Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
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([0, 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("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-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 | ||||||||
\(5\) | −1.56155 | −0.698348 | −0.349174 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349174 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.12311 | 0.941652 | 0.470826 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470826 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.56155 | −1.81985 | −0.909924 | − | 0.414776i | \(-0.863860\pi\) | ||||
−0.909924 | + | 0.414776i | \(0.863860\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.12311 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.12311 | 1.17532 | 0.587661 | − | 0.809108i | \(-0.300049\pi\) | ||||
0.587661 | + | 0.809108i | \(0.300049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.68466 | 0.768304 | 0.384152 | − | 0.923270i | \(-0.374494\pi\) | ||||
0.384152 | + | 0.923270i | \(0.374494\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56155 | −0.512311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.43845 | 1.00989 | 0.504947 | − | 0.863150i | \(-0.331512\pi\) | ||||
0.504947 | + | 0.863150i | \(0.331512\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.56155 | 0.460068 | 0.230034 | − | 0.973183i | \(-0.426116\pi\) | ||||
0.230034 | + | 0.973183i | \(0.426116\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.56155 | −0.263951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.56155 | 0.585516 | 0.292758 | − | 0.956187i | \(-0.405427\pi\) | ||||
0.292758 | + | 0.956187i | \(0.405427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.5616 | −1.80561 | −0.902806 | − | 0.430049i | \(-0.858496\pi\) | ||||
−0.902806 | + | 0.430049i | \(0.858496\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.24621 | −1.41003 | −0.705017 | − | 0.709190i | \(-0.749061\pi\) | ||||
−0.705017 | + | 0.709190i | \(0.749061\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.56155 | 0.519506 | 0.259753 | − | 0.965675i | \(-0.416359\pi\) | ||||
0.259753 | + | 0.965675i | \(0.416359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.68466 | 0.780848 | 0.390424 | − | 0.920635i | \(-0.372328\pi\) | ||||
0.390424 | + | 0.920635i | \(0.372328\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.87689 | −0.657600 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.123106 | −0.0160270 | −0.00801349 | − | 0.999968i | \(-0.502551\pi\) | ||||
−0.00801349 | + | 0.999968i | \(0.502551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.24621 | 1.05582 | 0.527910 | − | 0.849301i | \(-0.322976\pi\) | ||||
0.527910 | + | 0.849301i | \(0.322976\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.2462 | 1.27089 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.6847 | −1.91619 | −0.958093 | − | 0.286457i | \(-0.907522\pi\) | ||||
−0.958093 | + | 0.286457i | \(0.907522\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.56155 | 0.304000 | 0.152000 | − | 0.988380i | \(-0.451429\pi\) | ||||
0.152000 | + | 0.988380i | \(0.451429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.12311 | 0.131450 | 0.0657248 | − | 0.997838i | \(-0.479064\pi\) | ||||
0.0657248 | + | 0.997838i | \(0.479064\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.12311 | 0.355911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.43845 | −0.499364 | −0.249682 | − | 0.968328i | \(-0.580326\pi\) | ||||
−0.249682 | + | 0.968328i | \(0.580326\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.56155 | 0.171403 | 0.0857013 | − | 0.996321i | \(-0.472687\pi\) | ||||
0.0857013 | + | 0.996321i | \(0.472687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.43845 | 0.698348 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.6847 | −1.45057 | −0.725285 | − | 0.688448i | \(-0.758292\pi\) | ||||
−0.725285 | + | 0.688448i | \(0.758292\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.56155 | −0.687838 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.2462 | −1.85262 | −0.926311 | − | 0.376760i | \(-0.877038\pi\) | ||||
−0.926311 | + | 0.376760i | \(0.877038\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.5616 | −1.04066 | −0.520330 | − | 0.853965i | \(-0.674191\pi\) | ||||
−0.520330 | + | 0.853965i | \(0.674191\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4924 | 1.59438 | 0.797191 | − | 0.603727i | \(-0.206318\pi\) | ||||
0.797191 | + | 0.603727i | \(0.206318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.80776 | 0.364718 | 0.182359 | − | 0.983232i | \(-0.441627\pi\) | ||||
0.182359 | + | 0.983232i | \(0.441627\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.12311 | 0.293797 | 0.146899 | − | 0.989152i | \(-0.453071\pi\) | ||||
0.146899 | + | 0.989152i | \(0.453071\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.75379 | −0.536544 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.12311 | −0.377964 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.24621 | −0.113292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8078 | 1.05612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4384 | −1.28121 | −0.640603 | − | 0.767873i | \(-0.721315\pi\) | ||||
−0.640603 | + | 0.767873i | \(0.721315\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.6847 | −1.37037 | −0.685187 | − | 0.728367i | \(-0.740280\pi\) | ||||
−0.685187 | + | 0.728367i | \(0.740280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.12311 | 0.444230 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.12311 | 0.0959534 | 0.0479767 | − | 0.998848i | \(-0.484723\pi\) | ||||
0.0479767 | + | 0.998848i | \(0.484723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.4924 | −1.22923 | −0.614616 | − | 0.788827i | \(-0.710689\pi\) | ||||
−0.614616 | + | 0.788827i | \(0.710689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.4924 | −1.71366 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.49242 | −0.705257 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.9309 | −1.30511 | −0.652554 | − | 0.757742i | \(-0.726302\pi\) | ||||
−0.652554 | + | 0.757742i | \(0.726302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.56155 | −0.289835 | −0.144918 | − | 0.989444i | \(-0.546292\pi\) | ||||
−0.144918 | + | 0.989444i | \(0.546292\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.93087 | −0.792570 | −0.396285 | − | 0.918128i | \(-0.629701\pi\) | ||||
−0.396285 | + | 0.918128i | \(0.629701\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.68466 | 0.290392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3693 | 0.812188 | 0.406094 | − | 0.913831i | \(-0.366891\pi\) | ||||
0.406094 | + | 0.913831i | \(0.366891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.6847 | 0.981568 | 0.490784 | − | 0.871281i | \(-0.336710\pi\) | ||||
0.490784 | + | 0.871281i | \(0.336710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.0540 | 2.31184 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.36932 | −0.408222 | −0.204111 | − | 0.978948i | \(-0.565430\pi\) | ||||
−0.204111 | + | 0.978948i | \(0.565430\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.56155 | −0.193635 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.1231 | 1.72830 | 0.864151 | − | 0.503233i | \(-0.167856\pi\) | ||||
0.864151 | + | 0.503233i | \(0.167856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4384 | −1.14753 | −0.573765 | − | 0.819020i | \(-0.694518\pi\) | ||||
−0.573765 | + | 0.819020i | \(0.694518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.56155 | −0.408893 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.8769 | −0.941652 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.876894 | −0.0634499 | −0.0317249 | − | 0.999497i | \(-0.510100\pi\) | ||||
−0.0317249 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.6155 | −1.33998 | −0.669988 | − | 0.742372i | \(-0.733701\pi\) | ||||
−0.669988 | + | 0.742372i | \(0.733701\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.87689 | −0.489958 | −0.244979 | − | 0.969528i | \(-0.578781\pi\) | ||||
−0.244979 | + | 0.969528i | \(0.578781\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.68466 | −0.402975 | −0.201487 | − | 0.979491i | \(-0.564578\pi\) | ||||
−0.201487 | + | 0.979491i | \(0.564578\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.43845 | 0.381704 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.0540 | 1.26094 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0540 | 0.760987 | 0.380494 | − | 0.924784i | \(-0.375754\pi\) | ||||
0.380494 | + | 0.924784i | \(0.375754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.4384 | 0.984694 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.56155 | 0.173890 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.0540 | 1.81985 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.24621 | 0.418277 | 0.209139 | − | 0.977886i | \(-0.432934\pi\) | ||||
0.209139 | + | 0.977886i | \(0.432934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.19224 | 0.211876 | 0.105938 | − | 0.994373i | \(-0.466215\pi\) | ||||
0.105938 | + | 0.994373i | \(0.466215\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.49242 | 0.429031 | 0.214516 | − | 0.976721i | \(-0.431183\pi\) | ||||
0.214516 | + | 0.976721i | \(0.431183\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.2462 | −1.45740 | −0.728699 | − | 0.684834i | \(-0.759875\pi\) | ||||
−0.728699 | + | 0.684834i | \(0.759875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.56155 | −0.362796 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.1231 | 0.978232 | 0.489116 | − | 0.872219i | \(-0.337319\pi\) | ||||
0.489116 | + | 0.872219i | \(0.337319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.12311 | 0.587671 | 0.293835 | − | 0.955856i | \(-0.405068\pi\) | ||||
0.293835 | + | 0.955856i | \(0.405068\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.56155 | −0.0997639 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33.6155 | −2.13890 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.6847 | −1.55808 | −0.779041 | − | 0.626973i | \(-0.784294\pi\) | ||||
−0.779041 | + | 0.626973i | \(0.784294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5076 | 0.723475 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.00000 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.56155 | 0.221304 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −32.1771 | −1.98412 | −0.992062 | − | 0.125750i | \(-0.959866\pi\) | ||||
−0.992062 | + | 0.125750i | \(0.959866\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.87689 | −0.545303 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −32.3002 | −1.96938 | −0.984689 | − | 0.174323i | \(-0.944226\pi\) | ||||
−0.984689 | + | 0.174323i | \(0.944226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.0540 | −1.03596 | −0.517978 | − | 0.855394i | \(-0.673315\pi\) | ||||
−0.517978 | + | 0.855394i | \(0.673315\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.00000 | −0.482418 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.56155 | −0.0938246 | −0.0469123 | − | 0.998899i | \(-0.514938\pi\) | ||||
−0.0469123 | + | 0.998899i | \(0.514938\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.63068 | −0.276243 | −0.138122 | − | 0.990415i | \(-0.544107\pi\) | ||||
−0.138122 | + | 0.990415i | \(0.544107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.6155 | 1.16602 | 0.583011 | − | 0.812464i | \(-0.301874\pi\) | ||||
0.583011 | + | 0.812464i | \(0.301874\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.5616 | −0.682457 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.4384 | 1.19403 | 0.597013 | − | 0.802231i | \(-0.296354\pi\) | ||||
0.597013 | + | 0.802231i | \(0.296354\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.192236 | 0.0111924 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.1771 | −1.39820 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.24621 | −0.532943 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.8769 | −0.737329 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.1231 | −1.20556 | −0.602780 | − | 0.797908i | \(-0.705940\pi\) | ||||
−0.602780 | + | 0.797908i | \(0.705940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.31534 | −0.187996 | −0.0939979 | − | 0.995572i | \(-0.529965\pi\) | ||||
−0.0939979 | + | 0.995572i | \(0.529965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.75379 | −0.438270 | −0.219135 | − | 0.975695i | \(-0.570324\pi\) | ||||
−0.219135 | + | 0.975695i | \(0.570324\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.8769 | 1.28489 | 0.642447 | − | 0.766330i | \(-0.277919\pi\) | ||||
0.642447 | + | 0.766330i | \(0.277919\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.9848 | 0.950969 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.1231 | −1.17532 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.8078 | 0.932327 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.56155 | 0.196355 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.8769 | −0.762743 | −0.381372 | − | 0.924422i | \(-0.624548\pi\) | ||||
−0.381372 | + | 0.924422i | \(0.624548\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.4924 | 1.33816 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.2462 | 0.939461 | 0.469730 | − | 0.882810i | \(-0.344351\pi\) | ||||
0.469730 | + | 0.882810i | \(0.344351\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.8617 | −1.49570 | −0.747848 | − | 0.663870i | \(-0.768913\pi\) | ||||
−0.747848 | + | 0.663870i | \(0.768913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1771 | −0.865939 | −0.432970 | − | 0.901409i | \(-0.642534\pi\) | ||||
−0.432970 | + | 0.901409i | \(0.642534\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.9848 | −1.70238 | −0.851191 | − | 0.524856i | \(-0.824119\pi\) | ||||
−0.851191 | + | 0.524856i | \(0.824119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | −0.212298 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.19224 | 0.274036 | 0.137018 | − | 0.990569i | \(-0.456248\pi\) | ||||
0.137018 | + | 0.990569i | \(0.456248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.75379 | −0.0917975 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −37.0540 | −1.93420 | −0.967101 | − | 0.254393i | \(-0.918124\pi\) | ||||
−0.967101 | + | 0.254393i | \(0.918124\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.68466 | 0.295133 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.8078 | −0.922051 | −0.461026 | − | 0.887387i | \(-0.652518\pi\) | ||||
−0.461026 | + | 0.887387i | \(0.652518\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −35.6847 | −1.83785 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.6847 | −0.857033 | −0.428517 | − | 0.903534i | \(-0.640964\pi\) | ||||
−0.428517 | + | 0.903534i | \(0.640964\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0540 | −0.922515 | −0.461258 | − | 0.887266i | \(-0.652602\pi\) | ||||
−0.461258 | + | 0.887266i | \(0.652602\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.87689 | −0.248550 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.7538 | 0.798749 | 0.399374 | − | 0.916788i | \(-0.369227\pi\) | ||||
0.399374 | + | 0.916788i | \(0.369227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.1922 | −0.768304 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.93087 | 0.348730 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.6155 | −1.68711 | −0.843557 | − | 0.537039i | \(-0.819543\pi\) | ||||
−0.843557 | + | 0.537039i | \(0.819543\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.4924 | −0.923468 | −0.461734 | − | 0.887019i | \(-0.652772\pi\) | ||||
−0.461734 | + | 0.887019i | \(0.652772\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.8078 | −0.837254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.1231 | 0.551352 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3693 | 0.957751 | 0.478876 | − | 0.877883i | \(-0.341045\pi\) | ||||
0.478876 | + | 0.877883i | \(0.341045\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.123106 | −0.00605763 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.43845 | −0.119699 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.2462 | 1.03795 | 0.518973 | − | 0.854791i | \(-0.326315\pi\) | ||||
0.518973 | + | 0.854791i | \(0.326315\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.5616 | 0.512311 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.24621 | 0.399062 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1080 | 1.73524 | 0.867619 | − | 0.497230i | \(-0.165650\pi\) | ||||
0.867619 | + | 0.497230i | \(0.165650\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.8769 | 0.903004 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.0540 | 1.00485 | 0.502426 | − | 0.864620i | \(-0.332441\pi\) | ||||
0.502426 | + | 0.864620i | \(0.332441\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.12311 | 0.433452 | 0.216726 | − | 0.976232i | \(-0.430462\pi\) | ||||
0.216726 | + | 0.976232i | \(0.430462\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.3693 | 1.01300 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.492423 | 0.0232389 | 0.0116194 | − | 0.999932i | \(-0.496301\pi\) | ||||
0.0116194 | + | 0.999932i | \(0.496301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.1080 | −1.70026 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.2462 | 0.480350 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.19224 | −0.429995 | −0.214997 | − | 0.976615i | \(-0.568974\pi\) | ||||
−0.214997 | + | 0.976615i | \(0.568974\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.4233 | 1.37038 | 0.685190 | − | 0.728365i | \(-0.259719\pi\) | ||||
0.685190 | + | 0.728365i | \(0.259719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.5616 | −0.723207 | −0.361603 | − | 0.932332i | \(-0.617771\pi\) | ||||
−0.361603 | + | 0.932332i | \(0.617771\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.2462 | 0.659236 | 0.329618 | − | 0.944114i | \(-0.393080\pi\) | ||||
0.329618 | + | 0.944114i | \(0.393080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.6847 | −0.724250 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.8769 | −1.32776 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.1231 | −0.602129 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.0540 | 0.824907 | 0.412454 | − | 0.910979i | \(-0.364672\pi\) | ||||
0.412454 | + | 0.910979i | \(0.364672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.3693 | −1.06555 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.4924 | 1.29377 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.3693 | −1.42148 | −0.710740 | − | 0.703455i | \(-0.751640\pi\) | ||||
−0.710740 | + | 0.703455i | \(0.751640\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.2462 | 0.823440 | 0.411720 | − | 0.911310i | \(-0.364928\pi\) | ||||
0.411720 | + | 0.911310i | \(0.364928\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.4233 | −1.00989 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.56155 | 0.114901 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.93087 | −0.131204 | −0.0656019 | − | 0.997846i | \(-0.520897\pi\) | ||||
−0.0656019 | + | 0.997846i | \(0.520897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.8078 | −1.23989 | −0.619943 | − | 0.784646i | \(-0.712844\pi\) | ||||
−0.619943 | + | 0.784646i | \(0.712844\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6155 | −0.694882 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.0540 | 0.888877 | 0.444438 | − | 0.895809i | \(-0.353403\pi\) | ||||
0.444438 | + | 0.895809i | \(0.353403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.12311 | 0.0496833 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.4924 | 0.726743 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.1231 | 0.489194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.6307 | −0.684793 | −0.342396 | − | 0.939556i | \(-0.611239\pi\) | ||||
−0.342396 | + | 0.939556i | \(0.611239\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.3693 | −1.28423 | −0.642115 | − | 0.766608i | \(-0.721943\pi\) | ||||
−0.642115 | + | 0.766608i | \(0.721943\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.5616 | −0.460068 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.42329 | −0.409708 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 75.8617 | 3.28594 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.7538 | −1.11343 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.12311 | 0.134522 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.8078 | −1.36752 | −0.683761 | − | 0.729706i | \(-0.739657\pi\) | ||||
−0.683761 | + | 0.729706i | \(0.739657\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.94602 | −0.254700 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.3153 | −0.825864 | −0.412932 | − | 0.910762i | \(-0.635495\pi\) | ||||
−0.412932 | + | 0.910762i | \(0.635495\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.8617 | 1.18695 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.43845 | −0.188742 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.8078 | −1.39011 | −0.695055 | − | 0.718957i | \(-0.744620\pi\) | ||||
−0.695055 | + | 0.718957i | \(0.744620\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 60.6695 | 2.56605 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.9309 | 0.755696 | 0.377848 | − | 0.925868i | \(-0.376664\pi\) | ||||
0.377848 | + | 0.925868i | \(0.376664\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.87689 | −0.205172 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.24621 | −0.261855 | −0.130927 | − | 0.991392i | \(-0.541795\pi\) | ||||
−0.130927 | + | 0.991392i | \(0.541795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.8769 | 1.16661 | 0.583306 | − | 0.812253i | \(-0.301759\pi\) | ||||
0.583306 | + | 0.812253i | \(0.301759\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.43845 | −0.393610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.00000 | 0.249783 | 0.124892 | − | 0.992170i | \(-0.460142\pi\) | ||||
0.124892 | + | 0.992170i | \(0.460142\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.56155 | 0.0647841 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.7538 | 0.735287 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.3153 | −0.673406 | −0.336703 | − | 0.941611i | \(-0.609312\pi\) | ||||
−0.336703 | + | 0.941611i | \(0.609312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.1231 | 0.540728 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.94602 | −0.162044 | −0.0810219 | − | 0.996712i | \(-0.525818\pi\) | ||||
−0.0810219 | + | 0.996712i | \(0.525818\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.43845 | 0.263951 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.06913 | −0.329696 | −0.164848 | − | 0.986319i | \(-0.552713\pi\) | ||||
−0.164848 | + | 0.986319i | \(0.552713\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.4924 | −0.672740 | −0.336370 | − | 0.941730i | \(-0.609199\pi\) | ||||
−0.336370 | + | 0.941730i | \(0.609199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.94602 | 0.0791172 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.56155 | −0.347503 | −0.173751 | − | 0.984790i | \(-0.555589\pi\) | ||||
−0.173751 | + | 0.984790i | \(0.555589\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.3693 | −0.945421 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.7386 | 1.64542 | 0.822709 | − | 0.568463i | \(-0.192462\pi\) | ||||
0.822709 | + | 0.568463i | \(0.192462\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.12311 | 0.0452145 | 0.0226073 | − | 0.999744i | \(-0.492803\pi\) | ||||
0.0226073 | + | 0.999744i | \(0.492803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.61553 | −0.386481 | −0.193240 | − | 0.981151i | \(-0.561900\pi\) | ||||
−0.193240 | + | 0.981151i | \(0.561900\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.6847 | −0.548264 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.63068 | −0.225227 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.6847 | −0.585516 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.8078 | 1.90320 | 0.951599 | − | 0.307344i | \(-0.0994402\pi\) | ||||
0.951599 | + | 0.307344i | \(0.0994402\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.5464 | 0.894727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.56155 | −0.259978 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.3693 | 1.63399 | 0.816995 | − | 0.576645i | \(-0.195638\pi\) | ||||
0.816995 | + | 0.576645i | \(0.195638\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.6307 | 0.419233 | 0.209617 | − | 0.977784i | \(-0.432778\pi\) | ||||
0.209617 | + | 0.977784i | \(0.432778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.1231 | −0.830435 | −0.415217 | − | 0.909722i | \(-0.636295\pi\) | ||||
−0.415217 | + | 0.909722i | \(0.636295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.384472 | −0.0150918 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.0540 | −1.29350 | −0.646751 | − | 0.762701i | \(-0.723873\pi\) | ||||
−0.646751 | + | 0.762701i | \(0.723873\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.4924 | 0.956998 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.1231 | −1.21238 | −0.606192 | − | 0.795318i | \(-0.707304\pi\) | ||||
−0.606192 | + | 0.795318i | \(0.707304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.4924 | 1.18602 | 0.593009 | − | 0.805196i | \(-0.297940\pi\) | ||||
0.593009 | + | 0.805196i | \(0.297940\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0388 | 0.775906 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.7538 | 0.994214 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.8078 | 1.95850 | 0.979248 | − | 0.202667i | \(-0.0649609\pi\) | ||||
0.979248 | + | 0.202667i | \(0.0649609\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.1231 | 1.50362 | 0.751812 | − | 0.659378i | \(-0.229180\pi\) | ||||
0.751812 | + | 0.659378i | \(0.229180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.2462 | −0.700225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.4924 | 1.09023 | 0.545116 | − | 0.838361i | \(-0.316486\pi\) | ||||
0.545116 | + | 0.838361i | \(0.316486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.75379 | −0.0670088 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.3002 | −1.42102 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.6155 | 1.35488 | 0.677439 | − | 0.735579i | \(-0.263090\pi\) | ||||
0.677439 | + | 0.735579i | \(0.263090\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.6307 | 0.858431 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.6695 | 1.80561 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0000 | 0.377695 | 0.188847 | − | 0.982006i | \(-0.439525\pi\) | ||||
0.188847 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.2462 | 0.688169 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0000 | 0.376089 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.9309 | −0.710964 | −0.355482 | − | 0.934683i | \(-0.615683\pi\) | ||||
−0.355482 | + | 0.934683i | \(0.615683\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.43845 | 0.353473 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0000 | 1.19673 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.17708 | 0.0438977 | 0.0219489 | − | 0.999759i | \(-0.493013\pi\) | ||||
0.0219489 | + | 0.999759i | \(0.493013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5616 | −0.393333 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.9309 | −0.517380 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5616 | 0.540058 | 0.270029 | − | 0.962852i | \(-0.412967\pi\) | ||||
0.270029 | + | 0.962852i | \(0.412967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.1231 | 1.41003 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.8078 | −1.13791 | −0.568955 | − | 0.822368i | \(-0.692652\pi\) | ||||
−0.568955 | + | 0.822368i | \(0.692652\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.9848 | −1.80438 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000 | 0.147142 | 0.0735712 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735712 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.4384 | 0.933246 | 0.466623 | − | 0.884456i | \(-0.345470\pi\) | ||||
0.466623 | + | 0.884456i | \(0.345470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.8769 | 0.911419 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.4924 | 0.602620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.1080 | −0.806731 | −0.403365 | − | 0.915039i | \(-0.632160\pi\) | ||||
−0.403365 | + | 0.915039i | \(0.632160\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.56155 | 0.202406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.8078 | 1.59222 | 0.796110 | − | 0.605152i | \(-0.206888\pi\) | ||||
0.796110 | + | 0.605152i | \(0.206888\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.1231 | −1.38196 | −0.690981 | − | 0.722873i | \(-0.742821\pi\) | ||||
−0.690981 | + | 0.722873i | \(0.742821\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.80776 | 0.137850 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.807764 | 0.0291667 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.8617 | 0.644111 | 0.322055 | − | 0.946721i | \(-0.395626\pi\) | ||||
0.322055 | + | 0.946721i | \(0.395626\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5616 | 0.487775 | 0.243888 | − | 0.969804i | \(-0.421577\pi\) | ||||
0.243888 | + | 0.969804i | \(0.421577\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.56155 | −0.235698 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −59.2311 | −2.12217 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.5076 | 0.553489 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.63068 | 0.165066 | 0.0825330 | − | 0.996588i | \(-0.473699\pi\) | ||||
0.0825330 | + | 0.996588i | \(0.473699\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.12311 | 0.111045 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −54.1080 | −1.92143 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.9848 | −1.52260 | −0.761301 | − | 0.648399i | \(-0.775439\pi\) | ||||
−0.761301 | + | 0.648399i | \(0.775439\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.6847 | −0.519506 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.50758 | 0.123780 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.75379 | −0.202794 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.36932 | −0.188775 | −0.0943876 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943876 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.50758 | 0.0529382 | 0.0264691 | − | 0.999650i | \(-0.491574\pi\) | ||||
0.0264691 | + | 0.999650i | \(0.491574\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.1922 | −0.567189 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.3693 | −1.65724 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0691 | 0.351415 | 0.175708 | − | 0.984442i | \(-0.443779\pi\) | ||||
0.175708 | + | 0.984442i | \(0.443779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.438447 | 0.0152833 | 0.00764165 | − | 0.999971i | \(-0.497568\pi\) | ||||
0.00764165 | + | 0.999971i | \(0.497568\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.50758 | 0.0524236 | 0.0262118 | − | 0.999656i | \(-0.491656\pi\) | ||||
0.0262118 | + | 0.999656i | \(0.491656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.8769 | 1.21132 | 0.605662 | − | 0.795722i | \(-0.292908\pi\) | ||||
0.605662 | + | 0.795722i | \(0.292908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.12311 | −0.142857 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.8078 | −0.685476 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.9157 | −1.72328 | −0.861641 | − | 0.507518i | \(-0.830563\pi\) | ||||
−0.861641 | + | 0.507518i | \(0.830563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.576708 | 0.0198865 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −46.9309 | −1.61447 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.24621 | −0.0428203 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.1231 | 0.449854 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.05398 | −0.0360874 | −0.0180437 | − | 0.999837i | \(-0.505744\pi\) | ||||
−0.0180437 | + | 0.999837i | \(0.505744\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.8769 | 1.15721 | 0.578606 | − | 0.815607i | \(-0.303597\pi\) | ||||
0.578606 | + | 0.815607i | \(0.303597\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.4924 | 1.58630 | 0.793150 | − | 0.609026i | \(-0.208439\pi\) | ||||
0.793150 | + | 0.609026i | \(0.208439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.19224 | 0.312907 | 0.156454 | − | 0.987685i | \(-0.449994\pi\) | ||||
0.156454 | + | 0.987685i | \(0.449994\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.38447 | 0.285081 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.8617 | −0.470227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 102.916 | 3.48717 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.8078 | 0.399175 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.3153 | −0.652233 | −0.326116 | − | 0.945330i | \(-0.605740\pi\) | ||||
−0.326116 | + | 0.945330i | \(0.605740\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.4233 | 0.957605 | 0.478803 | − | 0.877923i | \(-0.341071\pi\) | ||||
0.478803 | + | 0.877923i | \(0.341071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.2311 | 1.15197 | 0.575983 | − | 0.817461i | \(-0.304619\pi\) | ||||
0.575983 | + | 0.817461i | \(0.304619\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.5616 | −0.858273 | −0.429136 | − | 0.903240i | \(-0.641182\pi\) | ||||
−0.429136 | + | 0.903240i | \(0.641182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.4384 | −0.484250 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.2462 | 0.610586 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.1080 | −1.20696 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.9309 | 0.464621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.4384 | −0.780848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.1080 | 0.801375 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.4384 | −0.745056 | −0.372528 | − | 0.928021i | \(-0.621509\pi\) | ||||
−0.372528 | + | 0.928021i | \(0.621509\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.3693 | −0.840523 | −0.420261 | − | 0.907403i | \(-0.638062\pi\) | ||||
−0.420261 | + | 0.907403i | \(0.638062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.87689 | 0.161402 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.6847 | −0.517953 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.1771 | 0.500646 | 0.250323 | − | 0.968162i | \(-0.419463\pi\) | ||||
0.250323 | + | 0.968162i | \(0.419463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.8078 | −0.553234 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.12311 | −0.299966 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.438447 | 0.0143850 | 0.00719249 | − | 0.999974i | \(-0.497711\pi\) | ||||
0.00719249 | + | 0.999974i | \(0.497711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.12311 | 0.167903 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.1080 | 0.657600 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.2462 | 0.857426 | 0.428713 | − | 0.903441i | \(-0.358967\pi\) | ||||
0.428713 | + | 0.903441i | \(0.358967\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.1922 | −0.332257 | −0.166129 | − | 0.986104i | \(-0.553127\pi\) | ||||
−0.166129 | + | 0.986104i | \(0.553127\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42.6004 | −1.38726 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.3693 | −1.27933 | −0.639665 | − | 0.768653i | \(-0.720927\pi\) | ||||
−0.639665 | + | 0.768653i | \(0.720927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.36932 | −0.239218 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.4924 | −1.82997 | −0.914985 | − | 0.403489i | \(-0.867797\pi\) | ||||
−0.914985 | + | 0.403489i | \(0.867797\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.36932 | 0.0443101 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.12311 | 0.0362670 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.4384 | −0.788337 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.0691 | 0.935768 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.9848 | −1.83251 | −0.916255 | − | 0.400597i | \(-0.868803\pi\) | ||||
−0.916255 | + | 0.400597i | \(0.868803\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.8769 | 0.702063 | 0.351031 | − | 0.936364i | \(-0.385831\pi\) | ||||
0.351031 | + | 0.936364i | \(0.385831\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.4924 | −0.464606 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.0000 | 0.703842 | 0.351921 | − | 0.936030i | \(-0.385529\pi\) | ||||
0.351921 | + | 0.936030i | \(0.385529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.7386 | −1.36593 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.80776 | −0.249029 | −0.124514 | − | 0.992218i | \(-0.539737\pi\) | ||||
−0.124514 | + | 0.992218i | \(0.539737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.7386 | 0.342161 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.0691 | −1.08334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.42329 | −0.172277 | −0.0861383 | − | 0.996283i | \(-0.527453\pi\) | ||||
−0.0861383 | + | 0.996283i | \(0.527453\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.87689 | 0.281416 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.6695 | 1.03465 | 0.517327 | − | 0.855788i | \(-0.326927\pi\) | ||||
0.517327 | + | 0.855788i | \(0.326927\pi\) | |||||||
\(998\) | 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.a.bf.1.1 | yes | 2 | |
3.2 | odd | 2 | 6048.2.a.bd.1.2 | yes | 2 | ||
4.3 | odd | 2 | 6048.2.a.be.1.1 | yes | 2 | ||
12.11 | even | 2 | 6048.2.a.bc.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bc.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
6048.2.a.bd.1.2 | yes | 2 | 3.2 | odd | 2 | ||
6048.2.a.be.1.1 | yes | 2 | 4.3 | odd | 2 | ||
6048.2.a.bf.1.1 | yes | 2 | 1.1 | even | 1 | trivial |