Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9216,2,Mod(1,9216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9216 = 2^{10} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9216.a (trivial) |
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: | yes |
Analytic conductor: | \(73.5901305028\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.10070523904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 8x^{6} + 24x^{5} + 30x^{4} - 16x^{3} - 20x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 144) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.79591\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(5\) | 0.841723 | 0.376430 | 0.188215 | − | 0.982128i | \(-0.439730\pi\) | ||||
0.188215 | + | 0.982128i | \(0.439730\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.64575 | −0.622036 | −0.311018 | − | 0.950404i | \(-0.600670\pi\) | ||||
−0.311018 | + | 0.950404i | \(0.600670\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.75216 | 1.43283 | 0.716415 | − | 0.697675i | \(-0.245782\pi\) | ||||
0.716415 | + | 0.697675i | \(0.245782\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.74166 | 1.03775 | 0.518875 | − | 0.854850i | \(-0.326351\pi\) | ||||
0.518875 | + | 0.854850i | \(0.326351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.53019 | −1.34127 | −0.670634 | − | 0.741788i | \(-0.733978\pi\) | ||||
−0.670634 | + | 0.741788i | \(0.733978\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.15587 | 1.18284 | 0.591419 | − | 0.806364i | \(-0.298568\pi\) | ||||
0.591419 | + | 0.806364i | \(0.298568\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.33981 | −0.904914 | −0.452457 | − | 0.891786i | \(-0.649452\pi\) | ||||
−0.452457 | + | 0.891786i | \(0.649452\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.29150 | −0.858301 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.66259 | 1.60860 | 0.804302 | − | 0.594221i | \(-0.202540\pi\) | ||||
0.804302 | + | 0.594221i | \(0.202540\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.64575 | 1.01401 | 0.507003 | − | 0.861944i | \(-0.330753\pi\) | ||||
0.507003 | + | 0.861944i | \(0.330753\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.38527 | −0.234153 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.913230 | −0.150134 | −0.0750671 | − | 0.997178i | \(-0.523917\pi\) | ||||
−0.0750671 | + | 0.997178i | \(0.523917\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.91094 | 1.23548 | 0.617741 | − | 0.786382i | \(-0.288048\pi\) | ||||
0.617741 | + | 0.786382i | \(0.288048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500983 | −0.0763992 | −0.0381996 | − | 0.999270i | \(-0.512162\pi\) | ||||
−0.0381996 | + | 0.999270i | \(0.512162\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.10132 | −1.32756 | −0.663782 | − | 0.747926i | \(-0.731050\pi\) | ||||
−0.663782 | + | 0.747926i | \(0.731050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.29150 | −0.613072 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.97915 | 0.958660 | 0.479330 | − | 0.877635i | \(-0.340880\pi\) | ||||
0.479330 | + | 0.877635i | \(0.340880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.13742 | −0.799025 | −0.399512 | − | 0.916728i | \(-0.630821\pi\) | ||||
−0.399512 | + | 0.916728i | \(0.630821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.913230 | 0.116927 | 0.0584636 | − | 0.998290i | \(-0.481380\pi\) | ||||
0.0584636 | + | 0.998290i | \(0.481380\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.14944 | 0.390640 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.65685 | 0.691095 | 0.345547 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345547 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.4411 | 1.59517 | 0.797584 | − | 0.603207i | \(-0.206111\pi\) | ||||
0.797584 | + | 0.603207i | \(0.206111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.29150 | −0.385241 | −0.192621 | − | 0.981273i | \(-0.561699\pi\) | ||||
−0.192621 | + | 0.981273i | \(0.561699\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.82087 | −0.891271 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.64575 | 1.08523 | 0.542616 | − | 0.839981i | \(-0.317434\pi\) | ||||
0.542616 | + | 0.839981i | \(0.317434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.75216 | 0.521617 | 0.260809 | − | 0.965391i | \(-0.416011\pi\) | ||||
0.260809 | + | 0.965391i | \(0.416011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.65489 | −0.504893 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.38075 | −0.252359 | −0.126180 | − | 0.992007i | \(-0.540272\pi\) | ||||
−0.126180 | + | 0.992007i | \(0.540272\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.15784 | −0.645517 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.33981 | 0.445256 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5830 | −1.07454 | −0.537271 | − | 0.843410i | \(-0.680545\pi\) | ||||
−0.537271 | + | 0.843410i | \(0.680545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.841723 | 0.0837546 | 0.0418773 | − | 0.999123i | \(-0.486666\pi\) | ||||
0.0418773 | + | 0.999123i | \(0.486666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9373 | 1.66888 | 0.834439 | − | 0.551101i | \(-0.185792\pi\) | ||||
0.834439 | + | 0.551101i | \(0.185792\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.36689 | 0.325490 | 0.162745 | − | 0.986668i | \(-0.447965\pi\) | ||||
0.162745 | + | 0.986668i | \(0.447965\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.39851 | −0.900214 | −0.450107 | − | 0.892975i | \(-0.648614\pi\) | ||||
−0.450107 | + | 0.892975i | \(0.648614\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.65292 | −0.340637 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.10132 | 0.834316 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.5830 | 1.05300 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.82087 | −0.699520 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.937254 | −0.0831678 | −0.0415839 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415839 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.50432 | 0.830396 | 0.415198 | − | 0.909731i | \(-0.363712\pi\) | ||||
0.415198 | + | 0.909731i | \(0.363712\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.48528 | −0.735767 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.2917 | −0.879279 | −0.439639 | − | 0.898174i | \(-0.644894\pi\) | ||||
−0.439639 | + | 0.898174i | \(0.644894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.6235 | −1.74926 | −0.874631 | − | 0.484790i | \(-0.838896\pi\) | ||||
−0.874631 | + | 0.484790i | \(0.838896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.7809 | 1.48692 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.29150 | 0.605526 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.4835 | −1.35038 | −0.675189 | − | 0.737645i | \(-0.735938\pi\) | ||||
−0.675189 | + | 0.737645i | \(0.735938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3542 | 0.842617 | 0.421308 | − | 0.906917i | \(-0.361571\pi\) | ||||
0.421308 | + | 0.906917i | \(0.361571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.75216 | 0.381703 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.39851 | 0.750083 | 0.375041 | − | 0.927008i | \(-0.377628\pi\) | ||||
0.375041 | + | 0.927008i | \(0.377628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.14226 | 0.562889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4696 | 1.29000 | 0.644999 | − | 0.764184i | \(-0.276858\pi\) | ||||
0.644999 | + | 0.764184i | \(0.276858\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.7809 | −1.37593 | −0.687965 | − | 0.725743i | \(-0.741496\pi\) | ||||
−0.687965 | + | 0.725743i | \(0.741496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.97915 | 0.530615 | 0.265307 | − | 0.964164i | \(-0.414527\pi\) | ||||
0.265307 | + | 0.964164i | \(0.414527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.06275 | 0.533893 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.36689 | 0.251653 | 0.125827 | − | 0.992052i | \(-0.459842\pi\) | ||||
0.125827 | + | 0.992052i | \(0.459842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.913230 | 0.0678799 | 0.0339399 | − | 0.999424i | \(-0.489195\pi\) | ||||
0.0339399 | + | 0.999424i | \(0.489195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.768687 | −0.0565150 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.2803 | −1.92181 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.10132 | −0.658548 | −0.329274 | − | 0.944234i | \(-0.606804\pi\) | ||||
−0.329274 | + | 0.944234i | \(0.606804\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8745 | 0.854746 | 0.427373 | − | 0.904075i | \(-0.359439\pi\) | ||||
0.427373 | + | 0.904075i | \(0.359439\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0295 | −0.857065 | −0.428533 | − | 0.903526i | \(-0.640969\pi\) | ||||
−0.428533 | + | 0.903526i | \(0.640969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6458 | 0.967322 | 0.483661 | − | 0.875256i | \(-0.339307\pi\) | ||||
0.483661 | + | 0.875256i | \(0.339307\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.2565 | −1.00061 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.65882 | 0.465072 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.5015 | 1.69481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.6235 | 1.41978 | 0.709890 | − | 0.704313i | \(-0.248745\pi\) | ||||
0.709890 | + | 0.704313i | \(0.248745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.421689 | −0.0287590 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.29150 | −0.630748 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.6921 | −1.39190 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.3542 | 0.961232 | 0.480616 | − | 0.876931i | \(-0.340413\pi\) | ||||
0.480616 | + | 0.876931i | \(0.340413\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.98162 | −0.131525 | −0.0657625 | − | 0.997835i | \(-0.520948\pi\) | ||||
−0.0657625 | + | 0.997835i | \(0.520948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.3671 | 1.67631 | 0.838153 | − | 0.545435i | \(-0.183636\pi\) | ||||
0.838153 | + | 0.545435i | \(0.183636\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.7400 | −1.29321 | −0.646606 | − | 0.762825i | \(-0.723812\pi\) | ||||
−0.646606 | + | 0.762825i | \(0.723812\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.66079 | −0.499735 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.0194 | −0.842158 | −0.421079 | − | 0.907024i | \(-0.638348\pi\) | ||||
−0.421079 | + | 0.907024i | \(0.638348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.29150 | 0.0831930 | 0.0415965 | − | 0.999134i | \(-0.486756\pi\) | ||||
0.0415965 | + | 0.999134i | \(0.486756\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.61226 | −0.230779 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.2915 | 1.22749 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.5313 | 1.67464 | 0.837321 | − | 0.546711i | \(-0.184121\pi\) | ||||
0.837321 | + | 0.546711i | \(0.184121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.6235 | −1.29659 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.2630 | −1.82538 | −0.912688 | − | 0.408656i | \(-0.865998\pi\) | ||||
−0.912688 | + | 0.408656i | \(0.865998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.50295 | 0.0933888 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.67963 | −0.535209 | −0.267604 | − | 0.963529i | \(-0.586232\pi\) | ||||
−0.267604 | + | 0.963529i | \(0.586232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.87451 | 0.360868 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.8000 | 0.902373 | 0.451186 | − | 0.892430i | \(-0.351001\pi\) | ||||
0.451186 | + | 0.892430i | \(0.351001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.35425 | 0.385993 | 0.192997 | − | 0.981199i | \(-0.438179\pi\) | ||||
0.192997 | + | 0.981199i | \(0.438179\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.3939 | −1.22980 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3632 | 1.40376 | 0.701879 | − | 0.712297i | \(-0.252345\pi\) | ||||
0.701879 | + | 0.712297i | \(0.252345\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.38075 | −0.142024 | −0.0710119 | − | 0.997475i | \(-0.522623\pi\) | ||||
−0.0710119 | + | 0.997475i | \(0.522623\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.65292 | 0.217144 | 0.108572 | − | 0.994089i | \(-0.465372\pi\) | ||||
0.108572 | + | 0.994089i | \(0.465372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.0194 | −0.768513 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5830 | 0.799000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.61226 | 0.211030 | 0.105515 | − | 0.994418i | \(-0.466351\pi\) | ||||
0.105515 | + | 0.994418i | \(0.466351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.16601 | −0.300777 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.2381 | −0.939074 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.824494 | 0.0475230 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.768687 | 0.0440149 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.2843 | 1.61427 | 0.807134 | − | 0.590368i | \(-0.201017\pi\) | ||||
0.807134 | + | 0.590368i | \(0.201017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.67963 | 0.492177 | 0.246088 | − | 0.969247i | \(-0.420855\pi\) | ||||
0.246088 | + | 0.969247i | \(0.420855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.29150 | −0.525187 | −0.262593 | − | 0.964907i | \(-0.584578\pi\) | ||||
−0.262593 | + | 0.964907i | \(0.584578\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.841723 | 0.0472759 | 0.0236379 | − | 0.999721i | \(-0.492475\pi\) | ||||
0.0236379 | + | 0.999721i | \(0.492475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 41.1660 | 2.30485 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.5129 | −1.58650 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0573 | −0.890701 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.9785 | 0.825792 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3137 | −0.621858 | −0.310929 | − | 0.950433i | \(-0.600640\pi\) | ||||
−0.310929 | + | 0.950433i | \(0.600640\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.76150 | 0.260149 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.70850 | −0.256488 | −0.128244 | − | 0.991743i | \(-0.540934\pi\) | ||||
−0.128244 | + | 0.991743i | \(0.540934\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.8295 | 1.45290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5830 | 1.00339 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.75216 | −0.255109 | −0.127555 | − | 0.991832i | \(-0.540713\pi\) | ||||
−0.127555 | + | 0.991832i | \(0.540713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.56615 | −0.244420 | −0.122210 | − | 0.992504i | \(-0.538998\pi\) | ||||
−0.122210 | + | 0.992504i | \(0.538998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.14226 | 0.380144 | 0.190072 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190072 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3137 | 0.600469 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.76150 | −0.251303 | −0.125651 | − | 0.992074i | \(-0.540102\pi\) | ||||
−0.125651 | + | 0.992074i | \(0.540102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.58301 | 0.399106 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.77053 | −0.145016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.8118 | 1.81716 | 0.908580 | − | 0.417712i | \(-0.137168\pi\) | ||||
0.908580 | + | 0.417712i | \(0.137168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.4859 | −0.596320 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.8818 | −0.874108 | −0.437054 | − | 0.899435i | \(-0.643978\pi\) | ||||
−0.437054 | + | 0.899435i | \(0.643978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.4125 | 1.66933 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.8147 | −0.606880 | −0.303440 | − | 0.952851i | \(-0.598135\pi\) | ||||
−0.303440 | + | 0.952851i | \(0.598135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.10132 | 0.465056 | 0.232528 | − | 0.972590i | \(-0.425300\pi\) | ||||
0.232528 | + | 0.972590i | \(0.425300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.58301 | −0.335501 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.3547 | 1.48834 | 0.744170 | − | 0.667990i | \(-0.232845\pi\) | ||||
0.744170 | + | 0.667990i | \(0.232845\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.11905 | 0.408514 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4024 | 0.572272 | 0.286136 | − | 0.958189i | \(-0.407629\pi\) | ||||
0.286136 | + | 0.958189i | \(0.407629\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5906 | −0.828494 | −0.414247 | − | 0.910165i | \(-0.635955\pi\) | ||||
−0.414247 | + | 0.910165i | \(0.635955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.1245 | 1.05228 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.33981 | −0.215117 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1660 | 1.24438 | 0.622190 | − | 0.782867i | \(-0.286243\pi\) | ||||
0.622190 | + | 0.782867i | \(0.286243\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.1007 | 0.497022 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.5313 | 1.29614 | 0.648070 | − | 0.761581i | \(-0.275576\pi\) | ||||
0.648070 | + | 0.761581i | \(0.275576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0573 | 0.782587 | 0.391293 | − | 0.920266i | \(-0.372028\pi\) | ||||
0.391293 | + | 0.920266i | \(0.372028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.7328 | 1.15121 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.50295 | −0.0727328 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.2221 | 1.50391 | 0.751957 | − | 0.659212i | \(-0.229110\pi\) | ||||
0.751957 | + | 0.659212i | \(0.229110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.3755 | −1.07037 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.479741 | 0.0228968 | 0.0114484 | − | 0.999934i | \(-0.496356\pi\) | ||||
0.0114484 | + | 0.999934i | \(0.496356\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.4946 | −1.44884 | −0.724420 | − | 0.689358i | \(-0.757893\pi\) | ||||
−0.724420 | + | 0.689358i | \(0.757893\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00393 | −0.0949955 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.44832 | 0.445894 | 0.222947 | − | 0.974831i | \(-0.428432\pi\) | ||||
0.222947 | + | 0.974831i | \(0.428432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.5940 | 1.77023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.18319 | −0.242992 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.41699 | 0.253396 | 0.126698 | − | 0.991941i | \(-0.459562\pi\) | ||||
0.126698 | + | 0.991941i | \(0.459562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0295 | 0.560269 | 0.280134 | − | 0.959961i | \(-0.409621\pi\) | ||||
0.280134 | + | 0.959961i | \(0.409621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.0627 | 0.700025 | 0.350013 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350013 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.0356 | 1.66753 | 0.833765 | − | 0.552119i | \(-0.186181\pi\) | ||||
0.833765 | + | 0.552119i | \(0.186181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.30978 | −0.429885 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.38075 | −0.109467 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.1264 | −1.01523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.1208 | 1.01072 | 0.505362 | − | 0.862908i | \(-0.331359\pi\) | ||||
0.505362 | + | 0.862908i | \(0.331359\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.41699 | −0.155802 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.90796 | −0.404490 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.22876 | 0.372881 | 0.186440 | − | 0.982466i | \(-0.440305\pi\) | ||||
0.186440 | + | 0.982466i | \(0.440305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.7792 | 0.982880 | 0.491440 | − | 0.870911i | \(-0.336471\pi\) | ||||
0.491440 | + | 0.870911i | \(0.336471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −47.9058 | −2.15757 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.1208 | −0.992252 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9666 | −0.669998 | −0.334999 | − | 0.942218i | \(-0.608736\pi\) | ||||
−0.334999 | + | 0.942218i | \(0.608736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.6438 | −1.41093 | −0.705463 | − | 0.708747i | \(-0.749261\pi\) | ||||
−0.705463 | + | 0.708747i | \(0.749261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.708497 | 0.0315277 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.8957 | 1.54673 | 0.773363 | − | 0.633963i | \(-0.218573\pi\) | ||||
0.773363 | + | 0.633963i | \(0.218573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.41699 | 0.239634 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2565 | 0.628215 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.2509 | −1.90217 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.2098 | −0.622543 | −0.311272 | − | 0.950321i | \(-0.600755\pi\) | ||||
−0.311272 | + | 0.950321i | \(0.600755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.7813 | −1.17107 | −0.585533 | − | 0.810649i | \(-0.699115\pi\) | ||||
−0.585533 | + | 0.810649i | \(0.699115\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.2221 | −1.36006 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.16601 | −0.181131 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.6000 | 1.28212 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.83399 | 0.122524 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.3939 | −0.878427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.3337 | 1.73408 | 0.867041 | − | 0.498236i | \(-0.166019\pi\) | ||||
0.867041 | + | 0.498236i | \(0.166019\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.91094 | −0.338868 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.1245 | 0.903217 | 0.451608 | − | 0.892216i | \(-0.350850\pi\) | ||||
0.451608 | + | 0.892216i | \(0.350850\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.6632 | 1.90272 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.8745 | −0.675053 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.5841 | −1.12641 | −0.563203 | − | 0.826319i | \(-0.690431\pi\) | ||||
−0.563203 | + | 0.826319i | \(0.690431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.87451 | −0.0792832 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.52269 | 0.317044 | 0.158522 | − | 0.987355i | \(-0.449327\pi\) | ||||
0.158522 | + | 0.987355i | \(0.449327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.0921 | −1.72267 | −0.861335 | − | 0.508038i | \(-0.830371\pi\) | ||||
−0.861335 | + | 0.508038i | \(0.830371\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.65685 | −0.236732 | −0.118366 | − | 0.992970i | \(-0.537766\pi\) | ||||
−0.118366 | + | 0.992970i | \(0.537766\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.6243 | 0.776688 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.0405 | −1.62528 | −0.812639 | − | 0.582767i | \(-0.801970\pi\) | ||||
−0.812639 | + | 0.582767i | \(0.801970\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.82087 | −0.324464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.1660 | 1.37360 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.73378 | −0.277933 | −0.138966 | − | 0.990297i | \(-0.544378\pi\) | ||||
−0.138966 | + | 0.990297i | \(0.544378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.1088 | 1.19941 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.1208 | −0.908391 | −0.454195 | − | 0.890902i | \(-0.650073\pi\) | ||||
−0.454195 | + | 0.890902i | \(0.650073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.66079 | 0.314062 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8628 | 0.566420 | 0.283210 | − | 0.959058i | \(-0.408601\pi\) | ||||
0.283210 | + | 0.959058i | \(0.408601\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.29150 | 0.134263 | 0.0671316 | − | 0.997744i | \(-0.478615\pi\) | ||||
0.0671316 | + | 0.997744i | \(0.478615\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.74968 | 0.396381 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.1033 | −0.572434 | −0.286217 | − | 0.958165i | \(-0.592398\pi\) | ||||
−0.286217 | + | 0.958165i | \(0.592398\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.0540 | −1.37768 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.6828 | 1.52199 | 0.760997 | − | 0.648756i | \(-0.224710\pi\) | ||||
0.760997 | + | 0.648756i | \(0.224710\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.6438 | 1.27393 | 0.636965 | − | 0.770893i | \(-0.280190\pi\) | ||||
0.636965 | + | 0.770893i | \(0.280190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.9333 | −1.20312 | −0.601560 | − | 0.798828i | \(-0.705454\pi\) | ||||
−0.601560 | + | 0.798828i | \(0.705454\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.91813 | 0.156976 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8745 | 0.594980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.05034 | 0.201370 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.22876 | 0.327582 | 0.163791 | − | 0.986495i | \(-0.447628\pi\) | ||||
0.163791 | + | 0.986495i | \(0.447628\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.788908 | −0.0313069 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.0573 | −0.636215 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5906 | 0.655288 | 0.327644 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327644 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.15587 | −0.203328 | −0.101664 | − | 0.994819i | \(-0.532417\pi\) | ||||
−0.101664 | + | 0.994819i | \(0.532417\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.33981 | 0.170616 | 0.0853079 | − | 0.996355i | \(-0.472813\pi\) | ||||
0.0853079 | + | 0.996355i | \(0.472813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.1660 | −1.14487 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.3547 | −1.14874 | −0.574369 | − | 0.818597i | \(-0.694752\pi\) | ||||
−0.574369 | + | 0.818597i | \(0.694752\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | 0.312586 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.2467 | −1.37302 | −0.686509 | − | 0.727121i | \(-0.740858\pi\) | ||||
−0.686509 | + | 0.727121i | \(0.740858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.91913 | 0.152436 | 0.0762182 | − | 0.997091i | \(-0.475715\pi\) | ||||
0.0762182 | + | 0.997091i | \(0.475715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.14226 | −0.276965 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.5940 | −1.45565 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.33981 | 0.167537 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.8504 | −0.762911 | −0.381456 | − | 0.924387i | \(-0.624577\pi\) | ||||
−0.381456 | + | 0.924387i | \(0.624577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4170 | 0.668403 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.788908 | −0.0301867 | −0.0150934 | − | 0.999886i | \(-0.504805\pi\) | ||||
−0.0150934 | + | 0.999886i | \(0.504805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.66275 | −0.330987 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.1136 | 0.994848 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.15587 | 0.196139 | 0.0980693 | − | 0.995180i | \(-0.468733\pi\) | ||||
0.0980693 | + | 0.995180i | \(0.468733\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.3593 | −0.658474 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43.7490 | −1.65711 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.89206 | 0.222540 | 0.111270 | − | 0.993790i | \(-0.464508\pi\) | ||||
0.111270 | + | 0.993790i | \(0.464508\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.70850 | −0.177584 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.38527 | −0.0520983 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4044 | −0.465857 | −0.232929 | − | 0.972494i | \(-0.574831\pi\) | ||||
−0.232929 | + | 0.972494i | \(0.574831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.5015 | −0.917589 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.9666 | 0.559720 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.3234 | −1.50381 | −0.751904 | − | 0.659272i | \(-0.770865\pi\) | ||||
−0.751904 | + | 0.659272i | \(0.770865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.8745 | −1.03810 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −37.1755 | −1.38066 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.3948 | 1.23854 | 0.619272 | − | 0.785177i | \(-0.287428\pi\) | ||||
0.619272 | + | 0.785177i | \(0.287428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.77053 | 0.102472 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.8838 | 0.660553 | 0.330276 | − | 0.943884i | \(-0.392858\pi\) | ||||
0.330276 | + | 0.943884i | \(0.392858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8823 | 0.990221 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.9627 | −0.476840 | −0.238420 | − | 0.971162i | \(-0.576630\pi\) | ||||
−0.238420 | + | 0.971162i | \(0.576630\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5425 | 0.827002 | 0.413501 | − | 0.910504i | \(-0.364306\pi\) | ||||
0.413501 | + | 0.910504i | \(0.364306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.8745 | −0.508323 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.54107 | −0.202466 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.9373 | 0.472087 | 0.236044 | − | 0.971742i | \(-0.424149\pi\) | ||||
0.236044 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.71541 | 0.317186 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.2230 | 0.371561 | 0.185781 | − | 0.982591i | \(-0.440519\pi\) | ||||
0.185781 | + | 0.982591i | \(0.440519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.91094 | −0.286771 | −0.143386 | − | 0.989667i | \(-0.545799\pi\) | ||||
−0.143386 | + | 0.989667i | \(0.545799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4676 | 0.559965 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.9641 | −0.829187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.2915 | 0.623548 | 0.311774 | − | 0.950156i | \(-0.399077\pi\) | ||||
0.311774 | + | 0.950156i | \(0.399077\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.4418 | −1.09491 | −0.547457 | − | 0.836834i | \(-0.684404\pi\) | ||||
−0.547457 | + | 0.836834i | \(0.684404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.2288 | −0.870323 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.7878 | 1.46137 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 63.8744 | 2.28561 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.91094 | 0.282354 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.80879 | −0.314000 | −0.157000 | − | 0.987599i | \(-0.550182\pi\) | ||||
−0.157000 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.41699 | 0.121341 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.4418 | −1.07830 | −0.539151 | − | 0.842209i | \(-0.681255\pi\) | ||||
−0.539151 | + | 0.842209i | \(0.681255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.3320 | 1.78062 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.6417 | −0.551985 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.01180 | 0.211888 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.4339 | −0.612945 | −0.306473 | − | 0.951880i | \(-0.599149\pi\) | ||||
−0.306473 | + | 0.951880i | \(0.599149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.1264 | −0.776964 | −0.388482 | − | 0.921456i | \(-0.627000\pi\) | ||||
−0.388482 | + | 0.921456i | \(0.627000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.8628 | 0.485593 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.58301 | −0.0903679 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.9424 | −0.381892 | −0.190946 | − | 0.981601i | \(-0.561156\pi\) | ||||
−0.190946 | + | 0.981601i | \(0.561156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.2288 | 1.12342 | 0.561712 | − | 0.827333i | \(-0.310143\pi\) | ||||
0.561712 | + | 0.827333i | \(0.310143\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.13742 | −0.213419 | −0.106710 | − | 0.994290i | \(-0.534032\pi\) | ||||
−0.106710 | + | 0.994290i | \(0.534032\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.7122 | −0.719365 | −0.359683 | − | 0.933075i | \(-0.617115\pi\) | ||||
−0.359683 | + | 0.933075i | \(0.617115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.7328 | 0.822294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.9666 | −0.517942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.9212 | −1.82704 | −0.913521 | − | 0.406793i | \(-0.866647\pi\) | ||||
−0.913521 | + | 0.406793i | \(0.866647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.0405 | 1.58760 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.841723 | 0.0289561 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.0627 | −0.655004 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.96325 | 0.135858 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.8818 | −0.578023 | −0.289011 | − | 0.957326i | \(-0.593327\pi\) | ||||
−0.289011 | + | 0.957326i | \(0.593327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.2917 | 0.351558 | 0.175779 | − | 0.984430i | \(-0.443756\pi\) | ||||
0.175779 | + | 0.984430i | \(0.443756\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.16177 | 0.278476 | 0.139238 | − | 0.990259i | \(-0.455535\pi\) | ||||
0.139238 | + | 0.990259i | \(0.455535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.3428 | −1.81581 | −0.907906 | − | 0.419174i | \(-0.862320\pi\) | ||||
−0.907906 | + | 0.419174i | \(0.862320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.87451 | 0.199739 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.8381 | 1.55495 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.1660 | 0.717183 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.8712 | 0.435126 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.0240 | −1.04760 | −0.523802 | − | 0.851840i | \(-0.675487\pi\) | ||||
−0.523802 | + | 0.851840i | \(0.675487\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.9785 | 0.504639 | 0.252319 | − | 0.967644i | \(-0.418807\pi\) | ||||
0.252319 | + | 0.967644i | \(0.418807\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.0558 | 1.68451 | 0.842255 | − | 0.539079i | \(-0.181228\pi\) | ||||
0.842255 | + | 0.539079i | \(0.181228\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.76150 | 0.159876 | 0.0799378 | − | 0.996800i | \(-0.474528\pi\) | ||||
0.0799378 | + | 0.996800i | \(0.474528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.54249 | 0.0517333 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.9252 | −1.57029 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.83399 | 0.0947298 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.9068 | 1.63113 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.5960 | −1.28582 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.768687 | 0.0255520 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.7735 | 0.756180 | 0.378090 | − | 0.925769i | \(-0.376581\pi\) | ||||
0.378090 | + | 0.925769i | \(0.376581\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.18319 | −0.171727 | −0.0858634 | − | 0.996307i | \(-0.527365\pi\) | ||||
−0.0858634 | + | 0.996307i | \(0.527365\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5830 | 0.747388 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.6417 | −0.516536 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.1033 | −1.38886 | −0.694429 | − | 0.719561i | \(-0.744343\pi\) | ||||
−0.694429 | + | 0.719561i | \(0.744343\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.2921 | 1.65539 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.91913 | 0.128860 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.7328 | −0.778649 | −0.389324 | − | 0.921101i | \(-0.627291\pi\) | ||||
−0.389324 | + | 0.921101i | \(0.627291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.1264 | −0.725165 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.1208 | −0.723426 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.1660 | 1.01815 | 0.509075 | − | 0.860722i | \(-0.329988\pi\) | ||||
0.509075 | + | 0.860722i | \(0.329988\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.5706 | 0.572784 | 0.286392 | − | 0.958113i | \(-0.407544\pi\) | ||||
0.286392 | + | 0.958113i | \(0.407544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.3320 | −1.11800 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.36689 | 0.109409 | 0.0547046 | − | 0.998503i | \(-0.482578\pi\) | ||||
0.0547046 | + | 0.998503i | \(0.482578\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.3157 | −0.399784 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.2702 | 0.818582 | 0.409291 | − | 0.912404i | \(-0.365776\pi\) | ||||
0.409291 | + | 0.912404i | \(0.365776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.66079 | −0.247897 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9376 | 0.546943 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.874508 | 0.0282099 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.99504 | 0.321752 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.3948 | −1.45980 | −0.729899 | − | 0.683555i | \(-0.760433\pi\) | ||||
−0.729899 | + | 0.683555i | \(0.760433\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.3019 | −0.940341 | −0.470171 | − | 0.882576i | \(-0.655808\pi\) | ||||
−0.470171 | + | 0.882576i | \(0.655808\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.9411 | 1.08810 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.5087 | 0.656131 | 0.328066 | − | 0.944655i | \(-0.393603\pi\) | ||||
0.328066 | + | 0.944655i | \(0.393603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.3137 | −0.361588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.8823 | 0.857411 | 0.428706 | − | 0.903444i | \(-0.358970\pi\) | ||||
0.428706 | + | 0.903444i | \(0.358970\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.1255 | −0.322625 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.17417 | 0.0691347 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.06275 | −0.0972913 | −0.0486457 | − | 0.998816i | \(-0.515491\pi\) | ||||
−0.0486457 | + | 0.998816i | \(0.515491\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.4859 | 0.364129 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.6474 | 1.63569 | 0.817846 | − | 0.575438i | \(-0.195168\pi\) | ||||
0.817846 | + | 0.575438i | \(0.195168\pi\) | |||||||
\(998\) | 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 | 9216.2.a.bt.1.6 | 8 | ||
3.2 | odd | 2 | inner | 9216.2.a.bt.1.4 | 8 | ||
4.3 | odd | 2 | 9216.2.a.bq.1.6 | 8 | |||
8.3 | odd | 2 | 9216.2.a.bq.1.3 | 8 | |||
8.5 | even | 2 | inner | 9216.2.a.bt.1.3 | 8 | ||
12.11 | even | 2 | 9216.2.a.bq.1.4 | 8 | |||
24.5 | odd | 2 | inner | 9216.2.a.bt.1.5 | 8 | ||
24.11 | even | 2 | 9216.2.a.bq.1.5 | 8 | |||
32.3 | odd | 8 | 1152.2.k.e.289.2 | 8 | |||
32.5 | even | 8 | 576.2.k.c.433.3 | 8 | |||
32.11 | odd | 8 | 1152.2.k.e.865.2 | 8 | |||
32.13 | even | 8 | 576.2.k.c.145.3 | 8 | |||
32.19 | odd | 8 | 144.2.k.c.109.1 | yes | 8 | ||
32.21 | even | 8 | 1152.2.k.d.865.2 | 8 | |||
32.27 | odd | 8 | 144.2.k.c.37.1 | ✓ | 8 | ||
32.29 | even | 8 | 1152.2.k.d.289.2 | 8 | |||
96.5 | odd | 8 | 576.2.k.c.433.2 | 8 | |||
96.11 | even | 8 | 1152.2.k.e.865.3 | 8 | |||
96.29 | odd | 8 | 1152.2.k.d.289.3 | 8 | |||
96.35 | even | 8 | 1152.2.k.e.289.3 | 8 | |||
96.53 | odd | 8 | 1152.2.k.d.865.3 | 8 | |||
96.59 | even | 8 | 144.2.k.c.37.4 | yes | 8 | ||
96.77 | odd | 8 | 576.2.k.c.145.2 | 8 | |||
96.83 | even | 8 | 144.2.k.c.109.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.k.c.37.1 | ✓ | 8 | 32.27 | odd | 8 | ||
144.2.k.c.37.4 | yes | 8 | 96.59 | even | 8 | ||
144.2.k.c.109.1 | yes | 8 | 32.19 | odd | 8 | ||
144.2.k.c.109.4 | yes | 8 | 96.83 | even | 8 | ||
576.2.k.c.145.2 | 8 | 96.77 | odd | 8 | |||
576.2.k.c.145.3 | 8 | 32.13 | even | 8 | |||
576.2.k.c.433.2 | 8 | 96.5 | odd | 8 | |||
576.2.k.c.433.3 | 8 | 32.5 | even | 8 | |||
1152.2.k.d.289.2 | 8 | 32.29 | even | 8 | |||
1152.2.k.d.289.3 | 8 | 96.29 | odd | 8 | |||
1152.2.k.d.865.2 | 8 | 32.21 | even | 8 | |||
1152.2.k.d.865.3 | 8 | 96.53 | odd | 8 | |||
1152.2.k.e.289.2 | 8 | 32.3 | odd | 8 | |||
1152.2.k.e.289.3 | 8 | 96.35 | even | 8 | |||
1152.2.k.e.865.2 | 8 | 32.11 | odd | 8 | |||
1152.2.k.e.865.3 | 8 | 96.11 | even | 8 | |||
9216.2.a.bq.1.3 | 8 | 8.3 | odd | 2 | |||
9216.2.a.bq.1.4 | 8 | 12.11 | even | 2 | |||
9216.2.a.bq.1.5 | 8 | 24.11 | even | 2 | |||
9216.2.a.bq.1.6 | 8 | 4.3 | odd | 2 | |||
9216.2.a.bt.1.3 | 8 | 8.5 | even | 2 | inner | ||
9216.2.a.bt.1.4 | 8 | 3.2 | odd | 2 | inner | ||
9216.2.a.bt.1.5 | 8 | 24.5 | odd | 2 | inner | ||
9216.2.a.bt.1.6 | 8 | 1.1 | even | 1 | trivial |