Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.31 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.c.5615.32 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 3.61017 | 1.61452 | 0.807259 | − | 0.590198i | \(-0.200950\pi\) | ||||
0.807259 | + | 0.590198i | \(0.200950\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00899i | 0.605734i | 0.953033 | + | 0.302867i | \(0.0979438\pi\) | ||||
−0.953033 | + | 0.302867i | \(0.902056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.59265i | 0.441722i | 0.975305 | + | 0.220861i | \(0.0708867\pi\) | ||||
−0.975305 | + | 0.220861i | \(0.929113\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.79257i | 1.88998i | 0.327106 | + | 0.944988i | \(0.393926\pi\) | ||||
−0.327106 | + | 0.944988i | \(0.606074\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.05480 | 1.15965 | 0.579825 | − | 0.814741i | \(-0.303121\pi\) | ||||
0.579825 | + | 0.814741i | \(0.303121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.14612 | −1.49007 | −0.745034 | − | 0.667026i | \(-0.767567\pi\) | ||||
−0.745034 | + | 0.667026i | \(0.767567\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.03333 | 1.60667 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.94298 | 0.917889 | 0.458945 | − | 0.888465i | \(-0.348228\pi\) | ||||
0.458945 | + | 0.888465i | \(0.348228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.53252i | 0.454853i | 0.973795 | + | 0.227427i | \(0.0730312\pi\) | ||||
−0.973795 | + | 0.227427i | \(0.926969\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.61017i | − 0.610230i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.76592i | 0.783512i | 0.920069 | + | 0.391756i | \(0.128132\pi\) | ||||
−0.920069 | + | 0.391756i | \(0.871868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 0.836835i | − 0.130692i | −0.997863 | − | 0.0653458i | \(-0.979185\pi\) | ||||
0.997863 | − | 0.0653458i | \(-0.0208151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.151434 | −0.0230934 | −0.0115467 | − | 0.999933i | \(-0.503676\pi\) | ||||
−0.0115467 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.795430 | −0.116025 | −0.0580127 | − | 0.998316i | \(-0.518476\pi\) | ||||
−0.0580127 | + | 0.998316i | \(0.518476\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.05980 | 0.145575 | 0.0727873 | − | 0.997347i | \(-0.476811\pi\) | ||||
0.0727873 | + | 0.997347i | \(0.476811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.25280i | 0.977968i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 8.34506i | − 1.08643i | −0.839592 | − | 0.543217i | \(-0.817206\pi\) | ||||
0.839592 | − | 0.543217i | \(-0.182794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2367i | 1.31067i | 0.755336 | + | 0.655337i | \(0.227474\pi\) | ||||
−0.755336 | + | 0.655337i | \(0.772526\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.74974i | 0.713168i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.655357 | −0.0800646 | −0.0400323 | − | 0.999198i | \(-0.512746\pi\) | ||||
−0.0400323 | + | 0.999198i | \(0.512746\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3675 | −1.34907 | −0.674536 | − | 0.738242i | \(-0.735656\pi\) | ||||
−0.674536 | + | 0.738242i | \(0.735656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.3835 | −1.68346 | −0.841728 | − | 0.539901i | \(-0.818462\pi\) | ||||
−0.841728 | + | 0.539901i | \(0.818462\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00899 | 0.228946 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 3.81177i | − 0.428858i | −0.976740 | − | 0.214429i | \(-0.931211\pi\) | ||||
0.976740 | − | 0.214429i | \(-0.0687890\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9522i | 1.64121i | 0.571494 | + | 0.820606i | \(0.306364\pi\) | ||||
−0.571494 | + | 0.820606i | \(0.693636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.1325i | 3.05140i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 0.0444167i | − 0.00470816i | −0.999997 | − | 0.00235408i | \(-0.999251\pi\) | ||||
0.999997 | − | 0.00235408i | \(-0.000749328\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.59265 | 0.166955 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.2487 | 1.87228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.87000 | 1.00215 | 0.501073 | − | 0.865405i | \(-0.332939\pi\) | ||||
0.501073 | + | 0.865405i | \(0.332939\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.43029 | −0.440830 | −0.220415 | − | 0.975406i | \(-0.570741\pi\) | ||||
−0.220415 | + | 0.975406i | \(0.570741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2939i | 1.11282i | 0.830906 | + | 0.556412i | \(0.187823\pi\) | ||||
−0.830906 | + | 0.556412i | \(0.812177\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.60018i | 0.831411i | 0.909499 | + | 0.415705i | \(0.136465\pi\) | ||||
−0.909499 | + | 0.415705i | \(0.863535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 19.9155i | − 1.90756i | −0.300512 | − | 0.953778i | \(-0.597158\pi\) | ||||
0.300512 | − | 0.953778i | \(-0.402842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.81372i | 0.358764i | 0.983779 | + | 0.179382i | \(0.0574098\pi\) | ||||
−0.983779 | + | 0.179382i | \(0.942590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.7987 | −2.40574 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.79257 | 0.714343 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.96395 | 0.633086 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.9508 | 0.979472 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 15.9943i | − 1.41926i | −0.704574 | − | 0.709630i | \(-0.748862\pi\) | ||||
0.704574 | − | 0.709630i | \(-0.251138\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.8839i | 1.73726i | 0.495460 | + | 0.868631i | \(0.335000\pi\) | ||||
−0.495460 | + | 0.868631i | \(0.665000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 5.05480i | − 0.438307i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.93576i | 0.763433i | 0.924279 | + | 0.381717i | \(0.124667\pi\) | ||||
−0.924279 | + | 0.381717i | \(0.875333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.20344 | −0.102074 | −0.0510372 | − | 0.998697i | \(-0.516253\pi\) | ||||
−0.0510372 | + | 0.998697i | \(0.516253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.19962 | −0.267566 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.8450 | 1.48195 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.6791 | −1.03871 | −0.519355 | − | 0.854559i | \(-0.673828\pi\) | ||||
−0.519355 | + | 0.854559i | \(0.673828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 17.5094i | − 1.42489i | −0.701727 | − | 0.712446i | \(-0.747588\pi\) | ||||
0.701727 | − | 0.712446i | \(-0.252412\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.14281i | 0.734368i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2891i | 1.22020i | 0.792324 | + | 0.610100i | \(0.208871\pi\) | ||||
−0.792324 | + | 0.610100i | \(0.791129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.14612i | 0.563193i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.5634 | −1.37567 | −0.687835 | − | 0.725867i | \(-0.741439\pi\) | ||||
−0.687835 | + | 0.725867i | \(0.741439\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.20290 | 0.325230 | 0.162615 | − | 0.986690i | \(-0.448007\pi\) | ||||
0.162615 | + | 0.986690i | \(0.448007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4635 | 0.804882 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0074 | 1.36907 | 0.684537 | − | 0.728978i | \(-0.260005\pi\) | ||||
0.684537 | + | 0.728978i | \(0.260005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 8.03333i | − 0.607263i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.886091i | 0.0662295i | 0.999452 | + | 0.0331148i | \(0.0105427\pi\) | ||||
−0.999452 | + | 0.0331148i | \(0.989457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.47338i | − 0.629821i | −0.949121 | − | 0.314911i | \(-0.898025\pi\) | ||||
0.949121 | − | 0.314911i | \(-0.101975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.2058i | 1.26499i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.6552 | −1.14482 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.6102 | 1.49130 | 0.745652 | − | 0.666335i | \(-0.232138\pi\) | ||||
0.745652 | + | 0.666335i | \(0.232138\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.2972 | 1.31706 | 0.658530 | − | 0.752555i | \(-0.271179\pi\) | ||||
0.658530 | + | 0.752555i | \(0.271179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6580 | 0.759353 | 0.379677 | − | 0.925119i | \(-0.376035\pi\) | ||||
0.379677 | + | 0.925119i | \(0.376035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 26.1305i | − 1.85234i | −0.377108 | − | 0.926169i | \(-0.623081\pi\) | ||||
0.377108 | − | 0.926169i | \(-0.376919\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.94298i | − 0.346929i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3.02112i | − 0.211004i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.1551i | 0.702440i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.1542 | 1.45632 | 0.728159 | − | 0.685409i | \(-0.240376\pi\) | ||||
0.728159 | + | 0.685409i | \(0.240376\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.546701 | −0.0372847 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.53252 | 0.171918 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.4108 | −0.834844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.04274i | 0.404652i | 0.979318 | + | 0.202326i | \(0.0648500\pi\) | ||||
−0.979318 | + | 0.202326i | \(0.935150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.0726i | 1.33227i | 0.745832 | + | 0.666134i | \(0.232052\pi\) | ||||
−0.745832 | + | 0.666134i | \(0.767948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 18.5176i | − 1.22368i | −0.790983 | − | 0.611838i | \(-0.790430\pi\) | ||||
0.790983 | − | 0.611838i | \(-0.209570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 17.1203i | − 1.12159i | −0.827956 | − | 0.560793i | \(-0.810496\pi\) | ||||
0.827956 | − | 0.560793i | \(-0.189504\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.87164 | −0.187325 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.95612 | 0.255900 | 0.127950 | − | 0.991781i | \(-0.459160\pi\) | ||||
0.127950 | + | 0.991781i | \(0.459160\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.3726 | −0.990235 | −0.495117 | − | 0.868826i | \(-0.664875\pi\) | ||||
−0.495117 | + | 0.868826i | \(0.664875\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.61017 | −0.230645 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.05054i | 0.512243i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 13.1732i | − 0.831482i | −0.909483 | − | 0.415741i | \(-0.863522\pi\) | ||||
0.909483 | − | 0.415741i | \(-0.136478\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 14.3565i | − 0.902585i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 26.9072i | − 1.67843i | −0.543802 | − | 0.839213i | \(-0.683016\pi\) | ||||
0.543802 | − | 0.839213i | \(-0.316984\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.76592 | 0.296140 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.15057 | −0.502586 | −0.251293 | − | 0.967911i | \(-0.580856\pi\) | ||||
−0.251293 | + | 0.967911i | \(0.580856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.82605 | 0.235033 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.84304 | −0.234314 | −0.117157 | − | 0.993113i | \(-0.537378\pi\) | ||||
−0.117157 | + | 0.993113i | \(0.537378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8705i | 0.781829i | 0.920427 | + | 0.390914i | \(0.127841\pi\) | ||||
−0.920427 | + | 0.390914i | \(0.872159\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.1389i | 0.973212i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.72420i | 0.163682i | 0.996645 | + | 0.0818408i | \(0.0260799\pi\) | ||||
−0.996645 | + | 0.0818408i | \(0.973920\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.91234i | 0.531666i | 0.964019 | + | 0.265833i | \(0.0856469\pi\) | ||||
−0.964019 | + | 0.265833i | \(0.914353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.90080 | −0.291322 | −0.145661 | − | 0.989335i | \(-0.546531\pi\) | ||||
−0.145661 | + | 0.989335i | \(0.546531\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.836835 | −0.0493968 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −43.7241 | −2.57201 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.1386 | 1.52704 | 0.763518 | − | 0.645786i | \(-0.223470\pi\) | ||||
0.763518 | + | 0.645786i | \(0.223470\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 30.1271i | − 1.75407i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 11.3813i | − 0.658196i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.151434i | 0.00872849i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.9562i | 2.11611i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.4257 | 1.33697 | 0.668487 | − | 0.743724i | \(-0.266942\pi\) | ||||
0.668487 | + | 0.743724i | \(0.266942\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4333 | 0.875143 | 0.437571 | − | 0.899184i | \(-0.355839\pi\) | ||||
0.437571 | + | 0.899184i | \(0.355839\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.1894 | −1.76293 | −0.881464 | − | 0.472251i | \(-0.843442\pi\) | ||||
−0.881464 | + | 0.472251i | \(0.843442\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.7471 | 1.72693 | 0.863466 | − | 0.504407i | \(-0.168289\pi\) | ||||
0.863466 | + | 0.504407i | \(0.168289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.93042i | 0.555997i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.3899i | 2.19171i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7943i | 0.709700i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.795430i | 0.0438535i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00125 | −0.0550339 | −0.0275169 | − | 0.999621i | \(-0.508760\pi\) | ||||
−0.0275169 | + | 0.999621i | \(0.508760\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.36595 | −0.129266 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.1818 | 1.53516 | 0.767580 | − | 0.640953i | \(-0.221461\pi\) | ||||
0.767580 | + | 0.640953i | \(0.221461\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.08780 | −0.275520 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 19.6496i | − 1.05485i | −0.849602 | − | 0.527424i | \(-0.823158\pi\) | ||||
0.849602 | − | 0.527424i | \(-0.176842\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2275i | 0.600993i | 0.953783 | + | 0.300497i | \(0.0971524\pi\) | ||||
−0.953783 | + | 0.300497i | \(0.902848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.2047i | 1.71408i | 0.515249 | + | 0.857041i | \(0.327700\pi\) | ||||
−0.515249 | + | 0.857041i | \(0.672300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −41.0385 | −2.17810 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.1918 | 1.06568 | 0.532842 | − | 0.846215i | \(-0.321124\pi\) | ||||
0.532842 | + | 0.846215i | \(0.321124\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.55100 | 0.344790 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −51.9267 | −2.71797 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.42641i | 0.0744578i | 0.999307 | + | 0.0372289i | \(0.0118531\pi\) | ||||
−0.999307 | + | 0.0372289i | \(0.988147\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.05980i | − 0.0550220i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 9.80760i | − 0.507818i | −0.967228 | − | 0.253909i | \(-0.918284\pi\) | ||||
0.967228 | − | 0.253909i | \(-0.0817165\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.87245i | 0.405452i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5378 | 0.900857 | 0.450428 | − | 0.892813i | \(-0.351271\pi\) | ||||
0.450428 | + | 0.892813i | \(0.351271\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.32355 | 0.425313 | 0.212657 | − | 0.977127i | \(-0.431788\pi\) | ||||
0.212657 | + | 0.977127i | \(0.431788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.25280 | 0.369637 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.79829 | −0.446091 | −0.223045 | − | 0.974808i | \(-0.571600\pi\) | ||||
−0.223045 | + | 0.974808i | \(0.571600\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 55.6866i | − 2.81619i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 13.7611i | − 0.692398i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 31.5495i | − 1.58342i | −0.610896 | − | 0.791711i | \(-0.709190\pi\) | ||||
0.610896 | − | 0.791711i | \(-0.290810\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 8.99955i | − 0.449416i | −0.974426 | − | 0.224708i | \(-0.927857\pi\) | ||||
0.974426 | − | 0.224708i | \(-0.0721428\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.03341 | −0.200919 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.57470 | −0.474600 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.7330 | −1.76688 | −0.883441 | − | 0.468542i | \(-0.844779\pi\) | ||||
−0.883441 | + | 0.468542i | \(0.844779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.34506 | −0.410633 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 53.9798i | 2.64976i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.1521i | 1.71729i | 0.512569 | + | 0.858646i | \(0.328694\pi\) | ||||
−0.512569 | + | 0.858646i | \(0.671306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 22.7156i | − 1.10709i | −0.832819 | − | 0.553546i | \(-0.813274\pi\) | ||||
0.832819 | − | 0.553546i | \(-0.186726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 62.6002i | 3.03656i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.2367 | 0.495388 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.00587 | 0.0484511 | 0.0242256 | − | 0.999707i | \(-0.492288\pi\) | ||||
0.0242256 | + | 0.999707i | \(0.492288\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.8256 | −1.62555 | −0.812776 | − | 0.582576i | \(-0.802045\pi\) | ||||
−0.812776 | + | 0.582576i | \(0.802045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −36.1222 | −1.72796 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 11.9514i | − 0.570411i | −0.958466 | − | 0.285206i | \(-0.907938\pi\) | ||||
0.958466 | − | 0.285206i | \(-0.0920619\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.6849i | 0.840234i | 0.907470 | + | 0.420117i | \(0.138011\pi\) | ||||
−0.907470 | + | 0.420117i | \(0.861989\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 0.160352i | − 0.00760141i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 33.4546i | − 1.57882i | −0.613867 | − | 0.789409i | \(-0.710387\pi\) | ||||
0.613867 | − | 0.789409i | \(-0.289613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.68120 | 0.0791644 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.74974 | 0.269552 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.7127 | 1.62379 | 0.811896 | − | 0.583802i | \(-0.198436\pi\) | ||||
0.811896 | + | 0.583802i | \(0.198436\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.30870 | 0.433549 | 0.216775 | − | 0.976222i | \(-0.430446\pi\) | ||||
0.216775 | + | 0.976222i | \(0.430446\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.56421i | 0.0726950i | 0.999339 | + | 0.0363475i | \(0.0115723\pi\) | ||||
−0.999339 | + | 0.0363475i | \(0.988428\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.47725i | 0.114633i | 0.998356 | + | 0.0573167i | \(0.0182545\pi\) | ||||
−0.998356 | + | 0.0573167i | \(0.981746\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.655357i | 0.0302616i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 0.304229i | − 0.0139885i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.6069 | 1.86317 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.20750 | 0.192245 | 0.0961227 | − | 0.995369i | \(-0.469356\pi\) | ||||
0.0961227 | + | 0.995369i | \(0.469356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.59045 | −0.346095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.6324 | 1.61798 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.7159i | 1.34656i | 0.739389 | + | 0.673278i | \(0.235114\pi\) | ||||
−0.739389 | + | 0.673278i | \(0.764886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 6.98629i | − 0.315287i | −0.987496 | − | 0.157643i | \(-0.949610\pi\) | ||||
0.987496 | − | 0.157643i | \(-0.0503896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.5185i | 1.73479i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.3675i | 0.509901i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.65859 | −0.432378 | −0.216189 | − | 0.976352i | \(-0.569363\pi\) | ||||
−0.216189 | + | 0.976352i | \(0.569363\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.8339 | 1.50858 | 0.754290 | − | 0.656542i | \(-0.227981\pi\) | ||||
0.754290 | + | 0.656542i | \(0.227981\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.9941 | −0.711728 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8961 | 0.571611 | 0.285806 | − | 0.958288i | \(-0.407739\pi\) | ||||
0.285806 | + | 0.958288i | \(0.407739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.3835i | 0.636287i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.7730i | 1.79667i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.59801i | − 0.0702805i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 15.4735i | − 0.677905i | −0.940803 | − | 0.338953i | \(-0.889927\pi\) | ||||
0.940803 | − | 0.338953i | \(-0.110073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0632 | 0.877301 | 0.438651 | − | 0.898658i | \(-0.355457\pi\) | ||||
0.438651 | + | 0.898658i | \(0.355457\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.7348 | −0.859661 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.0670 | 1.22031 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.33279 | 0.0577294 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.0481i | 1.34233i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.00899i | − 0.0865334i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5169i | 0.796103i | 0.917363 | + | 0.398052i | \(0.130313\pi\) | ||||
−0.917363 | + | 0.398052i | \(0.869687\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 71.8982i | − 3.07978i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.8132 | 1.06094 | 0.530468 | − | 0.847705i | \(-0.322016\pi\) | ||||
0.530468 | + | 0.847705i | \(0.322016\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.9858 | 1.06443 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.81177 | −0.162093 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.4177 | −0.822756 | −0.411378 | − | 0.911465i | \(-0.634952\pi\) | ||||
−0.411378 | + | 0.911465i | \(0.634952\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 0.241181i | − 0.0102009i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 14.6696i | − 0.618252i | −0.951021 | − | 0.309126i | \(-0.899964\pi\) | ||||
0.951021 | − | 0.309126i | \(-0.100036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.7682i | 0.579231i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 17.3133i | − 0.725809i | −0.931826 | − | 0.362905i | \(-0.881785\pi\) | ||||
0.931826 | − | 0.362905i | \(-0.118215\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.7082 | −0.489975 | −0.244987 | − | 0.969526i | \(-0.578784\pi\) | ||||
−0.244987 | + | 0.969526i | \(0.578784\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −57.4071 | −2.39404 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.79465 | 0.199604 | 0.0998020 | − | 0.995007i | \(-0.468179\pi\) | ||||
0.0998020 | + | 0.995007i | \(0.468179\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.9522 | 0.620320 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.12913i | 0.0881795i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.1643i | 1.24501i | 0.782615 | + | 0.622506i | \(0.213886\pi\) | ||||
−0.782615 | + | 0.622506i | \(0.786114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8014i | 0.527471i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.60974i | 0.107169i | 0.998563 | + | 0.0535847i | \(0.0170647\pi\) | ||||
−0.998563 | + | 0.0535847i | \(0.982935\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.1325 | 1.15332 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.6903 | −1.13139 | −0.565697 | − | 0.824613i | \(-0.691393\pi\) | ||||
−0.565697 | + | 0.824613i | \(0.691393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.3291 | 0.666079 | 0.333039 | − | 0.942913i | \(-0.391926\pi\) | ||||
0.333039 | + | 0.942913i | \(0.391926\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.1410 | 1.02213 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9385i | 0.525159i | 0.964910 | + | 0.262580i | \(0.0845732\pi\) | ||||
−0.964910 | + | 0.262580i | \(0.915427\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.26684i | − 0.0512509i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 21.7992i | − 0.880463i | −0.897884 | − | 0.440231i | \(-0.854896\pi\) | ||||
0.897884 | − | 0.440231i | \(-0.145104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.8226i | 1.68371i | 0.539700 | + | 0.841857i | \(0.318538\pi\) | ||||
−0.539700 | + | 0.841857i | \(0.681462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.82763 | 0.194039 | 0.0970193 | − | 0.995282i | \(-0.469069\pi\) | ||||
0.0970193 | + | 0.995282i | \(0.469069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0444167 | −0.00177952 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.632276 | −0.0252911 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.1388 | −1.48082 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.3929i | 0.811830i | 0.913911 | + | 0.405915i | \(0.133047\pi\) | ||||
−0.913911 | + | 0.405915i | \(0.866953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 57.7420i | − 2.29142i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.59265i | − 0.0631032i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.42755i | 0.372366i | 0.982515 | + | 0.186183i | \(0.0596117\pi\) | ||||
−0.982515 | + | 0.186183i | \(0.940388\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.2077 | 1.07297 | 0.536484 | − | 0.843911i | \(-0.319752\pi\) | ||||
0.536484 | + | 0.843911i | \(0.319752\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.24081 | 0.284666 | 0.142333 | − | 0.989819i | \(-0.454540\pi\) | ||||
0.142333 | + | 0.989819i | \(0.454540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.7652 | 0.658090 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.0954 | 1.17772 | 0.588861 | − | 0.808234i | \(-0.299576\pi\) | ||||
0.588861 | + | 0.808234i | \(0.299576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 71.7842i | 2.80484i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.9316i | 1.63342i | 0.577045 | + | 0.816712i | \(0.304206\pi\) | ||||
−0.577045 | + | 0.816712i | \(0.695794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 0.735053i | − 0.0285903i | −0.999898 | − | 0.0142951i | \(-0.995450\pi\) | ||||
0.999898 | − | 0.0142951i | \(-0.00455044\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 18.2487i | − 0.707654i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.3232 | −1.36772 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.5654 | −0.793920 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.6142 | −0.833165 | −0.416582 | − | 0.909098i | \(-0.636772\pi\) | ||||
−0.416582 | + | 0.909098i | \(0.636772\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.631879 | −0.0242851 | −0.0121425 | − | 0.999926i | \(-0.503865\pi\) | ||||
−0.0121425 | + | 0.999926i | \(0.503865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 9.87000i | − 0.378776i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 22.4241i | − 0.858033i | −0.903297 | − | 0.429017i | \(-0.858860\pi\) | ||||
0.903297 | − | 0.429017i | \(-0.141140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.2596i | 1.23258i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.68789i | 0.0643035i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.69349 | 0.102465 | 0.0512325 | − | 0.998687i | \(-0.483685\pi\) | ||||
0.0512325 | + | 0.998687i | \(0.483685\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.34462 | −0.164801 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.52109 | 0.247004 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.4555 | −1.07475 | −0.537375 | − | 0.843344i | \(-0.680584\pi\) | ||||
−0.537375 | + | 0.843344i | \(0.680584\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0908i | 0.908601i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.43029i | 0.166618i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 13.4255i | − 0.504204i | −0.967701 | − | 0.252102i | \(-0.918878\pi\) | ||||
0.967701 | − | 0.252102i | \(-0.0811218\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 18.0977i | − 0.677763i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.5512 | −0.431990 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.4437 | 1.84394 | 0.921969 | − | 0.387264i | \(-0.126580\pi\) | ||||
0.921969 | + | 0.387264i | \(0.126580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.2939 | 0.420608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.7086 | 1.47474 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 5.65644i | − 0.209786i | −0.994484 | − | 0.104893i | \(-0.966550\pi\) | ||||
0.994484 | − | 0.104893i | \(-0.0334500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.18006i | − 0.0436460i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 42.3705i | − 1.56499i | −0.622656 | − | 0.782495i | \(-0.713946\pi\) | ||||
0.622656 | − | 0.782495i | \(-0.286054\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.31661i | − 0.0484979i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.5942 | 1.53007 | 0.765034 | − | 0.643989i | \(-0.222722\pi\) | ||||
0.765034 | + | 0.643989i | \(0.222722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.5821 | 0.608338 | 0.304169 | − | 0.952618i | \(-0.401621\pi\) | ||||
0.304169 | + | 0.952618i | \(0.401621\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −45.7736 | −1.67702 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.60018 | 0.314244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 4.26395i | − 0.155594i | −0.996969 | − | 0.0777968i | \(-0.975211\pi\) | ||||
0.996969 | − | 0.0777968i | \(-0.0247886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 63.2118i | − 2.30051i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 19.5706i | − 0.711305i | −0.934618 | − | 0.355653i | \(-0.884259\pi\) | ||||
0.934618 | − | 0.355653i | \(-0.115741\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.1256i | 0.802053i | 0.916066 | + | 0.401027i | \(0.131347\pi\) | ||||
−0.916066 | + | 0.401027i | \(0.868653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.9155 | −0.720988 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2908 | 0.479902 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.1961 | −0.584046 | −0.292023 | − | 0.956411i | \(-0.594328\pi\) | ||||
−0.292023 | + | 0.956411i | \(0.594328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.34825 | −0.0844608 | −0.0422304 | − | 0.999108i | \(-0.513446\pi\) | ||||
−0.0422304 | + | 0.999108i | \(0.513446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.3445i | 0.730797i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 4.23003i | − 0.151557i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 22.8372i | − 0.817179i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55.1962i | 1.97004i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.9012 | −0.388586 | −0.194293 | − | 0.980943i | \(-0.562241\pi\) | ||||
−0.194293 | + | 0.980943i | \(0.562241\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.81372 | 0.135600 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.3035 | −0.578954 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.08600 | 0.180155 | 0.0900776 | − | 0.995935i | \(-0.471288\pi\) | ||||
0.0900776 | + | 0.995935i | \(0.471288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 6.19844i | − 0.219285i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 28.8963i | − 1.01973i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.7987i | 0.909285i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 26.8140i | − 0.942729i | −0.881938 | − | 0.471365i | \(-0.843762\pi\) | ||||
0.881938 | − | 0.471365i | \(-0.156238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.8383 | −1.36380 | −0.681899 | − | 0.731446i | \(-0.738846\pi\) | ||||
−0.681899 | + | 0.731446i | \(0.738846\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −63.4068 | −2.22104 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.765467 | −0.0267803 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.3421 | −1.02405 | −0.512023 | − | 0.858972i | \(-0.671104\pi\) | ||||
−0.512023 | + | 0.858972i | \(0.671104\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 23.9770i | − 0.835784i | −0.908497 | − | 0.417892i | \(-0.862769\pi\) | ||||
0.908497 | − | 0.417892i | \(-0.137231\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.92468i | 0.171248i | 0.996328 | + | 0.0856239i | \(0.0272883\pi\) | ||||
−0.996328 | + | 0.0856239i | \(0.972712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.00324i | 0.277964i | 0.990295 | + | 0.138982i | \(0.0443830\pi\) | ||||
−0.990295 | + | 0.138982i | \(0.955617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 7.79257i | − 0.269996i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.1732 | 0.525089 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.4595 | 1.08610 | 0.543051 | − | 0.839700i | \(-0.317269\pi\) | ||||
0.543051 | + | 0.839700i | \(0.317269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.56691 | −0.157479 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.7749 | 1.29950 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 6.96395i | − 0.239284i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 34.0578i | − 1.16749i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.31213i | 0.0449263i | 0.999748 | + | 0.0224632i | \(0.00715085\pi\) | ||||
−0.999748 | + | 0.0224632i | \(0.992849\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 24.2200i | − 0.827341i | −0.910427 | − | 0.413670i | \(-0.864247\pi\) | ||||
0.910427 | − | 0.413670i | \(-0.135753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.49401 | −0.289812 | −0.144906 | − | 0.989445i | \(-0.546288\pi\) | ||||
−0.144906 | + | 0.989445i | \(0.546288\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.8759 | −1.05103 | −0.525513 | − | 0.850785i | \(-0.676127\pi\) | ||||
−0.525513 | + | 0.850785i | \(0.676127\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 65.0096 | 2.21039 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.65782 | 0.259774 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.04376i | − 0.0353663i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 10.9508i | − 0.370206i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 33.4689i | − 1.13016i | −0.825035 | − | 0.565082i | \(-0.808845\pi\) | ||||
0.825035 | − | 0.565082i | \(-0.191155\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.7535i | 1.13719i | 0.822619 | + | 0.568593i | \(0.192512\pi\) | ||||
−0.822619 | + | 0.568593i | \(0.807488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.59496 | −0.0536746 | −0.0268373 | − | 0.999640i | \(-0.508544\pi\) | ||||
−0.0268373 | + | 0.999640i | \(0.508544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.9639 | −0.603167 | −0.301584 | − | 0.953440i | \(-0.597515\pi\) | ||||
−0.301584 | + | 0.953440i | \(0.597515\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.9943 | −0.536430 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.02074 | −0.134549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.19894i | 0.106929i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5182i | 0.417505i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.25855i | 0.275132i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 30.5903i | − 1.01686i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.9653 | −1.75868 | −0.879342 | − | 0.476190i | \(-0.842017\pi\) | ||||
−0.879342 | + | 0.476190i | \(0.842017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.6435 | −1.74416 | −0.872079 | − | 0.489365i | \(-0.837229\pi\) | ||||
−0.872079 | + | 0.489365i | \(0.837229\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.0388 | −0.994138 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.8839 | 0.656623 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 36.5794i | − 1.20664i | −0.797498 | − | 0.603322i | \(-0.793843\pi\) | ||||
0.797498 | − | 0.603322i | \(-0.206157\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 18.1044i | − 0.595915i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.2862i | 1.25884i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 24.8413i | − 0.815018i | −0.913201 | − | 0.407509i | \(-0.866398\pi\) | ||||
0.913201 | − | 0.407509i | \(-0.133602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.05480 | −0.165664 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −56.5180 | −1.84833 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.904448 | 0.0295470 | 0.0147735 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147735 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.11337 | −0.264488 | −0.132244 | − | 0.991217i | \(-0.542218\pi\) | ||||
−0.132244 | + | 0.991217i | \(0.542218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.98012i | 0.194740i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.2396i | 1.11264i | 0.830969 | + | 0.556319i | \(0.187787\pi\) | ||||
−0.830969 | + | 0.556319i | \(0.812213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 22.9078i | − 0.743620i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 5.47739i | − 0.177430i | −0.996057 | − | 0.0887151i | \(-0.971724\pi\) | ||||
0.996057 | − | 0.0887151i | \(-0.0282761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 74.4065 | 2.40774 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.93576 | 0.288551 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.5864 | 0.793109 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 66.0559 | 2.12641 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 45.0597i | − 1.44902i | −0.689262 | − | 0.724512i | \(-0.742065\pi\) | ||||
0.689262 | − | 0.724512i | \(-0.257935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 28.4013i | − 0.911442i | −0.890123 | − | 0.455721i | \(-0.849382\pi\) | ||||
0.890123 | − | 0.455721i | \(-0.150618\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.20344i | 0.0385805i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.06448i | 0.130034i | 0.997884 | + | 0.0650171i | \(0.0207102\pi\) | ||||
−0.997884 | + | 0.0650171i | \(0.979290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0892328 | 0.00285189 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0487 | −0.416189 | −0.208094 | − | 0.978109i | \(-0.566726\pi\) | ||||
−0.208094 | + | 0.978109i | \(0.566726\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.4773 | 1.22599 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.08216 | 0.0344108 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 0.598647i | − 0.0190166i | −0.999955 | − | 0.00950832i | \(-0.996973\pi\) | ||||
0.999955 | − | 0.00950832i | \(-0.00302664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 94.3354i | − 2.99063i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.04553i | 0.128123i | 0.997946 | + | 0.0640616i | \(0.0204054\pi\) | ||||
−0.997946 | + | 0.0640616i | \(0.979595\pi\) | |||||||
\(998\) | 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 | 6048.2.j.c.5615.31 | 32 | ||
3.2 | odd | 2 | inner | 6048.2.j.c.5615.2 | 32 | ||
4.3 | odd | 2 | 1512.2.j.c.323.5 | ✓ | 32 | ||
8.3 | odd | 2 | inner | 6048.2.j.c.5615.1 | 32 | ||
8.5 | even | 2 | 1512.2.j.c.323.27 | yes | 32 | ||
12.11 | even | 2 | 1512.2.j.c.323.28 | yes | 32 | ||
24.5 | odd | 2 | 1512.2.j.c.323.6 | yes | 32 | ||
24.11 | even | 2 | inner | 6048.2.j.c.5615.32 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.5 | ✓ | 32 | 4.3 | odd | 2 | ||
1512.2.j.c.323.6 | yes | 32 | 24.5 | odd | 2 | ||
1512.2.j.c.323.27 | yes | 32 | 8.5 | even | 2 | ||
1512.2.j.c.323.28 | yes | 32 | 12.11 | even | 2 | ||
6048.2.j.c.5615.1 | 32 | 8.3 | odd | 2 | inner | ||
6048.2.j.c.5615.2 | 32 | 3.2 | odd | 2 | inner | ||
6048.2.j.c.5615.31 | 32 | 1.1 | even | 1 | trivial | ||
6048.2.j.c.5615.32 | 32 | 24.11 | even | 2 | inner |