Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(2177,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.2177");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.h (of order \(2\), degree \(1\), not 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: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.959512576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2177.2 | ||
Root | \(-0.819051 - 1.52616i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.2177 |
Dual form | 2304.3.h.l.2177.1 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −8.04746 | −1.60949 | −0.804746 | − | 0.593619i | \(-0.797699\pi\) | ||||
−0.804746 | + | 0.593619i | \(0.797699\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.285714 | 0.142857 | − | 0.989743i | \(-0.454371\pi\) | ||||
0.142857 | + | 0.989743i | \(0.454371\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21.7518 | −1.97743 | −0.988717 | − | 0.149794i | \(-0.952139\pi\) | ||||
−0.988717 | + | 0.149794i | \(0.952139\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.3808i | 1.33699i | 0.743718 | + | 0.668494i | \(0.233061\pi\) | ||||
−0.743718 | + | 0.668494i | \(0.766939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.8523i | 0.697193i | 0.937273 | + | 0.348597i | \(0.113342\pi\) | ||||
−0.937273 | + | 0.348597i | \(0.886658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.7617i | 0.566403i | 0.959060 | + | 0.283202i | \(0.0913966\pi\) | ||||
−0.959060 | + | 0.283202i | \(0.908603\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.0183i | 1.52253i | 0.648439 | + | 0.761267i | \(0.275422\pi\) | ||||
−0.648439 | + | 0.761267i | \(0.724578\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 39.7617 | 1.59047 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11.7515 | −0.405225 | −0.202613 | − | 0.979259i | \(-0.564943\pi\) | ||||
−0.202613 | + | 0.979259i | \(0.564943\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.5233 | 1.14591 | 0.572957 | − | 0.819586i | \(-0.305796\pi\) | ||||
0.572957 | + | 0.819586i | \(0.305796\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.0949 | −0.459855 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 26.0000i | − 0.702703i | −0.936244 | − | 0.351351i | \(-0.885722\pi\) | ||||
0.936244 | − | 0.351351i | \(-0.114278\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.28985i | 0.0558500i | 0.999610 | + | 0.0279250i | \(0.00888996\pi\) | ||||
−0.999610 | + | 0.0279250i | \(0.991110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 65.5233i | 1.52380i | 0.647696 | + | 0.761899i | \(0.275733\pi\) | ||||
−0.647696 | + | 0.761899i | \(0.724267\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 27.2071i | − 0.578875i | −0.957197 | − | 0.289437i | \(-0.906532\pi\) | ||||
0.957197 | − | 0.289437i | \(-0.0934682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45.0000 | −0.918367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 49.5982 | 0.935816 | 0.467908 | − | 0.883777i | \(-0.345008\pi\) | ||||
0.467908 | + | 0.883777i | \(0.345008\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 175.047 | 3.18267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −73.5391 | −1.24643 | −0.623213 | − | 0.782052i | \(-0.714173\pi\) | ||||
−0.623213 | + | 0.782052i | \(0.714173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 7.52333i | − 0.123333i | −0.998097 | − | 0.0616666i | \(-0.980358\pi\) | ||||
0.998097 | − | 0.0616666i | \(-0.0196416\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 139.872i | − 2.15187i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 65.2383i | − 0.973707i | −0.873484 | − | 0.486853i | \(-0.838145\pi\) | ||||
0.873484 | − | 0.486853i | \(-0.161855\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 84.1787i | − 1.18562i | −0.805344 | − | 0.592808i | \(-0.798019\pi\) | ||||
0.805344 | − | 0.592808i | \(-0.201981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −84.5700 | −1.15849 | −0.579246 | − | 0.815152i | \(-0.696653\pi\) | ||||
−0.579246 | + | 0.815152i | \(0.696653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −43.5036 | −0.564981 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −75.5233 | −0.955991 | −0.477996 | − | 0.878362i | \(-0.658637\pi\) | ||||
−0.477996 | + | 0.878362i | \(0.658637\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −48.2848 | −0.581744 | −0.290872 | − | 0.956762i | \(-0.593945\pi\) | ||||
−0.290872 | + | 0.956762i | \(0.593945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 95.3808i | − 1.12213i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 146.067i | 1.64120i | 0.571501 | + | 0.820601i | \(0.306361\pi\) | ||||
−0.571501 | + | 0.820601i | \(0.693639\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34.7617i | 0.381996i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 86.6041i | − 0.911622i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −106.762 | −1.10064 | −0.550318 | − | 0.834955i | \(-0.685493\pi\) | ||||
−0.550318 | + | 0.834955i | \(0.685493\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 144.889 | 1.43455 | 0.717273 | − | 0.696792i | \(-0.245390\pi\) | ||||
0.717273 | + | 0.696792i | \(0.245390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −26.5700 | −0.257961 | −0.128980 | − | 0.991647i | \(-0.541170\pi\) | ||||
−0.128980 | + | 0.991647i | \(0.541170\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −71.3848 | −0.667148 | −0.333574 | − | 0.942724i | \(-0.608255\pi\) | ||||
−0.333574 | + | 0.942724i | \(0.608255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 118.619i | 1.08825i | 0.839004 | + | 0.544125i | \(0.183138\pi\) | ||||
−0.839004 | + | 0.544125i | \(0.816862\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 86.6701i | 0.766992i | 0.923543 | + | 0.383496i | \(0.125280\pi\) | ||||
−0.923543 | + | 0.383496i | \(0.874720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 281.808i | − 2.45051i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.7046i | 0.199198i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 352.140 | 2.91025 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −118.794 | −0.950352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −69.0467 | −0.543674 | −0.271837 | − | 0.962343i | \(-0.587631\pi\) | ||||
−0.271837 | + | 0.962343i | \(0.587631\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.25382 | −0.0401055 | −0.0200527 | − | 0.999799i | \(-0.506383\pi\) | ||||
−0.0200527 | + | 0.999799i | \(0.506383\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.5233i | 0.161830i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 120.139i | − 0.876924i | −0.898750 | − | 0.438462i | \(-0.855523\pi\) | ||||
0.898750 | − | 0.438462i | \(-0.144477\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 242.378i | − 1.74373i | −0.489747 | − | 0.871864i | \(-0.662911\pi\) | ||||
0.489747 | − | 0.871864i | \(-0.337089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 378.064i | − 2.64380i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 94.5700 | 0.652207 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −192.500 | −1.29194 | −0.645972 | − | 0.763361i | \(-0.723548\pi\) | ||||
−0.645972 | + | 0.763361i | \(0.723548\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.4300 | 0.115431 | 0.0577153 | − | 0.998333i | \(-0.481618\pi\) | ||||
0.0577153 | + | 0.998333i | \(0.481618\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −285.873 | −1.84434 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 213.617i | 1.36062i | 0.732927 | + | 0.680308i | \(0.238154\pi\) | ||||
−0.732927 | + | 0.680308i | \(0.761846\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 70.0366i | 0.435010i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 231.047i | − 1.41746i | −0.705478 | − | 0.708732i | \(-0.749268\pi\) | ||||
0.705478 | − | 0.708732i | \(-0.250732\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 126.202i | − 0.755701i | −0.925867 | − | 0.377850i | \(-0.876663\pi\) | ||||
0.925867 | − | 0.377850i | \(-0.123337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −133.093 | −0.787534 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 199.032 | 1.15048 | 0.575238 | − | 0.817986i | \(-0.304910\pi\) | ||||
0.575238 | + | 0.817986i | \(0.304910\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 79.5233 | 0.454419 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 170.915 | 0.954831 | 0.477415 | − | 0.878678i | \(-0.341574\pi\) | ||||
0.477415 | + | 0.878678i | \(0.341574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 38.6192i | − 0.213366i | −0.994293 | − | 0.106683i | \(-0.965977\pi\) | ||||
0.994293 | − | 0.106683i | \(-0.0340229\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 209.234i | 1.13099i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 257.808i | − 1.37865i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 269.778i | − 1.41245i | −0.707988 | − | 0.706224i | \(-0.750397\pi\) | ||||
0.707988 | − | 0.706224i | \(-0.249603\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −263.140 | −1.36342 | −0.681710 | − | 0.731623i | \(-0.738763\pi\) | ||||
−0.681710 | + | 0.731623i | \(0.738763\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −80.0368 | −0.406278 | −0.203139 | − | 0.979150i | \(-0.565114\pi\) | ||||
−0.203139 | + | 0.979150i | \(0.565114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 265.047 | 1.33189 | 0.665946 | − | 0.746000i | \(-0.268028\pi\) | ||||
0.665946 | + | 0.746000i | \(0.268028\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.5031 | −0.115779 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 18.4275i | − 0.0898902i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 234.085i | − 1.12003i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 159.332i | 0.755126i | 0.925984 | + | 0.377563i | \(0.123238\pi\) | ||||
−0.925984 | + | 0.377563i | \(0.876762\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 527.297i | − 2.45254i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 71.0467 | 0.327404 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −206.003 | −0.932138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 90.9533 | 0.407863 | 0.203931 | − | 0.978985i | \(-0.434628\pi\) | ||||
0.203931 | + | 0.978985i | \(0.434628\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −322.371 | −1.42014 | −0.710069 | − | 0.704133i | \(-0.751336\pi\) | ||||
−0.710069 | + | 0.704133i | \(0.751336\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 180.997i | − 0.790382i | −0.918599 | − | 0.395191i | \(-0.870678\pi\) | ||||
0.918599 | − | 0.395191i | \(-0.129322\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 329.241i | − 1.41305i | −0.707688 | − | 0.706525i | \(-0.750262\pi\) | ||||
0.707688 | − | 0.706525i | \(-0.249738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 218.948i | 0.931695i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 197.045i | 0.824455i | 0.911081 | + | 0.412227i | \(0.135249\pi\) | ||||
−0.911081 | + | 0.412227i | \(0.864751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 215.332 | 0.893492 | 0.446746 | − | 0.894661i | \(-0.352583\pi\) | ||||
0.446746 | + | 0.894661i | \(0.352583\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 362.136 | 1.47811 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −187.047 | −0.757274 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 245.329 | 0.977408 | 0.488704 | − | 0.872450i | \(-0.337470\pi\) | ||||
0.488704 | + | 0.872450i | \(0.337470\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 761.710i | − 3.01071i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 39.5320i | 0.153821i | 0.997038 | + | 0.0769105i | \(0.0245056\pi\) | ||||
−0.997038 | + | 0.0769105i | \(0.975494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 52.0000i | − 0.200772i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 217.921i | 0.828596i | 0.910141 | + | 0.414298i | \(0.135973\pi\) | ||||
−0.910141 | + | 0.414298i | \(0.864027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −399.140 | −1.50619 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 205.433 | 0.763691 | 0.381845 | − | 0.924226i | \(-0.375289\pi\) | ||||
0.381845 | + | 0.924226i | \(0.375289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 441.047 | 1.62748 | 0.813739 | − | 0.581230i | \(-0.197428\pi\) | ||||
0.813739 | + | 0.581230i | \(0.197428\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −864.887 | −3.14504 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 185.951i | 0.671303i | 0.941986 | + | 0.335651i | \(0.108956\pi\) | ||||
−0.941986 | + | 0.335651i | \(0.891044\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 87.7472i | 0.312268i | 0.987736 | + | 0.156134i | \(0.0499031\pi\) | ||||
−0.987736 | + | 0.156134i | \(0.950097\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 46.0933i | 0.162874i | 0.996678 | + | 0.0814369i | \(0.0259509\pi\) | ||||
−0.996678 | + | 0.0814369i | \(0.974049\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.57970i | 0.0159571i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 148.523 | 0.513922 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 118.287 | 0.403708 | 0.201854 | − | 0.979416i | \(-0.435303\pi\) | ||||
0.201854 | + | 0.979416i | \(0.435303\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 591.803 | 2.00611 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −608.647 | −2.03561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 131.047i | 0.435371i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 60.5437i | 0.198504i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 116.285i | − 0.378778i | −0.981902 | − | 0.189389i | \(-0.939349\pi\) | ||||
0.981902 | − | 0.189389i | \(-0.0606508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 261.564i | − 0.841040i | −0.907283 | − | 0.420520i | \(-0.861848\pi\) | ||||
0.907283 | − | 0.420520i | \(-0.138152\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −310.000 | −0.990415 | −0.495208 | − | 0.868775i | \(-0.664908\pi\) | ||||
−0.495208 | + | 0.868775i | \(0.664908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −223.279 | −0.704350 | −0.352175 | − | 0.935934i | \(-0.614558\pi\) | ||||
−0.352175 | + | 0.935934i | \(0.614558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 255.617 | 0.801306 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −127.550 | −0.394893 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 691.091i | 2.12643i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 54.4142i | − 0.165393i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 353.238i | − 1.06719i | −0.845742 | − | 0.533593i | \(-0.820842\pi\) | ||||
0.845742 | − | 0.533593i | \(-0.179158\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 525.003i | 1.56717i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 316.000 | 0.937685 | 0.468843 | − | 0.883282i | \(-0.344671\pi\) | ||||
0.468843 | + | 0.883282i | \(0.344671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −772.696 | −2.26597 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −188.000 | −0.548105 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −230.916 | −0.665465 | −0.332732 | − | 0.943021i | \(-0.607971\pi\) | ||||
−0.332732 | + | 0.943021i | \(0.607971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 189.233i | 0.542216i | 0.962549 | + | 0.271108i | \(0.0873900\pi\) | ||||
−0.962549 | + | 0.271108i | \(0.912610\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 151.050i | 0.427903i | 0.976844 | + | 0.213952i | \(0.0686335\pi\) | ||||
−0.976844 | + | 0.213952i | \(0.931367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 677.425i | 1.90824i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 217.789i | − 0.606654i | −0.952886 | − | 0.303327i | \(-0.901903\pi\) | ||||
0.952886 | − | 0.303327i | \(-0.0980975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 245.187 | 0.679187 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 680.574 | 1.86459 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 444.093 | 1.21006 | 0.605032 | − | 0.796201i | \(-0.293160\pi\) | ||||
0.605032 | + | 0.796201i | \(0.293160\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 99.1965 | 0.267376 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 124.663i | − 0.334218i | −0.985938 | − | 0.167109i | \(-0.946557\pi\) | ||||
0.985938 | − | 0.167109i | \(-0.0534432\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 204.251i | − 0.541781i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 419.332i | − 1.10642i | −0.833043 | − | 0.553208i | \(-0.813403\pi\) | ||||
0.833043 | − | 0.553208i | \(-0.186597\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 218.060i | 0.569347i | 0.958625 | + | 0.284674i | \(0.0918852\pi\) | ||||
−0.958625 | + | 0.284674i | \(0.908115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 350.093 | 0.909333 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −214.988 | −0.552669 | −0.276334 | − | 0.961062i | \(-0.589120\pi\) | ||||
−0.276334 | + | 0.961062i | \(0.589120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −415.047 | −1.06150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 607.771 | 1.53866 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 506.187i | 1.27503i | 0.770438 | + | 0.637515i | \(0.220037\pi\) | ||||
−0.770438 | + | 0.637515i | \(0.779963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 718.820i | 1.79257i | 0.443480 | + | 0.896284i | \(0.353744\pi\) | ||||
−0.443480 | + | 0.896284i | \(0.646256\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 617.425i | 1.53207i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 565.546i | 1.38955i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.2383 | 0.0714874 | 0.0357437 | − | 0.999361i | \(-0.488620\pi\) | ||||
0.0357437 | + | 0.999361i | \(0.488620\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −147.078 | −0.356122 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 388.570 | 0.936313 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.22387 | −0.00530757 | −0.00265379 | − | 0.999996i | \(-0.500845\pi\) | ||||
−0.00265379 | + | 0.999996i | \(0.500845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 117.194i | 0.278371i | 0.990266 | + | 0.139186i | \(0.0444484\pi\) | ||||
−0.990266 | + | 0.139186i | \(0.955552\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 471.267i | 1.10886i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 15.0467i | − 0.0352381i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 755.315i | − 1.75247i | −0.481884 | − | 0.876235i | \(-0.660047\pi\) | ||||
0.481884 | − | 0.876235i | \(-0.339953\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −433.233 | −1.00054 | −0.500269 | − | 0.865870i | \(-0.666766\pi\) | ||||
−0.500269 | + | 0.865870i | \(0.666766\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −376.855 | −0.862368 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −231.140 | −0.526515 | −0.263257 | − | 0.964726i | \(-0.584797\pi\) | ||||
−0.263257 | + | 0.964726i | \(0.584797\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.08983 | −0.0205188 | −0.0102594 | − | 0.999947i | \(-0.503266\pi\) | ||||
−0.0102594 | + | 0.999947i | \(0.503266\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1175.47i | − 2.64150i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 290.921i | 0.647932i | 0.946069 | + | 0.323966i | \(0.105016\pi\) | ||||
−0.946069 | + | 0.323966i | \(0.894984\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 49.8083i | − 0.110440i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 279.743i | − 0.614820i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 333.042 | 0.728756 | 0.364378 | − | 0.931251i | \(-0.381282\pi\) | ||||
0.364378 | + | 0.931251i | \(0.381282\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 132.971 | 0.288440 | 0.144220 | − | 0.989546i | \(-0.453933\pi\) | ||||
0.144220 | + | 0.989546i | \(0.453933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −391.140 | −0.844795 | −0.422397 | − | 0.906411i | \(-0.638811\pi\) | ||||
−0.422397 | + | 0.906411i | \(0.638811\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 469.310 | 1.00495 | 0.502473 | − | 0.864593i | \(-0.332423\pi\) | ||||
0.502473 | + | 0.864593i | \(0.332423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 130.477i | − 0.278202i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1425.25i | − 3.01321i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 427.902i | 0.900846i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 355.708i | − 0.742605i | −0.928512 | − | 0.371302i | \(-0.878911\pi\) | ||||
0.928512 | − | 0.371302i | \(-0.121089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 451.902 | 0.939504 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 859.161 | 1.77147 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −839.897 | −1.72463 | −0.862317 | − | 0.506369i | \(-0.830987\pi\) | ||||
−0.862317 | + | 0.506369i | \(0.830987\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 388.572 | 0.791388 | 0.395694 | − | 0.918382i | \(-0.370504\pi\) | ||||
0.395694 | + | 0.918382i | \(0.370504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 139.282i | − 0.282520i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 168.357i | − 0.338747i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 488.373i | − 0.978704i | −0.872086 | − | 0.489352i | \(-0.837233\pi\) | ||||
0.872086 | − | 0.489352i | \(-0.162767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 533.488i | − 1.06061i | −0.847806 | − | 0.530307i | \(-0.822077\pi\) | ||||
0.847806 | − | 0.530307i | \(-0.177923\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1165.99 | −2.30889 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 179.094 | 0.351855 | 0.175927 | − | 0.984403i | \(-0.443708\pi\) | ||||
0.175927 | + | 0.984403i | \(0.443708\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −169.140 | −0.330998 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 213.821 | 0.415186 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 591.803i | 1.14469i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 397.456i | 0.762872i | 0.924395 | + | 0.381436i | \(0.124570\pi\) | ||||
−0.924395 | + | 0.381436i | \(0.875430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 987.135i | − 1.88745i | −0.330735 | − | 0.943724i | \(-0.607297\pi\) | ||||
0.330735 | − | 0.943724i | \(-0.392703\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 421.033i | 0.798923i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −697.280 | −1.31811 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −39.7995 | −0.0746707 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 574.467 | 1.07377 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 978.830 | 1.81601 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 214.992i | 0.397398i | 0.980061 | + | 0.198699i | \(0.0636716\pi\) | ||||
−0.980061 | + | 0.198699i | \(0.936328\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 954.583i | − 1.75153i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 381.710i | − 0.697824i | −0.937155 | − | 0.348912i | \(-0.886551\pi\) | ||||
0.937155 | − | 0.348912i | \(-0.113449\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 126.466i | − 0.229521i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −151.047 | −0.273140 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 924.388 | 1.65958 | 0.829792 | − | 0.558073i | \(-0.188459\pi\) | ||||
0.829792 | + | 0.558073i | \(0.188459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1138.85 | −2.03730 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 70.5092 | 0.125238 | 0.0626191 | − | 0.998037i | \(-0.480055\pi\) | ||||
0.0626191 | + | 0.998037i | \(0.480055\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 697.474i | − 1.23447i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 607.844i | 1.06827i | 0.845400 | + | 0.534134i | \(0.179362\pi\) | ||||
−0.845400 | + | 0.534134i | \(0.820638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 455.430i | 0.797601i | 0.917038 | + | 0.398800i | \(0.130573\pi\) | ||||
−0.917038 | + | 0.398800i | \(0.869427\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1392.39i | 2.42154i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 501.233 | 0.868688 | 0.434344 | − | 0.900747i | \(-0.356980\pi\) | ||||
0.434344 | + | 0.900747i | \(0.356980\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −96.5696 | −0.166213 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1078.85 | −1.85051 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −178.059 | −0.303337 | −0.151669 | − | 0.988431i | \(-0.548465\pi\) | ||||
−0.151669 | + | 0.988431i | \(0.548465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 382.290i | 0.649049i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 960.244i | − 1.61930i | −0.586914 | − | 0.809649i | \(-0.699657\pi\) | ||||
0.586914 | − | 0.809649i | \(-0.300343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 190.762i | − 0.320608i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 680.706i | 1.13640i | 0.822889 | + | 0.568202i | \(0.192361\pi\) | ||||
−0.822889 | + | 0.568202i | \(0.807639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −239.327 | −0.398214 | −0.199107 | − | 0.979978i | \(-0.563804\pi\) | ||||
−0.199107 | + | 0.979978i | \(0.563804\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2833.83 | −4.68402 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1177.80 | −1.94037 | −0.970184 | − | 0.242370i | \(-0.922075\pi\) | ||||
−0.970184 | + | 0.242370i | \(0.922075\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 472.882 | 0.773948 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1106.56i | − 1.80515i | −0.430528 | − | 0.902577i | \(-0.641673\pi\) | ||||
0.430528 | − | 0.902577i | \(-0.358327\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 271.185i | 0.439522i | 0.975554 | + | 0.219761i | \(0.0705277\pi\) | ||||
−0.975554 | + | 0.219761i | \(0.929472\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 447.430i | 0.722827i | 0.932406 | + | 0.361414i | \(0.117706\pi\) | ||||
−0.932406 | + | 0.361414i | \(0.882294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 292.134i | 0.468915i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −38.0517 | −0.0608828 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 308.159 | 0.489920 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 369.047 | 0.584860 | 0.292430 | − | 0.956287i | \(-0.405536\pi\) | ||||
0.292430 | + | 0.956287i | \(0.405536\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 555.650 | 0.875040 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 782.137i | − 1.22785i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 319.198i | 0.497970i | 0.968507 | + | 0.248985i | \(0.0800969\pi\) | ||||
−0.968507 | + | 0.248985i | \(0.919903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 41.3266i | − 0.0642715i | −0.999484 | − | 0.0321357i | \(-0.989769\pi\) | ||||
0.999484 | − | 0.0321357i | \(-0.0102309\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 160.011i | 0.247313i | 0.992325 | + | 0.123656i | \(0.0394620\pi\) | ||||
−0.992325 | + | 0.123656i | \(0.960538\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1599.61 | 2.46472 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1111.54 | 1.70220 | 0.851100 | − | 0.525003i | \(-0.175936\pi\) | ||||
0.851100 | + | 0.525003i | \(0.175936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42.2799 | 0.0645495 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 800.313 | 1.21444 | 0.607218 | − | 0.794536i | \(-0.292286\pi\) | ||||
0.607218 | + | 0.794536i | \(0.292286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1142.18i | 1.72795i | 0.503533 | + | 0.863976i | \(0.332033\pi\) | ||||
−0.503533 | + | 0.863976i | \(0.667967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 173.208i | − 0.260463i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 411.518i | − 0.616969i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 163.646i | 0.243883i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −169.047 | −0.251184 | −0.125592 | − | 0.992082i | \(-0.540083\pi\) | ||||
−0.125592 | + | 0.992082i | \(0.540083\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 533.801 | 0.788481 | 0.394240 | − | 0.919007i | \(-0.371008\pi\) | ||||
0.394240 | + | 0.919007i | \(0.371008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −213.523 | −0.314467 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 408.711 | 0.598406 | 0.299203 | − | 0.954189i | \(-0.403279\pi\) | ||||
0.299203 | + | 0.954189i | \(0.403279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 966.811i | 1.41140i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 862.059i | 1.25117i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 331.233i | 0.479353i | 0.970853 | + | 0.239677i | \(0.0770415\pi\) | ||||
−0.970853 | + | 0.239677i | \(0.922959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1950.53i | 2.80652i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.1400 | −0.0389382 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −116.814 | −0.166638 | −0.0833192 | − | 0.996523i | \(-0.526552\pi\) | ||||
−0.0833192 | + | 0.996523i | \(0.526552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 279.803 | 0.398013 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 289.778 | 0.409870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 737.469i | 1.04015i | 0.854119 | + | 0.520077i | \(0.174097\pi\) | ||||
−0.854119 | + | 0.520077i | \(0.825903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1243.97i | 1.74469i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3042.46i | 4.25518i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1017.28i | − 1.41486i | −0.706785 | − | 0.707428i | \(-0.749855\pi\) | ||||
0.706785 | − | 0.707428i | \(-0.250145\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −53.1400 | −0.0737031 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −467.260 | −0.644497 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 277.430 | 0.381609 | 0.190805 | − | 0.981628i | \(-0.438890\pi\) | ||||
0.190805 | + | 0.981628i | \(0.438890\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −776.601 | −1.06238 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 405.371i | 0.553030i | 0.961010 | + | 0.276515i | \(0.0891795\pi\) | ||||
−0.961010 | + | 0.276515i | \(0.910821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1419.05i | 1.92544i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 295.036i | 0.399237i | 0.979874 | + | 0.199619i | \(0.0639704\pi\) | ||||
−0.979874 | + | 0.199619i | \(0.936030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 486.350i | 0.654576i | 0.944925 | + | 0.327288i | \(0.106135\pi\) | ||||
−0.944925 | + | 0.327288i | \(0.893865\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1549.13 | 2.07938 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −142.770 | −0.190614 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −705.430 | −0.939321 | −0.469660 | − | 0.882847i | \(-0.655624\pi\) | ||||
−0.469660 | + | 0.882847i | \(0.655624\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −140.267 | −0.185785 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1362.89i | − 1.80039i | −0.435489 | − | 0.900194i | \(-0.643424\pi\) | ||||
0.435489 | − | 0.900194i | \(-0.356576\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 625.746i | − 0.822268i | −0.911575 | − | 0.411134i | \(-0.865133\pi\) | ||||
0.911575 | − | 0.411134i | \(-0.134867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 237.238i | 0.310928i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1278.17i | − 1.66645i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −637.813 | −0.829406 | −0.414703 | − | 0.909957i | \(-0.636115\pi\) | ||||
−0.414703 | + | 0.909957i | \(0.636115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −536.282 | −0.693767 | −0.346884 | − | 0.937908i | \(-0.612760\pi\) | ||||
−0.346884 | + | 0.937908i | \(0.612760\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1412.47 | 1.82254 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.6426 | −0.0316336 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1831.04i | 2.34448i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1719.07i | − 2.18990i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 769.425i | 0.977668i | 0.872377 | + | 0.488834i | \(0.162578\pi\) | ||||
−0.872377 | + | 0.488834i | \(0.837422\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 173.340i | 0.219140i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 130.762 | 0.164895 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −765.593 | −0.960594 | −0.480297 | − | 0.877106i | \(-0.659471\pi\) | ||||
−0.480297 | + | 0.877106i | \(0.659471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 322.467 | 0.403588 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1839.55 | 2.29084 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 563.617i | − 0.700145i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 865.488i | − 1.06982i | −0.844908 | − | 0.534912i | \(-0.820345\pi\) | ||||
0.844908 | − | 0.534912i | \(-0.179655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 292.472i | − 0.360631i | −0.983609 | − | 0.180315i | \(-0.942288\pi\) | ||||
0.983609 | − | 0.180315i | \(-0.0577118\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1859.34i | 2.28140i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −705.140 | −0.863084 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −343.616 | −0.418533 | −0.209266 | − | 0.977859i | \(-0.567108\pi\) | ||||
−0.209266 | + | 0.977859i | \(0.567108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −773.430 | −0.939769 | −0.469885 | − | 0.882728i | \(-0.655704\pi\) | ||||
−0.469885 | + | 0.882728i | \(0.655704\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −854.310 | −1.03302 | −0.516511 | − | 0.856280i | \(-0.672770\pi\) | ||||
−0.516511 | + | 0.856280i | \(0.672770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 85.5674i | − 0.103218i | −0.998667 | − | 0.0516088i | \(-0.983565\pi\) | ||||
0.998667 | − | 0.0516088i | \(-0.0164349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 533.353i | − 0.640280i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1015.61i | 1.21630i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1653.28i | 1.97054i | 0.171011 | + | 0.985269i | \(0.445297\pi\) | ||||
−0.171011 | + | 0.985269i | \(0.554703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −702.902 | −0.835793 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1071.06 | 1.26753 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 704.280 | 0.831499 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 910.475 | 1.06989 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1045.62i | − 1.22581i | −0.790156 | − | 0.612905i | \(-0.790001\pi\) | ||||
0.790156 | − | 0.612905i | \(-0.209999\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 939.437i | 1.09619i | 0.836415 | + | 0.548096i | \(0.184647\pi\) | ||||
−0.836415 | + | 0.548096i | \(0.815353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1249.52i | 1.45463i | 0.686306 | + | 0.727313i | \(0.259231\pi\) | ||||
−0.686306 | + | 0.727313i | \(0.740769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1470.64i | 1.70411i | 0.523456 | + | 0.852053i | \(0.324642\pi\) | ||||
−0.523456 | + | 0.852053i | \(0.675358\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1601.70 | −1.85168 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1642.77 | 1.89041 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1133.90 | 1.30183 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −237.588 | −0.271529 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 195.720i | 0.223170i | 0.993755 | + | 0.111585i | \(0.0355927\pi\) | ||||
−0.993755 | + | 0.111585i | \(0.964407\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 533.686i | − 0.605773i | −0.953027 | − | 0.302887i | \(-0.902050\pi\) | ||||
0.953027 | − | 0.302887i | \(-0.0979504\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 963.803i | 1.09151i | 0.837945 | + | 0.545755i | \(0.183757\pi\) | ||||
−0.837945 | + | 0.545755i | \(0.816243\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 507.769i | − 0.572456i | −0.958162 | − | 0.286228i | \(-0.907598\pi\) | ||||
0.958162 | − | 0.286228i | \(-0.0924015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −138.093 | −0.155336 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 292.794 | 0.327877 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1375.43 | −1.53679 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −417.453 | −0.464353 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 587.852i | 0.652444i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 310.786i | 0.343410i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.3834i | 0.0533444i | 0.999644 | + | 0.0266722i | \(0.00849103\pi\) | ||||
−0.999644 | + | 0.0266722i | \(0.991509\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 318.257i | 0.349349i | 0.984626 | + | 0.174674i | \(0.0558873\pi\) | ||||
−0.984626 | + | 0.174674i | \(0.944113\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1050.28 | 1.15036 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.5076 | −0.0114587 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −583.513 | −0.634944 | −0.317472 | − | 0.948268i | \(-0.602834\pi\) | ||||
−0.317472 | + | 0.948268i | \(0.602834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1463.10 | 1.58515 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1033.80i | − 1.11763i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 322.847i | − 0.347521i | −0.984788 | − | 0.173761i | \(-0.944408\pi\) | ||||
0.984788 | − | 0.173761i | \(-0.0555919\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 484.275i | − 0.520166i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2074.70i | 2.21893i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −468.467 | −0.499964 | −0.249982 | − | 0.968250i | \(-0.580425\pi\) | ||||
−0.249982 | + | 0.968250i | \(0.580425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 469.964 | 0.499430 | 0.249715 | − | 0.968319i | \(-0.419663\pi\) | ||||
0.249715 | + | 0.968319i | \(0.419663\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −80.1866 | −0.0850335 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 200.686 | 0.211918 | 0.105959 | − | 0.994370i | \(-0.466209\pi\) | ||||
0.105959 | + | 0.994370i | \(0.466209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1469.90i | − 1.54889i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 493.081i | 0.517398i | 0.965958 | + | 0.258699i | \(0.0832939\pi\) | ||||
−0.965958 | + | 0.258699i | \(0.916706\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2171.03i | 2.27333i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 240.277i | − 0.250550i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 300.907 | 0.313118 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2117.61 | 2.19441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 204.467 | 0.211444 | 0.105722 | − | 0.994396i | \(-0.466285\pi\) | ||||
0.105722 | + | 0.994396i | \(0.466285\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −250.986 | −0.258482 | −0.129241 | − | 0.991613i | \(-0.541254\pi\) | ||||
−0.129241 | + | 0.991613i | \(0.541254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 484.757i | − 0.498208i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 520.823i | 0.533084i | 0.963823 | + | 0.266542i | \(0.0858811\pi\) | ||||
−0.963823 | + | 0.266542i | \(0.914119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3177.22i | − 3.24537i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 569.174i | − 0.579017i | −0.957175 | − | 0.289508i | \(-0.906508\pi\) | ||||
0.957175 | − | 0.289508i | \(-0.0934918\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 644.093 | 0.653902 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2294.51 | −2.32003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 97.2434 | 0.0981266 | 0.0490633 | − | 0.998796i | \(-0.484376\pi\) | ||||
0.0490633 | + | 0.998796i | \(0.484376\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2132.95 | −2.14367 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 112.290i | 0.112628i | 0.998413 | + | 0.0563140i | \(0.0179348\pi\) | ||||
−0.998413 | + | 0.0563140i | \(0.982065\pi\) | |||||||
\(998\) | 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 | 2304.3.h.l.2177.2 | 8 | ||
3.2 | odd | 2 | inner | 2304.3.h.l.2177.8 | 8 | ||
4.3 | odd | 2 | 2304.3.h.j.2177.2 | 8 | |||
8.3 | odd | 2 | 2304.3.h.j.2177.7 | 8 | |||
8.5 | even | 2 | inner | 2304.3.h.l.2177.7 | 8 | ||
12.11 | even | 2 | 2304.3.h.j.2177.8 | 8 | |||
16.3 | odd | 4 | 1152.3.e.e.1025.4 | yes | 4 | ||
16.5 | even | 4 | 1152.3.e.c.1025.1 | yes | 4 | ||
16.11 | odd | 4 | 1152.3.e.g.1025.1 | yes | 4 | ||
16.13 | even | 4 | 1152.3.e.a.1025.4 | yes | 4 | ||
24.5 | odd | 2 | inner | 2304.3.h.l.2177.1 | 8 | ||
24.11 | even | 2 | 2304.3.h.j.2177.1 | 8 | |||
48.5 | odd | 4 | 1152.3.e.c.1025.4 | yes | 4 | ||
48.11 | even | 4 | 1152.3.e.g.1025.4 | yes | 4 | ||
48.29 | odd | 4 | 1152.3.e.a.1025.1 | ✓ | 4 | ||
48.35 | even | 4 | 1152.3.e.e.1025.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.e.a.1025.1 | ✓ | 4 | 48.29 | odd | 4 | ||
1152.3.e.a.1025.4 | yes | 4 | 16.13 | even | 4 | ||
1152.3.e.c.1025.1 | yes | 4 | 16.5 | even | 4 | ||
1152.3.e.c.1025.4 | yes | 4 | 48.5 | odd | 4 | ||
1152.3.e.e.1025.1 | yes | 4 | 48.35 | even | 4 | ||
1152.3.e.e.1025.4 | yes | 4 | 16.3 | odd | 4 | ||
1152.3.e.g.1025.1 | yes | 4 | 16.11 | odd | 4 | ||
1152.3.e.g.1025.4 | yes | 4 | 48.11 | even | 4 | ||
2304.3.h.j.2177.1 | 8 | 24.11 | even | 2 | |||
2304.3.h.j.2177.2 | 8 | 4.3 | odd | 2 | |||
2304.3.h.j.2177.7 | 8 | 8.3 | odd | 2 | |||
2304.3.h.j.2177.8 | 8 | 12.11 | even | 2 | |||
2304.3.h.l.2177.1 | 8 | 24.5 | odd | 2 | inner | ||
2304.3.h.l.2177.2 | 8 | 1.1 | even | 1 | trivial | ||
2304.3.h.l.2177.7 | 8 | 8.5 | even | 2 | inner | ||
2304.3.h.l.2177.8 | 8 | 3.2 | odd | 2 | inner |