Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,7,Mod(161,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.h (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: | \(132.511152165\) |
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: | \( x^{16} - 8 x^{15} + 964 x^{14} - 6608 x^{13} + 404616 x^{12} - 2342156 x^{11} + 95125730 x^{10} - 454315424 x^{9} + 13646460877 x^{8} + \cdots + 39\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{36} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.14 | ||
Root | \(3.36747 + 7.23051i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.161 |
Dual form | 576.7.h.a.161.13 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 168.989 | 1.35191 | 0.675955 | − | 0.736943i | \(-0.263731\pi\) | ||||
0.675955 | + | 0.736943i | \(0.263731\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.9908 | −0.0407895 | −0.0203948 | − | 0.999792i | \(-0.506492\pi\) | ||||
−0.0203948 | + | 0.999792i | \(0.506492\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1500.86 | 1.12762 | 0.563809 | − | 0.825905i | \(-0.309335\pi\) | ||||
0.563809 | + | 0.825905i | \(0.309335\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 744.941i | 0.339072i | 0.985524 | + | 0.169536i | \(0.0542269\pi\) | ||||
−0.985524 | + | 0.169536i | \(0.945773\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2963.54i | − 0.603203i | −0.953434 | − | 0.301602i | \(-0.902479\pi\) | ||||
0.953434 | − | 0.301602i | \(-0.0975213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6311.61i | 0.920194i | 0.887869 | + | 0.460097i | \(0.152185\pi\) | ||||
−0.887869 | + | 0.460097i | \(0.847815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 9997.60i | − 0.821698i | −0.911703 | − | 0.410849i | \(-0.865232\pi\) | ||||
0.911703 | − | 0.410849i | \(-0.134768\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12932.2 | 0.827662 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20393.1 | 0.836161 | 0.418081 | − | 0.908410i | \(-0.362703\pi\) | ||||
0.418081 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39212.3 | 1.31625 | 0.658123 | − | 0.752910i | \(-0.271350\pi\) | ||||
0.658123 | + | 0.752910i | \(0.271350\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2364.29 | −0.0551438 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 89287.8i | 1.76273i | 0.472432 | + | 0.881367i | \(0.343376\pi\) | ||||
−0.472432 | + | 0.881367i | \(0.656624\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20087.0i | 0.291450i | 0.989325 | + | 0.145725i | \(0.0465515\pi\) | ||||
−0.989325 | + | 0.145725i | \(0.953448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 55492.9i | − 0.697962i | −0.937130 | − | 0.348981i | \(-0.886528\pi\) | ||||
0.937130 | − | 0.348981i | \(-0.113472\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 108404.i | − 1.04412i | −0.852909 | − | 0.522060i | \(-0.825164\pi\) | ||||
0.852909 | − | 0.522060i | \(-0.174836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −117453. | −0.998336 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 143755. | 0.965596 | 0.482798 | − | 0.875732i | \(-0.339621\pi\) | ||||
0.482798 | + | 0.875732i | \(0.339621\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 253629. | 1.52444 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11065.7 | −0.0538792 | −0.0269396 | − | 0.999637i | \(-0.508576\pi\) | ||||
−0.0269396 | + | 0.999637i | \(0.508576\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 175980.i | 0.775305i | 0.921806 | + | 0.387653i | \(0.126714\pi\) | ||||
−0.921806 | + | 0.387653i | \(0.873286\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 125887.i | 0.458395i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42074.2i | 0.139892i | 0.997551 | + | 0.0699458i | \(0.0222826\pi\) | ||||
−0.997551 | + | 0.0699458i | \(0.977717\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 103977.i | − 0.290511i | −0.989394 | − | 0.145256i | \(-0.953600\pi\) | ||||
0.989394 | − | 0.145256i | \(-0.0464005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 539416. | 1.38661 | 0.693307 | − | 0.720643i | \(-0.256153\pi\) | ||||
0.693307 | + | 0.720643i | \(0.256153\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −20998.3 | −0.0459951 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −479208. | −0.971946 | −0.485973 | − | 0.873974i | \(-0.661535\pi\) | ||||
−0.485973 | + | 0.873974i | \(0.661535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 485444. | 0.848995 | 0.424498 | − | 0.905429i | \(-0.360451\pi\) | ||||
0.424498 | + | 0.905429i | \(0.360451\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 500805.i | − 0.815477i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 310114.i | − 0.439898i | −0.975511 | − | 0.219949i | \(-0.929411\pi\) | ||||
0.975511 | − | 0.219949i | \(-0.0705891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 10422.3i | − 0.0138306i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.06659e6i | 1.24402i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −199839. | −0.218960 | −0.109480 | − | 0.993989i | \(-0.534919\pi\) | ||||
−0.109480 | + | 0.993989i | \(0.534919\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.20189e6 | −1.16654 | −0.583270 | − | 0.812279i | \(-0.698227\pi\) | ||||
−0.583270 | + | 0.812279i | \(0.698227\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −416228. | −0.380907 | −0.190454 | − | 0.981696i | \(-0.560996\pi\) | ||||
−0.190454 | + | 0.981696i | \(0.560996\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 664061. | 0.542071 | 0.271036 | − | 0.962569i | \(-0.412634\pi\) | ||||
0.271036 | + | 0.962569i | \(0.412634\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.42279e6i | − 1.09865i | −0.835608 | − | 0.549326i | \(-0.814885\pi\) | ||||
0.835608 | − | 0.549326i | \(-0.185115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.58232e6i | 1.78968i | 0.446390 | + | 0.894838i | \(0.352709\pi\) | ||||
−0.446390 | + | 0.894838i | \(0.647291\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.68948e6i | − 1.11086i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 41462.3i | 0.0246044i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 481022. | 0.271524 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −455049. | −0.232985 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.13676e6 | −1.53134 | −0.765668 | − | 0.643237i | \(-0.777591\pi\) | ||||
−0.765668 | + | 0.643237i | \(0.777591\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 418255. | 0.186049 | 0.0930245 | − | 0.995664i | \(-0.470347\pi\) | ||||
0.0930245 | + | 0.995664i | \(0.470347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 88304.6i | − 0.0375343i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.05135e6i | 0.797772i | 0.917000 | + | 0.398886i | \(0.130603\pi\) | ||||
−0.917000 | + | 0.398886i | \(0.869397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.00434e6i | − 0.746322i | −0.927767 | − | 0.373161i | \(-0.878274\pi\) | ||||
0.927767 | − | 0.373161i | \(-0.121726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.11805e6i | 0.382344i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.44621e6 | 1.13042 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.32337e6 | 0.702361 | 0.351180 | − | 0.936308i | \(-0.385780\pi\) | ||||
0.351180 | + | 0.936308i | \(0.385780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.44651e6 | 1.87238 | 0.936190 | − | 0.351493i | \(-0.114326\pi\) | ||||
0.936190 | + | 0.351493i | \(0.114326\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.62644e6 | 1.77945 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.70983e6i | 0.700233i | 0.936706 | + | 0.350117i | \(0.113858\pi\) | ||||
−0.936706 | + | 0.350117i | \(0.886142\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 139875.i | 0.0335167i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 940013.i | − 0.217056i | −0.994093 | − | 0.108528i | \(-0.965386\pi\) | ||||
0.994093 | − | 0.108528i | \(-0.0346136\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 8.67355e6i | − 1.86229i | −0.364647 | − | 0.931146i | \(-0.618810\pi\) | ||||
0.364647 | − | 0.931146i | \(-0.381190\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.27187e6 | 0.885030 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.50876e6 | 0.291395 | 0.145697 | − | 0.989329i | \(-0.453457\pi\) | ||||
0.145697 | + | 0.989329i | \(0.453457\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −180932. | −0.0337600 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.07397e7 | 1.87255 | 0.936277 | − | 0.351262i | \(-0.114247\pi\) | ||||
0.936277 | + | 0.351262i | \(0.114247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.45716e6i | 1.08894i | 0.838779 | + | 0.544472i | \(0.183270\pi\) | ||||
−0.838779 | + | 0.544472i | \(0.816730\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.50886e7i | 2.38306i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.44786e6i | − 0.680183i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.54231e6i | 1.08244i | 0.840881 | + | 0.541220i | \(0.182038\pi\) | ||||
−0.840881 | + | 0.541220i | \(0.817962\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.76476e6 | 1.21918 | 0.609591 | − | 0.792716i | \(-0.291334\pi\) | ||||
0.609591 | + | 0.792716i | \(0.291334\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.83274e6 | 0.501315 | 0.250657 | − | 0.968076i | \(-0.419353\pi\) | ||||
0.250657 | + | 0.968076i | \(0.419353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.16120e7 | 1.47349 | 0.736744 | − | 0.676171i | \(-0.236362\pi\) | ||||
0.736744 | + | 0.676171i | \(0.236362\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −285317. | −0.0341066 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.39449e6i | 0.394015i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.47285e6i | 1.03763i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.50589e7i | − 1.60305i | −0.597962 | − | 0.801524i | \(-0.704023\pi\) | ||||
0.597962 | − | 0.801524i | \(-0.295977\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 9.37768e6i | − 0.943583i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −548612. | −0.0536891 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.20766e6 | 0.204529 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.46388e7 | −1.32005 | −0.660027 | − | 0.751242i | \(-0.729455\pi\) | ||||
−0.660027 | + | 0.751242i | \(0.729455\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.60373e7 | 1.37105 | 0.685526 | − | 0.728048i | \(-0.259572\pi\) | ||||
0.685526 | + | 0.728048i | \(0.259572\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.16093e7i | − 0.966721i | −0.875421 | − | 0.483360i | \(-0.839416\pi\) | ||||
0.875421 | − | 0.483360i | \(-0.160584\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.35696e7i | 1.07275i | 0.843980 | + | 0.536375i | \(0.180207\pi\) | ||||
−0.843980 | + | 0.536375i | \(0.819793\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.83190e7i | − 1.41156i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.26081e6i | 0.312103i | 0.987749 | + | 0.156052i | \(0.0498766\pi\) | ||||
−0.987749 | + | 0.156052i | \(0.950123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.40563e7 | 1.00420 | 0.502101 | − | 0.864809i | \(-0.332561\pi\) | ||||
0.502101 | + | 0.864809i | \(0.332561\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.98483e7 | −1.34966 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.70178e6 | −0.312012 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.96750e7 | 1.87659 | 0.938296 | − | 0.345833i | \(-0.112404\pi\) | ||||
0.938296 | + | 0.345833i | \(0.112404\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.50050e7i | − 0.926562i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.40873e7i | 1.41902i | 0.704696 | + | 0.709509i | \(0.251083\pi\) | ||||
−0.704696 | + | 0.709509i | \(0.748917\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.24921e6i | − 0.0719011i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.72669e7i | 1.49888i | 0.662070 | + | 0.749442i | \(0.269678\pi\) | ||||
−0.662070 | + | 0.749442i | \(0.730322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.42930e7 | 1.30540 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.01871e6 | −0.206457 | −0.103229 | − | 0.994658i | \(-0.532917\pi\) | ||||
−0.103229 | + | 0.994658i | \(0.532917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.31382e7 | −1.16258 | −0.581288 | − | 0.813698i | \(-0.697451\pi\) | ||||
−0.581288 | + | 0.813698i | \(0.697451\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.94095e7 | 0.933288 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 6.24314e6i | − 0.293740i | −0.989156 | − | 0.146870i | \(-0.953080\pi\) | ||||
0.989156 | − | 0.146870i | \(-0.0469200\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.15373e6i | 0.232275i | 0.993233 | + | 0.116137i | \(0.0370513\pi\) | ||||
−0.993233 | + | 0.116137i | \(0.962949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.21978e7i | 0.538174i | 0.963116 | + | 0.269087i | \(0.0867218\pi\) | ||||
−0.963116 | + | 0.269087i | \(0.913278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 281034.i | − 0.0118881i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.53550e7 | 0.636146 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.58367e6 | 0.381003 | 0.190502 | − | 0.981687i | \(-0.438989\pi\) | ||||
0.190502 | + | 0.981687i | \(0.438989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.86997e6 | −0.0728399 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.44761e6 | 0.278614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 776391.i | 0.0284696i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.97386e7i | 1.04814i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.65639e7i | − 1.26368i | −0.775098 | − | 0.631841i | \(-0.782300\pi\) | ||||
0.775098 | − | 0.631841i | \(-0.217700\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 2.14969e7i | − 0.714653i | −0.933980 | − | 0.357327i | \(-0.883688\pi\) | ||||
0.933980 | − | 0.357327i | \(-0.116312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.15571e7 | 0.703004 | 0.351502 | − | 0.936187i | \(-0.385671\pi\) | ||||
0.351502 | + | 0.936187i | \(0.385671\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.84431e7 | −1.20681 | −0.603407 | − | 0.797433i | \(-0.706190\pi\) | ||||
−0.603407 | + | 0.797433i | \(0.706190\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.06073e7 | 0.942871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.87047e7 | 0.555064 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.63374e6i | 0.280637i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.51665e6i | 0.0425892i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.00607e7i | − 1.10467i | −0.833621 | − | 0.552337i | \(-0.813736\pi\) | ||||
0.833621 | − | 0.552337i | \(-0.186264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.11007e6i | 0.189121i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.98363e7 | −1.04085 | −0.520426 | − | 0.853907i | \(-0.674227\pi\) | ||||
−0.520426 | + | 0.853907i | \(0.674227\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.88522e7 | 1.48422 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.28927e6 | 0.0815112 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.80254e6 | 0.0910092 | 0.0455046 | − | 0.998964i | \(-0.485510\pi\) | ||||
0.0455046 | + | 0.998964i | \(0.485510\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.37735e7i | 0.559263i | 0.960107 | + | 0.279632i | \(0.0902123\pi\) | ||||
−0.960107 | + | 0.279632i | \(0.909788\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.78223e7i | 0.632512i | 0.948674 | + | 0.316256i | \(0.102426\pi\) | ||||
−0.948674 | + | 0.316256i | \(0.897574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.75710e7i | − 0.392745i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 2.62940e7i | − 0.568293i | −0.958781 | − | 0.284147i | \(-0.908290\pi\) | ||||
0.958781 | − | 0.284147i | \(-0.0917103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.20942e6 | 0.153242 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.11553e7 | 1.87458 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.54421e7 | 1.32391 | 0.661956 | − | 0.749542i | \(-0.269726\pi\) | ||||
0.661956 | + | 0.749542i | \(0.269726\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.01125e6 | −0.0393862 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.34853e7i | 1.22334i | 0.791114 | + | 0.611669i | \(0.209502\pi\) | ||||
−0.791114 | + | 0.611669i | \(0.790498\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.51917e7i | 0.283519i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.56684e7i | 1.57363i | 0.617188 | + | 0.786816i | \(0.288272\pi\) | ||||
−0.617188 | + | 0.786816i | \(0.711728\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 9.73160e7i | − 1.73216i | −0.499906 | − | 0.866080i | \(-0.666632\pi\) | ||||
0.499906 | − | 0.866080i | \(-0.333368\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.54847e6 | −0.0621812 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.00954e8 | −1.71504 | −0.857519 | − | 0.514452i | \(-0.827995\pi\) | ||||
−0.857519 | + | 0.514452i | \(0.827995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.96283e7 | −0.495651 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.09807e7 | −1.31398 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.94102e7i | 0.470031i | 0.971992 | + | 0.235015i | \(0.0755140\pi\) | ||||
−0.971992 | + | 0.235015i | \(0.924486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 9.81649e7i | − 1.52238i | −0.648529 | − | 0.761190i | \(-0.724616\pi\) | ||||
0.648529 | − | 0.761190i | \(-0.275384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.92108e7i | 0.446302i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.34009e8i | 1.98769i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.36974e7 | 0.346363 | 0.173181 | − | 0.984890i | \(-0.444595\pi\) | ||||
0.173181 | + | 0.984890i | \(0.444595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 154818. | 0.00219771 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.20347e7 | 1.14777 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.91039e7 | 1.21131 | 0.605654 | − | 0.795728i | \(-0.292911\pi\) | ||||
0.605654 | + | 0.795728i | \(0.292911\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 8.70306e7i | − 1.16634i | −0.812350 | − | 0.583170i | \(-0.801812\pi\) | ||||
0.812350 | − | 0.583170i | \(-0.198188\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 3.83251e7i | − 0.499249i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.46210e6i | − 0.0316244i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 3.98013e7i | − 0.497125i | −0.968616 | − | 0.248563i | \(-0.920042\pi\) | ||||
0.968616 | − | 0.248563i | \(-0.0799582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.08244e7 | 0.256512 | 0.128256 | − | 0.991741i | \(-0.459062\pi\) | ||||
0.128256 | + | 0.991741i | \(0.459062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.31010e7 | 0.756122 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.38090e8 | −1.63218 | −0.816090 | − | 0.577926i | \(-0.803862\pi\) | ||||
−0.816090 | + | 0.577926i | \(0.803862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.08013e7 | −1.04443 | −0.522217 | − | 0.852813i | \(-0.674895\pi\) | ||||
−0.522217 | + | 0.852813i | \(0.674895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 5.24058e7i | − 0.594702i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 8.73485e7i | − 0.964976i | −0.875903 | − | 0.482488i | \(-0.839733\pi\) | ||||
0.875903 | − | 0.482488i | \(-0.160267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.01479e7i | 0.328645i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 1.76126e6i | − 0.0186977i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.75726e8 | −1.84114 | −0.920570 | − | 0.390578i | \(-0.872275\pi\) | ||||
−0.920570 | + | 0.390578i | \(0.872275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.37345e8 | −1.40187 | −0.700936 | − | 0.713224i | \(-0.747234\pi\) | ||||
−0.700936 | + | 0.713224i | \(0.747234\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.30418e7 | −0.332905 | −0.166452 | − | 0.986049i | \(-0.553231\pi\) | ||||
−0.166452 | + | 0.986049i | \(0.553231\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.48968e8 | −1.46266 | −0.731330 | − | 0.682024i | \(-0.761100\pi\) | ||||
−0.731330 | + | 0.682024i | \(0.761100\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 588652.i | − 0.00570611i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 8.32871e7i | − 0.787036i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.16232e7i | 0.761610i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.47748e8i | 1.34436i | 0.740389 | + | 0.672178i | \(0.234641\pi\) | ||||
−0.740389 | + | 0.672178i | \(0.765359\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.65141e7 | −0.597693 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.37705e7 | −0.296014 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.43723e8 | −1.24434 | −0.622170 | − | 0.782882i | \(-0.713749\pi\) | ||||
−0.622170 | + | 0.782882i | \(0.713749\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.74135e8 | −1.47110 | −0.735550 | − | 0.677471i | \(-0.763076\pi\) | ||||
−0.735550 | + | 0.677471i | \(0.763076\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6.04358e7i | − 0.504375i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.45473e6i | 0.0118498i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.57033e7i | 0.206865i | 0.994636 | + | 0.103433i | \(0.0329826\pi\) | ||||
−0.994636 | + | 0.103433i | \(0.967017\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.86336e6i | 0.0539303i | 0.999636 | + | 0.0269651i | \(0.00858431\pi\) | ||||
−0.999636 | + | 0.0269651i | \(0.991416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.03105e8 | −1.57706 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.26759e6 | 0.0247784 | 0.0123892 | − | 0.999923i | \(-0.496056\pi\) | ||||
0.0123892 | + | 0.999923i | \(0.496056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.54687e6 | −0.0565593 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.03378e7 | −0.514953 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.62699e8i | − 1.17737i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 7.16898e7i | − 0.506926i | −0.967345 | − | 0.253463i | \(-0.918430\pi\) | ||||
0.967345 | − | 0.253463i | \(-0.0815695\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.78584e8i | 1.24835i | 0.781284 | + | 0.624176i | \(0.214565\pi\) | ||||
−0.781284 | + | 0.624176i | \(0.785435\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.16207e8i | − 0.793964i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.80840e7 | 0.324813 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.49637e7 | −0.0988226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.12219e8 | 0.732832 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.76281e8 | −1.12574 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 5.04327e7i | − 0.318508i | −0.987238 | − | 0.159254i | \(-0.949091\pi\) | ||||
0.987238 | − | 0.159254i | \(-0.0509089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 2.40435e8i | − 1.48528i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5.13884e7i | − 0.313981i | −0.987600 | − | 0.156990i | \(-0.949821\pi\) | ||||
0.987600 | − | 0.156990i | \(-0.0501791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.28714e8i | 0.769431i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.70450e6 | 0.0396453 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.14558e8 | 0.662920 | 0.331460 | − | 0.943469i | \(-0.392459\pi\) | ||||
0.331460 | + | 0.943469i | \(0.392459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.13389e7 | 0.236659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.54440e7 | 0.478803 | 0.239401 | − | 0.970921i | \(-0.423049\pi\) | ||||
0.239401 | + | 0.970921i | \(0.423049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.36383e8i | 2.41948i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 3.26748e8i | − 1.77368i | −0.462074 | − | 0.886841i | \(-0.652895\pi\) | ||||
0.462074 | − | 0.886841i | \(-0.347105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.77811e8i | 1.49225i | 0.665806 | + | 0.746125i | \(0.268088\pi\) | ||||
−0.665806 | + | 0.746125i | \(0.731912\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1.29291e8i | − 0.680088i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.83022e8 | −0.952744 | −0.476372 | − | 0.879244i | \(-0.658048\pi\) | ||||
−0.476372 | + | 0.879244i | \(0.658048\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.79176e6 | −0.0346301 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.15756e8 | 1.08882 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.57537e8 | −1.27328 | −0.636641 | − | 0.771160i | \(-0.719677\pi\) | ||||
−0.636641 | + | 0.771160i | \(0.719677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.47493e8i | 1.21120i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.96060e8i | − 0.940210i | −0.882610 | − | 0.470105i | \(-0.844216\pi\) | ||||
0.882610 | − | 0.470105i | \(-0.155784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.00667e6i | 0.0332629i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1.79045e8i | − 0.833072i | −0.909119 | − | 0.416536i | \(-0.863244\pi\) | ||||
0.909119 | − | 0.416536i | \(-0.136756\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.01945e8 | 0.469617 | 0.234808 | − | 0.972042i | \(-0.424554\pi\) | ||||
0.234808 | + | 0.972042i | \(0.424554\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.12873e7 | 0.367077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.68302e7 | −0.254105 | −0.127052 | − | 0.991896i | \(-0.540552\pi\) | ||||
−0.127052 | + | 0.991896i | \(0.540552\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.07542e7 | 0.354031 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.94135e8i | − 0.842797i | −0.906876 | − | 0.421399i | \(-0.861539\pi\) | ||||
0.906876 | − | 0.421399i | \(-0.138461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.21008e8i | 0.515180i | 0.966254 | + | 0.257590i | \(0.0829284\pi\) | ||||
−0.966254 | + | 0.257590i | \(0.917072\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.38818e8i | 1.42855i | 0.699867 | + | 0.714273i | \(0.253243\pi\) | ||||
−0.699867 | + | 0.714273i | \(0.746757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.33875e6i | 0.0179432i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.78964e8 | −1.14264 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.64608e8 | 1.06329 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.31097e8 | 0.919827 | 0.459913 | − | 0.887964i | \(-0.347880\pi\) | ||||
0.459913 | + | 0.887964i | \(0.347880\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.30078e8 | −2.07023 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8.74957e7i | − 0.338508i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.38832e8i | 0.527125i | 0.964642 | + | 0.263563i | \(0.0848976\pi\) | ||||
−0.964642 | + | 0.263563i | \(0.915102\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.50268e8i | − 0.565242i | −0.959232 | − | 0.282621i | \(-0.908796\pi\) | ||||
0.959232 | − | 0.282621i | \(-0.0912039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.22339e8i | − 0.820922i | −0.911878 | − | 0.410461i | \(-0.865368\pi\) | ||||
0.911878 | − | 0.410461i | \(-0.134632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.66080e7 | −0.0607552 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.97454e7 | 0.322309 | 0.161155 | − | 0.986929i | \(-0.448478\pi\) | ||||
0.161155 | + | 0.986929i | \(0.448478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.06804e7 | 0.251521 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.46917e8 | 0.862770 | 0.431385 | − | 0.902168i | \(-0.358025\pi\) | ||||
0.431385 | + | 0.902168i | \(0.358025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.72712e8i | 0.598024i | 0.954249 | + | 0.299012i | \(0.0966571\pi\) | ||||
−0.954249 | + | 0.299012i | \(0.903343\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1.49225e7i | − 0.0507430i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.03882e8i | − 0.687072i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.64121e8i | 0.874249i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.66236e8 | −0.545356 | −0.272678 | − | 0.962105i | \(-0.587909\pi\) | ||||
−0.272678 | + | 0.962105i | \(0.587909\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.38587e8 | −1.09120 | −0.545601 | − | 0.838045i | \(-0.683698\pi\) | ||||
−0.545601 | + | 0.838045i | \(0.683698\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.79591e6 | 0.00893127 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.36588e7 | −0.0428698 | −0.0214349 | − | 0.999770i | \(-0.506823\pi\) | ||||
−0.0214349 | + | 0.999770i | \(0.506823\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.46656e8i | 1.07852i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.07089e8i | 0.327406i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.87568e8i | − 0.871577i | −0.900049 | − | 0.435789i | \(-0.856470\pi\) | ||||
0.900049 | − | 0.435789i | \(-0.143530\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 3.38711e8i | − 1.00896i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.95287e7 | 0.175804 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.04539e8 | −0.884075 | −0.442037 | − | 0.896997i | \(-0.645744\pi\) | ||||
−0.442037 | + | 0.896997i | \(0.645744\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.63550e8 | −1.62206 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.68154e7 | 0.0475826 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 5.94975e8i | − 1.66940i | −0.550706 | − | 0.834699i | \(-0.685642\pi\) | ||||
0.550706 | − | 0.834699i | \(-0.314358\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 3.92029e8i | − 1.08156i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.88938e8i | 0.516894i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.96990e8i | 1.87517i | 0.347760 | + | 0.937583i | \(0.386942\pi\) | ||||
−0.347760 | + | 0.937583i | \(0.613058\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.82336e6 | 0.0155370 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.63729e8 | 0.692059 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.97034e7 | −0.207431 | −0.103716 | − | 0.994607i | \(-0.533073\pi\) | ||||
−0.103716 | + | 0.994607i | \(0.533073\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.64455e8 | −0.421013 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5.90402e8i | − 1.49912i | −0.661937 | − | 0.749559i | \(-0.730266\pi\) | ||||
0.661937 | − | 0.749559i | \(-0.269734\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.31475e7i | 0.157744i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.48328e7i | 0.135865i | 0.997690 | + | 0.0679324i | \(0.0216402\pi\) | ||||
−0.997690 | + | 0.0679324i | \(0.978360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.92105e8i | 0.712153i | 0.934457 | + | 0.356076i | \(0.115886\pi\) | ||||
−0.934457 | + | 0.356076i | \(0.884114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.92624e8 | 0.949529 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.29075e6 | −0.0221108 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.91813e8 | −1.16113 | −0.580564 | − | 0.814215i | \(-0.697168\pi\) | ||||
−0.580564 | + | 0.814215i | \(0.697168\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.08939e9 | 2.53129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.26268e8i | 0.291076i | 0.989353 | + | 0.145538i | \(0.0464912\pi\) | ||||
−0.989353 | + | 0.145538i | \(0.953509\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.59472e8i | 1.26947i | 0.772728 | + | 0.634737i | \(0.218892\pi\) | ||||
−0.772728 | + | 0.634737i | \(0.781108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.99059e7i | 0.0448135i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 8.24326e6i | − 0.0182689i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.51300e8 | 1.65209 | 0.826046 | − | 0.563603i | \(-0.190585\pi\) | ||||
0.826046 | + | 0.563603i | \(0.190585\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.22477e8 | −1.56417 | −0.782087 | − | 0.623169i | \(-0.785845\pi\) | ||||
−0.782087 | + | 0.623169i | \(0.785845\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.07102e8 | 1.08941 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.26782e8 | −0.268191 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.56055e8i | − 0.327586i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.57931e8i | 0.946653i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4.69415e8i | − 0.963014i | −0.876442 | − | 0.481507i | \(-0.840090\pi\) | ||||
0.876442 | − | 0.481507i | \(-0.159910\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 3.61288e7i | − 0.0730001i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.31094e8 | −0.262884 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.15029e8 | −1.01732 | −0.508659 | − | 0.860968i | \(-0.669859\pi\) | ||||
−0.508659 | + | 0.860968i | \(0.669859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.21258e8 | −0.629816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.09588e8 | 1.56357 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.36372e7i | 0.0453116i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.78752e8i | 0.715335i | 0.933849 | + | 0.357668i | \(0.116428\pi\) | ||||
−0.933849 | + | 0.357668i | \(0.883572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.01790e8i | 1.50314i | 0.659656 | + | 0.751568i | \(0.270702\pi\) | ||||
−0.659656 | + | 0.751568i | \(0.729298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1.58852e8i | − 0.293440i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.50250e8 | 0.642261 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.04505e9 | 1.88845 | 0.944226 | − | 0.329298i | \(-0.106812\pi\) | ||||
0.944226 | + | 0.329298i | \(0.106812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.24543e7 | −0.0940982 | −0.0470491 | − | 0.998893i | \(-0.514982\pi\) | ||||
−0.0470491 | + | 0.998893i | \(0.514982\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.55035e8 | −0.627703 | −0.313851 | − | 0.949472i | \(-0.601619\pi\) | ||||
−0.313851 | + | 0.949472i | \(0.601619\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 3.06153e8i | − 0.537372i | −0.963228 | − | 0.268686i | \(-0.913411\pi\) | ||||
0.963228 | − | 0.268686i | \(-0.0865894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.48077e8i | 0.602200i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.46573e9i | − 2.51765i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 5.16944e8i | − 0.875301i | −0.899145 | − | 0.437650i | \(-0.855811\pi\) | ||||
0.899145 | − | 0.437650i | \(-0.144189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78943e8 | −0.300834 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.21899e8 | 1.19648 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.72989e6 | −0.0110754 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.92663e8 | 1.44844 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.67664e8i | 1.23687i | 0.785836 | + | 0.618435i | \(0.212233\pi\) | ||||
−0.785836 | + | 0.618435i | \(0.787767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.58878e8i | 0.729045i | 0.931195 | + | 0.364523i | \(0.118768\pi\) | ||||
−0.931195 | + | 0.364523i | \(0.881232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 7.79347e8i | − 1.22957i | −0.788697 | − | 0.614783i | \(-0.789244\pi\) | ||||
0.788697 | − | 0.614783i | \(-0.210756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.69372e8i | 0.263518i | 0.991282 | + | 0.131759i | \(0.0420625\pi\) | ||||
−0.991282 | + | 0.131759i | \(0.957937\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.54963e8 | 0.393940 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.19224e8 | −1.09599 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.13428e7 | −0.0474333 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.36650e6 | 0.00950335 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.85516e8i | 1.01629i | 0.861271 | + | 0.508146i | \(0.169669\pi\) | ||||
−0.861271 | + | 0.508146i | \(0.830331\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.99510e7i | 0.131546i | 0.997835 | + | 0.0657731i | \(0.0209513\pi\) | ||||
−0.997835 | + | 0.0657731i | \(0.979049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 7.65510e8i | − 1.11191i | −0.831213 | − | 0.555954i | \(-0.812353\pi\) | ||||
0.831213 | − | 0.555954i | \(-0.187647\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.43357e8i | 0.921894i | 0.887428 | + | 0.460947i | \(0.152490\pi\) | ||||
−0.887428 | + | 0.460947i | \(0.847510\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.38858e7 | 0.0624625 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.84202e8 | 0.960793 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.81489e9 | 2.53153 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.99662e8 | 1.10059 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 4.26023e8i | − 0.582450i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.09119e9i | 1.47216i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.38011e8i | 0.318988i | 0.987199 | + | 0.159494i | \(0.0509863\pi\) | ||||
−0.987199 | + | 0.159494i | \(0.949014\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.29557e9i | − 1.71358i | −0.515664 | − | 0.856791i | \(-0.672455\pi\) | ||||
0.515664 | − | 0.856791i | \(-0.327545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.28584e8 | 0.957343 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.85173e6 | −0.00758885 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.83739e8 | 0.236731 | 0.118366 | − | 0.992970i | \(-0.462234\pi\) | ||||
0.118366 | + | 0.992970i | \(0.462234\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.74568e7 | 0.0985042 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.15469e9i | 1.45895i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.72117e8i | 1.08775i | 0.839167 | + | 0.543873i | \(0.183043\pi\) | ||||
−0.839167 | + | 0.543873i | \(0.816957\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 7.41319e8i | − 0.918663i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 7.51638e8i | − 0.919547i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.39899e8 | 0.899402 | 0.449701 | − | 0.893179i | \(-0.351531\pi\) | ||||
0.449701 | + | 0.893179i | \(0.351531\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.86767e8 | −0.704201 | −0.352101 | − | 0.935962i | \(-0.614532\pi\) | ||||
−0.352101 | + | 0.935962i | \(0.614532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.00822e8 | 0.239484 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.35408e9 | 1.59439 | 0.797195 | − | 0.603722i | \(-0.206316\pi\) | ||||
0.797195 | + | 0.603722i | \(0.206316\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.01833e8i | 0.470161i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.06231e8i | 0.931495i | 0.884918 | + | 0.465748i | \(0.154215\pi\) | ||||
−0.884918 | + | 0.465748i | \(0.845785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.27457e9i | 1.46336i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2.87001e7i | − 0.0325408i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.50102e8 | 0.732506 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.48115e9 | 1.64822 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.61478e8 | −0.731536 | −0.365768 | − | 0.930706i | \(-0.619194\pi\) | ||||
−0.365768 | + | 0.930706i | \(0.619194\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.01203e8 | −0.438234 | −0.219117 | − | 0.975699i | \(-0.570318\pi\) | ||||
−0.219117 | + | 0.975699i | \(0.570318\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.80423e7i | 0.0304422i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 7.93550e8i | − 0.850924i | −0.904976 | − | 0.425462i | \(-0.860112\pi\) | ||||
0.904976 | − | 0.425462i | \(-0.139888\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 4.65438e8i | − 0.496037i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.47001e8i | 0.681153i | 0.940217 | + | 0.340576i | \(0.110622\pi\) | ||||
−0.940217 | + | 0.340576i | \(0.889378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.47690e8 | 0.677733 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.54796e8 | −0.573514 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.18163e8 | −0.224161 | −0.112081 | − | 0.993699i | \(-0.535752\pi\) | ||||
−0.112081 | + | 0.993699i | \(0.535752\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.96229e9 | 1.99203 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.47959e9i | − 1.49299i | −0.665393 | − | 0.746494i | \(-0.731736\pi\) | ||||
0.665393 | − | 0.746494i | \(-0.268264\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 576.7.h.a.161.14 | yes | 16 | |
3.2 | odd | 2 | inner | 576.7.h.a.161.2 | yes | 16 | |
4.3 | odd | 2 | inner | 576.7.h.a.161.16 | yes | 16 | |
8.3 | odd | 2 | inner | 576.7.h.a.161.3 | yes | 16 | |
8.5 | even | 2 | inner | 576.7.h.a.161.1 | ✓ | 16 | |
12.11 | even | 2 | inner | 576.7.h.a.161.4 | yes | 16 | |
24.5 | odd | 2 | inner | 576.7.h.a.161.13 | yes | 16 | |
24.11 | even | 2 | inner | 576.7.h.a.161.15 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.7.h.a.161.1 | ✓ | 16 | 8.5 | even | 2 | inner | |
576.7.h.a.161.2 | yes | 16 | 3.2 | odd | 2 | inner | |
576.7.h.a.161.3 | yes | 16 | 8.3 | odd | 2 | inner | |
576.7.h.a.161.4 | yes | 16 | 12.11 | even | 2 | inner | |
576.7.h.a.161.13 | yes | 16 | 24.5 | odd | 2 | inner | |
576.7.h.a.161.14 | yes | 16 | 1.1 | even | 1 | trivial | |
576.7.h.a.161.15 | yes | 16 | 24.11 | even | 2 | inner | |
576.7.h.a.161.16 | yes | 16 | 4.3 | odd | 2 | inner |