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.22762e10 | −0.938839 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 3.29265e10i | − 2.49554i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 5.89008e9i | − 0.442428i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.14078e9 | 0.308259 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.84275e8 | 0.0504878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.84916e10i | 1.35227i | 0.736780 | + | 0.676133i | \(0.236345\pi\) | ||||
−0.736780 | + | 0.676133i | \(0.763655\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.39059e10i | 1.00793i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.95060e10 | 1.40136 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.75872e9 | 0.481292 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.95580e10i | − 1.38051i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.24812e10i | − 0.873279i | −0.899636 | − | 0.436640i | \(-0.856168\pi\) | ||||
0.899636 | − | 0.436640i | \(-0.143832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.10332e10 | 1.45879 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.31600e9 | 0.159230 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.46356e10i | 0.997481i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.47805e9i | 0.505246i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.39274e10 | −0.932854 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.91309e9 | 0.326238 | 0.163119 | − | 0.986606i | \(-0.447845\pi\) | ||||
0.163119 | + | 0.986606i | \(0.447845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.33853e10i | − 0.881163i | −0.897713 | − | 0.440582i | \(-0.854772\pi\) | ||||
0.897713 | − | 0.440582i | \(-0.145228\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.93969e8i | − 0.0126595i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.91923e9 | 0.641840 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.96336e10 | 1.90111 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.85193e9i | 0.117796i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.59686e10i | − 1.00708i | −0.863972 | − | 0.503541i | \(-0.832030\pi\) | ||||
0.863972 | − | 0.503541i | \(-0.167970\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.10577e10 | −1.31678 | −0.658388 | − | 0.752679i | \(-0.728761\pi\) | ||||
−0.658388 | + | 0.752679i | \(0.728761\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.92817e10 | −1.19552 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.86289e10i | 1.14529i | 0.819802 | + | 0.572647i | \(0.194084\pi\) | ||||
−0.819802 | + | 0.572647i | \(0.805916\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.26711e10i | 0.772458i | 0.922403 | + | 0.386229i | \(0.126223\pi\) | ||||
−0.922403 | + | 0.386229i | \(0.873777\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.00556e10 | −0.607860 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.02582e9 | −0.181378 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.05933e10i | 1.81854i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.94350e9i | 0.114563i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.02505e10 | 1.18377 | 0.591887 | − | 0.806021i | \(-0.298383\pi\) | ||||
0.591887 | + | 0.806021i | \(0.298383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.70070e10 | −1.56564 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 6.23082e9i | − 0.358219i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.58307e10i | 1.47278i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.07448e9 | −0.0607585 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.63401e9 | 0.0916384 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.02613e10i | − 0.570753i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.31306e10i | − 1.27605i | −0.770018 | − | 0.638023i | \(-0.779753\pi\) | ||||
0.770018 | − | 0.638023i | \(-0.220247\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.07714e10 | −1.13654 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.26288e10 | −0.685375 | −0.342687 | − | 0.939450i | \(-0.611337\pi\) | ||||
−0.342687 | + | 0.939450i | \(0.611337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.10559e10i | − 1.13344i | −0.823912 | − | 0.566718i | \(-0.808213\pi\) | ||||
0.823912 | − | 0.566718i | \(-0.191787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.25018e10i | − 0.667513i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.68819e10 | 0.894094 | 0.447047 | − | 0.894510i | \(-0.352476\pi\) | ||||
0.447047 | + | 0.894510i | \(0.352476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.03347e10 | −1.06827 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.59270e9i | − 0.0829977i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.71449e9i | 0.450477i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00087e9 | 0.307717 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.73108e9 | −0.0880575 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.14578e10i | − 1.58745i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.53077e10i | − 0.766321i | −0.923682 | − | 0.383161i | \(-0.874836\pi\) | ||||
0.923682 | − | 0.383161i | \(-0.125164\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.31115e9 | 0.114780 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.25753e10 | −1.60499 | −0.802497 | − | 0.596657i | \(-0.796495\pi\) | ||||
−0.802497 | + | 0.596657i | \(0.796495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.59810e10i | − 0.781164i | −0.920568 | − | 0.390582i | \(-0.872274\pi\) | ||||
0.920568 | − | 0.390582i | \(-0.127726\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 5.43378e9i | − 0.263512i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.40697e10 | 0.676944 | 0.338472 | − | 0.940976i | \(-0.390090\pi\) | ||||
0.338472 | + | 0.940976i | \(0.390090\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.24016e10 | −1.06936 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.42296e9i | 0.114756i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.70943e10i | − 2.68295i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.46226e10 | 1.14803 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.54797e9 | −0.0716124 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 2.07722e10i | − 0.953508i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.23882e10i | − 1.47520i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.12515e10 | 0.508514 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.75700e10 | 2.13335 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.65877e10i | − 1.18319i | −0.806235 | − | 0.591596i | \(-0.798498\pi\) | ||||
0.806235 | − | 0.591596i | \(-0.201502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 3.72634e9i | − 0.164554i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.29192e9 | 0.275721 | 0.137860 | − | 0.990452i | \(-0.455978\pi\) | ||||
0.137860 | + | 0.990452i | \(0.455978\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.04268e10 | −0.453421 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.87826e10i | 1.24210i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 3.28560e10i | − 1.40709i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.48465e10 | −1.90601 | −0.953003 | − | 0.302961i | \(-0.902025\pi\) | ||||
−0.953003 | + | 0.302961i | \(0.902025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.01908e10 | 0.851620 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.96863e9i | 0.166125i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.61200e10i | 3.57773i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.68209e9 | 0.316738 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.21912e10 | 0.498873 | 0.249436 | − | 0.968391i | \(-0.419755\pi\) | ||||
0.249436 | + | 0.968391i | \(0.419755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.21355e9i | 0.333585i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.38470e9i | 0.0961275i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.78565e10 | −1.91470 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.15735e9 | −0.165093 | −0.0825464 | − | 0.996587i | \(-0.526305\pi\) | ||||
−0.0825464 | + | 0.996587i | \(0.526305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.53536e9i | 0.297012i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.56765e9i | − 0.100455i | −0.998738 | − | 0.0502276i | \(-0.984005\pi\) | ||||
0.998738 | − | 0.0502276i | \(-0.0159947\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.04498e10 | 0.405804 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.88663e9 | −0.304005 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.08480e10i | 0.797699i | 0.917016 | + | 0.398850i | \(0.130590\pi\) | ||||
−0.917016 | + | 0.398850i | \(0.869410\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 9.86118e9i | − 0.374539i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.55459e9 | −0.247123 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.94449e10 | −1.47627 | −0.738136 | − | 0.674652i | \(-0.764294\pi\) | ||||
−0.738136 | + | 0.674652i | \(0.764294\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.72993e10i | 1.01424i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.58967e10i | − 0.955109i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.11528e8 | −0.0223899 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.77630e10 | −0.645633 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 4.50938e9i | − 0.162714i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.48023e10i | 0.530254i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.48161e10 | 0.526917 | 0.263459 | − | 0.964671i | \(-0.415137\pi\) | ||||
0.263459 | + | 0.964671i | \(0.415137\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.43976e10 | −1.21449 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.49709e10i | − 0.875320i | −0.899141 | − | 0.437660i | \(-0.855807\pi\) | ||||
0.899141 | − | 0.437660i | \(-0.144193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.57467e10i | − 0.896037i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.29917e10 | 0.448899 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.62341e10 | −0.899986 | −0.449993 | − | 0.893032i | \(-0.648573\pi\) | ||||
−0.449993 | + | 0.893032i | \(0.648573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.44845e10i | − 0.493359i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 7.01793e9i | − 0.237338i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.57411e10 | −1.20014 | −0.600068 | − | 0.799949i | \(-0.704860\pi\) | ||||
−0.600068 | + | 0.799949i | \(0.704860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.63322e10 | −3.21177 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.16780e10i | − 0.717643i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.40474e9i | 0.309143i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.91765e10 | −1.27870 | −0.639349 | − | 0.768917i | \(-0.720796\pi\) | ||||
−0.639349 | + | 0.768917i | \(0.720796\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.12669e10 | 0.689257 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.30796e10i | 2.67370i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.56332e8i | − 0.0113873i | −0.999984 | − | 0.00569366i | \(-0.998188\pi\) | ||||
0.999984 | − | 0.00569366i | \(-0.00181236\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.08219e10 | 0.343420 |
(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.193.8 | yes | 16 | |
4.3 | odd | 2 | inner | 384.8.d.f.193.16 | yes | 16 | |
8.3 | odd | 2 | inner | 384.8.d.f.193.1 | ✓ | 16 | |
8.5 | even | 2 | inner | 384.8.d.f.193.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.f.193.1 | ✓ | 16 | 8.3 | odd | 2 | inner | |
384.8.d.f.193.8 | yes | 16 | 1.1 | even | 1 | trivial | |
384.8.d.f.193.9 | yes | 16 | 8.5 | even | 2 | inner | |
384.8.d.f.193.16 | yes | 16 | 4.3 | odd | 2 | inner |