Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.34292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 1.14637 | 0.661854 | 0.330927 | − | 0.943656i | \(-0.392639\pi\) | ||||
0.330927 | + | 0.943656i | \(0.392639\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.34292 | 1.49500 | 0.747500 | − | 0.664261i | \(-0.231254\pi\) | ||||
0.747500 | + | 0.664261i | \(0.231254\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.34292 | −1.26351 | −0.631753 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631753 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.68585 | −0.561949 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.489289 | 0.147526 | 0.0737630 | − | 0.997276i | \(-0.476499\pi\) | ||||
0.0737630 | + | 0.997276i | \(0.476499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.29273 | −0.635889 | −0.317945 | − | 0.948109i | \(-0.602993\pi\) | ||||
−0.317945 | + | 0.948109i | \(0.602993\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.83221 | 0.989473 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.196558 | 0.0476722 | 0.0238361 | − | 0.999716i | \(-0.492412\pi\) | ||||
0.0238361 | + | 0.999716i | \(0.492412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.83221 | −0.836257 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.17513 | 1.23503 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.37169 | −1.03378 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.12494 | −1.13737 | −0.568687 | − | 0.822554i | \(-0.692548\pi\) | ||||
−0.568687 | + | 0.822554i | \(0.692548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.22533 | 1.47731 | 0.738656 | − | 0.674082i | \(-0.235461\pi\) | ||||
0.738656 | + | 0.674082i | \(0.235461\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.560904 | 0.0976408 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.1751 | −1.88894 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.83221 | −0.630012 | −0.315006 | − | 0.949090i | \(-0.602006\pi\) | ||||
−0.315006 | + | 0.949090i | \(0.602006\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.62831 | −0.420866 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.12494 | 0.644208 | 0.322104 | − | 0.946704i | \(-0.395610\pi\) | ||||
0.322104 | + | 0.946704i | \(0.395610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.17513 | −1.09420 | −0.547099 | − | 0.837068i | \(-0.684268\pi\) | ||||
−0.547099 | + | 0.837068i | \(0.684268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.63565 | −0.840114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.0073 | −1.60559 | −0.802793 | − | 0.596258i | \(-0.796654\pi\) | ||||
−0.802793 | + | 0.596258i | \(0.796654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.17513 | 0.596448 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.225327 | 0.0315521 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.81079 | 0.660813 | 0.330406 | − | 0.943839i | \(-0.392814\pi\) | ||||
0.330406 | + | 0.943839i | \(0.392814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.63565 | 0.220552 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.14637 | −0.151840 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.31415 | 0.691844 | 0.345922 | − | 0.938263i | \(-0.387566\pi\) | ||||
0.345922 | + | 0.938263i | \(0.387566\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.73604 | 0.990498 | 0.495249 | − | 0.868751i | \(-0.335077\pi\) | ||||
0.495249 | + | 0.868751i | \(0.335077\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.63565 | 0.710026 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.66442 | −0.950655 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.4966 | −1.89322 | −0.946608 | − | 0.322388i | \(-0.895514\pi\) | ||||
−0.946608 | + | 0.322388i | \(0.895514\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.58546 | −0.552025 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.2713 | −1.33766 | −0.668829 | − | 0.743416i | \(-0.733204\pi\) | ||||
−0.668829 | + | 0.743416i | \(0.733204\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.4679 | 1.81038 | 0.905188 | − | 0.425011i | \(-0.139730\pi\) | ||||
0.905188 | + | 0.425011i | \(0.139730\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.07896 | 0.817408 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.63565 | −0.186400 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5181 | −1.18337 | −0.591687 | − | 0.806168i | \(-0.701538\pi\) | ||||
−0.591687 | + | 0.806168i | \(0.701538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10038 | −0.122265 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.728692 | −0.0799843 | −0.0399922 | − | 0.999200i | \(-0.512733\pi\) | ||||
−0.0399922 | + | 0.999200i | \(0.512733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.657077 | 0.0712700 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.02142 | −0.752776 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.51806 | −0.902912 | −0.451456 | − | 0.892293i | \(-0.649095\pi\) | ||||
−0.451456 | + | 0.892293i | \(0.649095\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.66442 | 0.803450 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.42923 | 0.977766 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.34292 | −0.342977 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.31415 | −0.336501 | −0.168251 | − | 0.985744i | \(-0.553812\pi\) | ||||
−0.168251 | + | 0.985744i | \(0.553812\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.824865 | −0.0829021 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6858 | −1.06328 | −0.531641 | − | 0.846970i | \(-0.678424\pi\) | ||||
−0.531641 | + | 0.846970i | \(0.678424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0575 | −1.18806 | −0.594032 | − | 0.804441i | \(-0.702465\pi\) | ||||
−0.594032 | + | 0.804441i | \(0.702465\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.8108 | −1.25020 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.39312 | 0.811393 | 0.405697 | − | 0.914008i | \(-0.367029\pi\) | ||||
0.405697 | + | 0.914008i | \(0.367029\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.22533 | −0.787843 | −0.393922 | − | 0.919144i | \(-0.628882\pi\) | ||||
−0.393922 | + | 0.919144i | \(0.628882\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.39312 | −0.416976 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4966 | 1.26966 | 0.634828 | − | 0.772653i | \(-0.281071\pi\) | ||||
0.634828 | + | 0.772653i | \(0.281071\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.3717 | −1.24692 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.86519 | 0.357337 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.657077 | −0.0602341 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7606 | −0.978236 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.72869 | 0.426372 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.92839 | 0.351365 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.53948 | −0.136607 | −0.0683034 | − | 0.997665i | \(-0.521759\pi\) | ||||
−0.0683034 | + | 0.997665i | \(0.521759\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.22533 | −0.724200 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.56825 | −0.311759 | −0.155880 | − | 0.987776i | \(-0.549821\pi\) | ||||
−0.155880 | + | 0.987776i | \(0.549821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.34292 | 0.289868 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.9572 | −1.54551 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.1537 | 0.867490 | 0.433745 | − | 0.901036i | \(-0.357192\pi\) | ||||
0.433745 | + | 0.901036i | \(0.357192\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.90383 | −0.331118 | −0.165559 | − | 0.986200i | \(-0.552943\pi\) | ||||
−0.165559 | + | 0.986200i | \(0.552943\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.6184 | −1.06266 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.12181 | −0.0938102 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.4752 | −1.70037 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.78623 | 0.394762 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3576 | −1.42199 | −0.710996 | − | 0.703196i | \(-0.751755\pi\) | ||||
−0.710996 | + | 0.703196i | \(0.751755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.05754 | −0.330198 | −0.165099 | − | 0.986277i | \(-0.552794\pi\) | ||||
−0.165099 | + | 0.986277i | \(0.552794\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.331366 | −0.0267893 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.4966 | 2.20858 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.35027 | −0.187572 | −0.0937860 | − | 0.995592i | \(-0.529897\pi\) | ||||
−0.0937860 | + | 0.995592i | \(0.529897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.51492 | 0.437362 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.3717 | 1.05384 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7648 | 1.07814 | 0.539071 | − | 0.842260i | \(-0.318775\pi\) | ||||
0.539071 | + | 0.842260i | \(0.318775\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.87506 | 0.145973 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.417674 | 0.0323206 | 0.0161603 | − | 0.999869i | \(-0.494856\pi\) | ||||
0.0161603 | + | 0.999869i | \(0.494856\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.74338 | −0.595645 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.68585 | 0.128920 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.60688 | −0.274226 | −0.137113 | − | 0.990555i | \(-0.543782\pi\) | ||||
−0.137113 | + | 0.990555i | \(0.543782\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.6430 | −1.56046 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.09196 | 0.457900 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.51806 | −0.487183 | −0.243591 | − | 0.969878i | \(-0.578326\pi\) | ||||
−0.243591 | + | 0.969878i | \(0.578326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.31415 | 0.0976803 | 0.0488401 | − | 0.998807i | \(-0.484448\pi\) | ||||
0.0488401 | + | 0.998807i | \(0.484448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.86833 | 0.655566 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.8108 | −0.941868 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0961734 | 0.00703289 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.9572 | 1.30619 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.24254 | −0.668767 | −0.334383 | − | 0.942437i | \(-0.608528\pi\) | ||||
−0.334383 | + | 0.942437i | \(0.608528\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.85363 | 0.637299 | 0.318649 | − | 0.947873i | \(-0.396771\pi\) | ||||
0.318649 | + | 0.947873i | \(0.396771\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.78623 | −0.629195 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.3288 | 1.94710 | 0.973550 | − | 0.228475i | \(-0.0733738\pi\) | ||||
0.973550 | + | 0.228475i | \(0.0733738\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3643 | −1.30181 | −0.650907 | − | 0.759157i | \(-0.725611\pi\) | ||||
−0.650907 | + | 0.759157i | \(0.725611\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.7648 | −1.25303 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.4752 | 1.43708 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.7894 | 0.963091 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.74338 | 0.468698 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.489289 | −0.0338448 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3503 | 1.26328 | 0.631642 | − | 0.775260i | \(-0.282381\pi\) | ||||
0.631642 | + | 0.775260i | \(0.282381\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.9210 | −0.885335 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.9859 | −1.63583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.4966 | −1.86659 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.7318 | 1.19821 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.450654 | −0.0303142 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3748 | 1.23047 | 0.615235 | − | 0.788344i | \(-0.289061\pi\) | ||||
0.615235 | + | 0.788344i | \(0.289061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.4103 | −0.694022 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.9933 | 1.26063 | 0.630314 | − | 0.776340i | \(-0.282926\pi\) | ||||
0.630314 | + | 0.776340i | \(0.282926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.05019 | −0.598054 | −0.299027 | − | 0.954245i | \(-0.596662\pi\) | ||||
−0.299027 | + | 0.954245i | \(0.596662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.87506 | −0.123370 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.76060 | 0.639438 | 0.319719 | − | 0.947512i | \(-0.396411\pi\) | ||||
0.319719 | + | 0.947512i | \(0.396411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.7967 | −2.40035 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0575 | −0.783221 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.9645 | 0.838604 | 0.419302 | − | 0.907847i | \(-0.362275\pi\) | ||||
0.419302 | + | 0.907847i | \(0.362275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3257 | −1.30929 | −0.654647 | − | 0.755935i | \(-0.727183\pi\) | ||||
−0.654647 | + | 0.755935i | \(0.727183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8536 | 0.952861 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.9572 | 0.891690 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.29273 | 0.145883 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.835347 | −0.0529380 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.05333 | −0.382083 | −0.191041 | − | 0.981582i | \(-0.561186\pi\) | ||||
−0.191041 | + | 0.981582i | \(0.561186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.95715 | −0.123045 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.753250 | 0.0471704 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0575 | 0.876885 | 0.438443 | − | 0.898759i | \(-0.355530\pi\) | ||||
0.438443 | + | 0.898759i | \(0.355530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.8108 | 0.796024 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3257 | 0.639145 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.26396 | −0.509578 | −0.254789 | − | 0.966997i | \(-0.582006\pi\) | ||||
−0.254789 | + | 0.966997i | \(0.582006\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.0821 | 0.987915 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.76481 | −0.597597 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.18921 | −0.194450 | −0.0972248 | − | 0.995262i | \(-0.530997\pi\) | ||||
−0.0972248 | + | 0.995262i | \(0.530997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.89962 | −0.601359 | −0.300679 | − | 0.953725i | \(-0.597213\pi\) | ||||
−0.300679 | + | 0.953725i | \(0.597213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.78623 | 0.531767 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.02142 | 0.182199 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7722 | −0.767404 | −0.383702 | − | 0.923457i | \(-0.625351\pi\) | ||||
−0.383702 | + | 0.923457i | \(0.625351\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.8666 | −0.830174 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.5296 | 1.76159 | 0.880795 | − | 0.473499i | \(-0.157009\pi\) | ||||
0.880795 | + | 0.473499i | \(0.157009\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.3246 | −1.50539 | −0.752697 | − | 0.658367i | \(-0.771247\pi\) | ||||
−0.752697 | + | 0.658367i | \(0.771247\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.83221 | −0.227001 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.7894 | −0.813961 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9614 | −0.997727 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.79923 | −0.222715 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.8353 | 0.983531 | 0.491766 | − | 0.870728i | \(-0.336352\pi\) | ||||
0.491766 | + | 0.870728i | \(0.336352\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.7648 | 1.03431 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.62831 | −0.152510 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.17092 | 0.530368 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.9859 | 1.38253 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.2499 | −0.703738 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.8610 | 1.48080 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7894 | 1.01529 | 0.507646 | − | 0.861566i | \(-0.330516\pi\) | ||||
0.507646 | + | 0.861566i | \(0.330516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.8223 | −0.786326 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3215 | −1.15233 | −0.576163 | − | 0.817335i | \(-0.695451\pi\) | ||||
−0.576163 | + | 0.817335i | \(0.695451\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.8929 | 1.97226 | 0.986131 | − | 0.165967i | \(-0.0530746\pi\) | ||||
0.986131 | + | 0.165967i | \(0.0530746\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.8396 | 1.06149 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.7287 | −0.714915 | −0.357457 | − | 0.933929i | \(-0.616356\pi\) | ||||
−0.357457 | + | 0.933929i | \(0.616356\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.99686 | −0.167792 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.62158 | 0.537024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.196558 | −0.0109368 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1579 | −0.785340 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.42923 | −0.521438 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.7967 | 2.02867 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.4605 | −1.01468 | −0.507341 | − | 0.861745i | \(-0.669372\pi\) | ||||
−0.507341 | + | 0.861745i | \(0.669372\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.46052 | 0.354034 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −51.8041 | −2.83036 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.5510 | 1.55527 | 0.777637 | − | 0.628713i | \(-0.216418\pi\) | ||||
0.777637 | + | 0.628713i | \(0.216418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.4721 | 0.840328 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.02456 | 0.217942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.44331 | 0.509891 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.3288 | −0.825277 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.3116 | 1.62721 | 0.813607 | − | 0.581415i | \(-0.197501\pi\) | ||||
0.813607 | + | 0.581415i | \(0.197501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.6503 | 1.05186 | 0.525929 | − | 0.850528i | \(-0.323718\pi\) | ||||
0.525929 | + | 0.850528i | \(0.323718\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.3158 | 0.657371 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.80765 | 0.0962117 | 0.0481058 | − | 0.998842i | \(-0.484682\pi\) | ||||
0.0481058 | + | 0.998842i | \(0.484682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.6791 | −1.99980 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.753250 | −0.0398662 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.4496 | 1.23762 | 0.618811 | − | 0.785540i | \(-0.287615\pi\) | ||||
0.618811 | + | 0.785540i | \(0.287615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.3356 | −0.647450 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 51.7079 | 2.70651 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.2499 | 0.848237 | 0.424119 | − | 0.905607i | \(-0.360584\pi\) | ||||
0.424119 | + | 0.905607i | \(0.360584\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.95402 | −0.362012 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.0821 | −0.834941 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.8353 | 0.871701 | 0.435851 | − | 0.900019i | \(-0.356448\pi\) | ||||
0.435851 | + | 0.900019i | \(0.356448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.50337 | 0.232553 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.0428 | 0.723243 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.68585 | 0.137963 | 0.0689813 | − | 0.997618i | \(-0.478025\pi\) | ||||
0.0689813 | + | 0.997618i | \(0.478025\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.76481 | −0.0904138 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.110250 | −0.00563350 | −0.00281675 | − | 0.999996i | \(-0.500897\pi\) | ||||
−0.00281675 | + | 0.999996i | \(0.500897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.46787 | −0.278668 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.0962 | 0.614883 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.24254 | 0.468615 | 0.234308 | − | 0.972162i | \(-0.424718\pi\) | ||||
0.234308 | + | 0.972162i | \(0.424718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.786230 | −0.0397614 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.09052 | −0.206339 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.1611 | −1.76914 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.9070 | −1.65155 | −0.825777 | − | 0.563997i | \(-0.809263\pi\) | ||||
−0.825777 | + | 0.563997i | \(0.809263\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.83221 | 0.191851 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.9817 | −1.19759 | −0.598795 | − | 0.800902i | \(-0.704353\pi\) | ||||
−0.598795 | + | 0.800902i | \(0.704353\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.8585 | −0.939407 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.67850 | −0.182786 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.87506 | −0.0929431 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.182481 | 0.00902311 | 0.00451156 | − | 0.999990i | \(-0.498564\pi\) | ||||
0.00451156 | + | 0.999990i | \(0.498564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.6399 | 0.574152 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.7648 | −0.874149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.43596 | −0.119577 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.47521 | −0.219152 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.6497 | −0.666833 | −0.333416 | − | 0.942780i | \(-0.608202\pi\) | ||||
−0.333416 | + | 0.942780i | \(0.608202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4324 | 0.703390 | 0.351695 | − | 0.936115i | \(-0.385605\pi\) | ||||
0.351695 | + | 0.936115i | \(0.385605\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.5567 | 0.902257 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.21377 | 0.0588765 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.8610 | −1.25150 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.28600 | −0.0620887 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.1218 | −0.824728 | −0.412364 | − | 0.911019i | \(-0.635297\pi\) | ||||
−0.412364 | + | 0.911019i | \(0.635297\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.3748 | −1.36361 | −0.681804 | − | 0.731535i | \(-0.738804\pi\) | ||||
−0.681804 | + | 0.731535i | \(0.738804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.4721 | −1.12540 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | 0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.5823 | 0.743704 | 0.371852 | − | 0.928292i | \(-0.378723\pi\) | ||||
0.371852 | + | 0.928292i | \(0.378723\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.03863 | −0.335173 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.7476 | −1.17579 | −0.587897 | − | 0.808936i | \(-0.700044\pi\) | ||||
−0.587897 | + | 0.808936i | \(0.700044\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.4752 | −1.34985 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.8982 | −0.941151 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.7220 | −1.78021 | −0.890105 | − | 0.455756i | \(-0.849369\pi\) | ||||
−0.890105 | + | 0.455756i | \(0.849369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.01829 | 0.0950374 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.65142 | −0.218543 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.6216 | 1.20116 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.6258 | −1.01161 | −0.505806 | − | 0.862647i | \(-0.668805\pi\) | ||||
−0.505806 | + | 0.862647i | \(0.668805\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.05585 | −0.0492827 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.5353 | 0.537251 | 0.268626 | − | 0.963245i | \(-0.413431\pi\) | ||||
0.268626 | + | 0.963245i | \(0.413431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.4282 | −1.87886 | −0.939428 | − | 0.342747i | \(-0.888643\pi\) | ||||
−0.939428 | + | 0.342747i | \(0.888643\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.5212 | 1.46176 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.7606 | 1.28461 | 0.642304 | − | 0.766450i | \(-0.277979\pi\) | ||||
0.642304 | + | 0.766450i | \(0.277979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.8041 | 2.39209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.69427 | −0.124145 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.51071 | −0.161423 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.17513 | −0.283335 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.11025 | −0.371343 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.4935 | 0.479460 | 0.239730 | − | 0.970840i | \(-0.422941\pi\) | ||||
0.239730 | + | 0.970840i | \(0.422941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.78623 | 0.400618 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.3288 | 0.697487 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.0790 | −0.503070 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.2646 | −0.827647 | −0.413824 | − | 0.910357i | \(-0.635807\pi\) | ||||
−0.413824 | + | 0.910357i | \(0.635807\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.7795 | 0.713574 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.6791 | 1.88095 | 0.940476 | − | 0.339860i | \(-0.110380\pi\) | ||||
0.940476 | + | 0.339860i | \(0.110380\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.20390 | −0.0542211 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.75746 | −0.123939 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.6791 | 1.69014 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0748 | 0.585306 | 0.292653 | − | 0.956219i | \(-0.405462\pi\) | ||||
0.292653 | + | 0.956219i | \(0.405462\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.478807 | 0.0213915 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.4935 | 0.824584 | 0.412292 | − | 0.911052i | \(-0.364728\pi\) | ||||
0.412292 | + | 0.911052i | \(0.364728\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.7220 | −1.58961 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.87675 | −0.394230 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.8652 | 0.525915 | 0.262958 | − | 0.964807i | \(-0.415302\pi\) | ||||
0.262958 | + | 0.964807i | \(0.415302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −51.7079 | −2.28742 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.37169 | 0.237166 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.3074 | −1.77616 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.38577 | −0.236866 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.13481 | −0.181498 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.3832 | −1.06825 | −0.534125 | − | 0.845406i | \(-0.679359\pi\) | ||||
−0.534125 | + | 0.845406i | \(0.679359\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.5510 | −1.68572 | −0.842860 | − | 0.538134i | \(-0.819130\pi\) | ||||
−0.842860 | + | 0.538134i | \(0.819130\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.6644 | −1.03280 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.61675 | 0.0704268 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.95885 | −0.388781 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.45738 | −0.409645 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.0575 | 1.21303 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.47208 | −0.322444 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.04285 | 0.0879916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.857845 | −0.0368817 | −0.0184408 | − | 0.999830i | \(-0.505870\pi\) | ||||
−0.0184408 | + | 0.999830i | \(0.505870\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.50650 | 0.0646501 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.4966 | −1.17783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8291 | −0.463018 | −0.231509 | − | 0.972833i | \(-0.574366\pi\) | ||||
−0.231509 | + | 0.972833i | \(0.574366\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.0418 | −0.556609 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.12494 | 0.260931 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.1611 | 1.49520 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.6858 | −0.623379 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.7722 | 1.55809 | 0.779043 | − | 0.626970i | \(-0.215705\pi\) | ||||
0.779043 | + | 0.626970i | \(0.215705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.4507 | 0.695789 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.110250 | 0.00465475 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.8469 | 1.25790 | 0.628949 | − | 0.777447i | \(-0.283486\pi\) | ||||
0.628949 | + | 0.777447i | \(0.283486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 45.1182 | 1.89814 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.67850 | 0.154482 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.2646 | −1.52029 | −0.760145 | − | 0.649753i | \(-0.774872\pi\) | ||||
−0.760145 | + | 0.649753i | \(0.774872\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3570 | −0.475276 | −0.237638 | − | 0.971354i | \(-0.576373\pi\) | ||||
−0.237638 | + | 0.971354i | \(0.576373\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.5953 | −0.442626 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.7005 | −1.03008 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.2113 | 0.758144 | 0.379072 | − | 0.925367i | \(-0.376243\pi\) | ||||
0.379072 | + | 0.925367i | \(0.376243\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.1495 | 0.421799 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.43596 | 0.101061 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.35386 | 0.0974871 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.9210 | 0.534219 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.4464 | −1.09156 | −0.545781 | − | 0.837928i | \(-0.683767\pi\) | ||||
−0.545781 | + | 0.837928i | \(0.683767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.22533 | −0.338919 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.3288 | 1.28870 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.8929 | −1.10436 | −0.552179 | − | 0.833725i | \(-0.686204\pi\) | ||||
−0.552179 | + | 0.833725i | \(0.686204\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.19656 | −0.0900501 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0523 | −0.861611 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.5181 | −1.41037 | −0.705185 | − | 0.709024i | \(-0.749136\pi\) | ||||
−0.705185 | + | 0.709024i | \(0.749136\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.8715 | −1.13690 | −0.568450 | − | 0.822718i | \(-0.692457\pi\) | ||||
−0.568450 | + | 0.822718i | \(0.692457\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.1249 | 1.06389 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.9718 | −1.46246 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.5787 | −1.11939 | −0.559693 | − | 0.828700i | \(-0.689081\pi\) | ||||
−0.559693 | + | 0.828700i | \(0.689081\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.4721 | 0.951137 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.2369 | 1.02098 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.67177 | −0.107912 | −0.0539559 | − | 0.998543i | \(-0.517183\pi\) | ||||
−0.0539559 | + | 0.998543i | \(0.517183\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.8077 | 0.637426 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0832 | 0.607226 | 0.303613 | − | 0.952795i | \(-0.401807\pi\) | ||||
0.303613 | + | 0.952795i | \(0.401807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.7220 | −1.27501 | −0.637507 | − | 0.770445i | \(-0.720034\pi\) | ||||
−0.637507 | + | 0.770445i | \(0.720034\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.4868 | 0.862234 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.4752 | 1.14084 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.7434 | −0.709735 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.560904 | −0.0224003 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.753250 | −0.0300341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.1800 | 1.87820 | 0.939102 | − | 0.343638i | \(-0.111659\pi\) | ||||
0.939102 | + | 0.343638i | \(0.111659\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.0361 | 0.836111 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.14637 | −0.204227 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.57246 | −0.379275 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.0017 | 0.751695 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.1067 | 1.34713 | 0.673566 | − | 0.739127i | \(-0.264762\pi\) | ||||
0.673566 | + | 0.739127i | \(0.264762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.6686 | 0.854528 | 0.427264 | − | 0.904127i | \(-0.359478\pi\) | ||||
0.427264 | + | 0.904127i | \(0.359478\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.4966 | −1.08268 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.8427 | −1.40912 | −0.704561 | − | 0.709644i | \(-0.748856\pi\) | ||||
−0.704561 | + | 0.709644i | \(0.748856\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.60015 | 0.102065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.5212 | −1.23541 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.7507 | −0.851172 | −0.425586 | − | 0.904918i | \(-0.639932\pi\) | ||||
−0.425586 | + | 0.904918i | \(0.639932\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.9284 | −0.466081 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.0764 | −1.01734 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3012 | 0.401276 | 0.200638 | − | 0.979665i | \(-0.435699\pi\) | ||||
0.200638 | + | 0.979665i | \(0.435699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.95715 | −0.0761245 | −0.0380622 | − | 0.999275i | \(-0.512119\pi\) | ||||
−0.0380622 | + | 0.999275i | \(0.512119\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.516614 | −0.0200636 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.1751 | 0.433353 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.4998 | 0.948635 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.0643 | 0.814392 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.78516 | 0.146124 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0428457 | −0.00165158 | −0.000825790 | − | 1.00000i | \(-0.500263\pi\) | ||||
−0.000825790 | 1.00000i | \(0.500263\pi\) | ||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −33.1709 | −1.27675 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.1543 | −1.62012 | −0.810061 | − | 0.586345i | \(-0.800566\pi\) | ||||
−0.810061 | + | 0.586345i | \(0.800566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.0790 | 0.425172 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.7732 | 0.834352 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.8353 | −1.10335 | −0.551677 | − | 0.834058i | \(-0.686012\pi\) | ||||
−0.551677 | + | 0.834058i | \(0.686012\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.9431 | 1.29690 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.3748 | −0.395824 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0298 | −0.420204 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.4103 | 0.814487 | 0.407244 | − | 0.913320i | \(-0.366490\pi\) | ||||
0.407244 | + | 0.913320i | \(0.366490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.75746 | 0.104747 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.0502 | −0.495022 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.810789 | 0.0307108 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.1892 | 0.423215 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.07054 | 0.115973 | 0.0579863 | − | 0.998317i | \(-0.481532\pi\) | ||||
0.0579863 | + | 0.998317i | \(0.481532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.83221 | 0.144535 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −42.1825 | −1.58868 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 35.7220 | 1.34346 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.8500 | −1.60927 | −0.804634 | − | 0.593772i | \(-0.797638\pi\) | ||||
−0.804634 | + | 0.593772i | \(0.797638\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.7318 | 0.664995 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.9013 | −1.23216 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.75011 | −0.140246 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.8621 | 0.555034 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.5285 | 1.28770 | 0.643849 | − | 0.765153i | \(-0.277337\pi\) | ||||
0.643849 | + | 0.765153i | \(0.277337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.3074 | 1.50113 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.3007 | −0.866562 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −37.8223 | −1.40469 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.0350 | 1.63317 | 0.816585 | − | 0.577226i | \(-0.195865\pi\) | ||||
0.816585 | + | 0.577226i | \(0.195865\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.3288 | 0.752920 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.41033 | −0.0521628 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.4721 | 1.31019 | 0.655096 | − | 0.755546i | \(-0.272628\pi\) | ||||
0.655096 | + | 0.755546i | \(0.272628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.0000 | 0.590169 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.58233 | −0.279299 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.4956 | 1.26894 | 0.634470 | − | 0.772948i | \(-0.281218\pi\) | ||||
0.634470 | + | 0.772948i | \(0.281218\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.62831 | 0.0965533 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.40298 | −0.0881568 | −0.0440784 | − | 0.999028i | \(-0.514035\pi\) | ||||
−0.0440784 | + | 0.999028i | \(0.514035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −58.0252 | −2.12588 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.22846 | 0.0449471 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.0575 | −1.02520 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.3221 | 1.69032 | 0.845159 | − | 0.534515i | \(-0.179506\pi\) | ||||
0.845159 | + | 0.534515i | \(0.179506\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.93933 | −0.252883 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.5640 | −0.493646 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.5798 | 1.03875 | 0.519375 | − | 0.854546i | \(-0.326165\pi\) | ||||
0.519375 | + | 0.854546i | \(0.326165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.24361 | −0.0814380 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.5401 | 0.780828 | 0.390414 | − | 0.920639i | \(-0.372332\pi\) | ||||
0.390414 | + | 0.920639i | \(0.372332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.4966 | 0.995445 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.10773 | −0.0400501 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.1839 | −0.439936 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.6472 | 0.600314 | 0.300157 | − | 0.953890i | \(-0.402961\pi\) | ||||
0.300157 | + | 0.953890i | \(0.402961\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.1151 | 0.580370 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.8009 | 1.39557 | 0.697786 | − | 0.716306i | \(-0.254169\pi\) | ||||
0.697786 | + | 0.716306i | \(0.254169\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 50.7925 | 1.82452 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.6858 | 0.526852 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.12494 | −0.147791 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.51492 | −0.197339 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.9013 | 1.17580 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.85677 | −0.280420 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.8652 | 0.850702 | 0.425351 | − | 0.905028i | \(-0.360151\pi\) | ||||
0.425351 | + | 0.905028i | \(0.360151\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.47352 | −0.337266 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −45.1182 | −1.60422 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.7367 | −0.629847 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.4360 | 0.653856 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.01829 | 0.0714914 | 0.0357457 | − | 0.999361i | \(-0.488619\pi\) | ||||
0.0357457 | + | 0.999361i | \(0.488619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.16358 | −0.0765419 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3601 | 0.507390 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.56825 | 0.267078 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44.7005 | 1.57549 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.65600 | −0.128697 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −52.0533 | −1.83010 | −0.915049 | − | 0.403343i | \(-0.867848\pi\) | ||||
−0.915049 | + | 0.403343i | \(0.867848\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.1579 | −1.19945 | −0.599723 | − | 0.800207i | \(-0.704723\pi\) | ||||
−0.599723 | + | 0.800207i | \(0.704723\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3486 | −0.398012 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46.0147 | 1.61182 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.17513 | 0.251026 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.9210 | −0.451498 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.2787 | −1.05673 | −0.528366 | − | 0.849017i | \(-0.677195\pi\) | ||||
−0.528366 | + | 0.849017i | \(0.677195\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.9284 | 1.39182 | 0.695908 | − | 0.718131i | \(-0.255002\pi\) | ||||
0.695908 | + | 0.718131i | \(0.255002\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.46365 | 0.120589 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0330 | 0.418428 | 0.209214 | − | 0.977870i | \(-0.432910\pi\) | ||||
0.209214 | + | 0.977870i | \(0.432910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.84208 | −0.341829 | −0.170915 | − | 0.985286i | \(-0.554672\pi\) | ||||
−0.170915 | + | 0.985286i | \(0.554672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.6416 | −0.507910 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.820654 | 0.0284340 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.39625 | 0.0483192 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −44.1839 | −1.52722 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2713 | −0.665319 | −0.332660 | − | 0.943047i | \(-0.607946\pi\) | ||||
−0.332660 | + | 0.943047i | \(0.607946\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.51492 | 0.293618 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.8517 | 1.16592 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.8855 | −0.890490 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.9718 | 1.23601 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.0313 | −0.996351 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.3288 | 0.525466 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.4721 | −0.940626 | −0.470313 | − | 0.882500i | \(-0.655859\pi\) | ||||
−0.470313 | + | 0.882500i | \(0.655859\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.63565 | 0.192735 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.292731 | 0.00999950 | 0.00499975 | − | 0.999988i | \(-0.498409\pi\) | ||||
0.00499975 | + | 0.999988i | \(0.498409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.9614 | 0.817551 | 0.408776 | − | 0.912635i | \(-0.365956\pi\) | ||||
0.408776 | + | 0.912635i | \(0.365956\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.8077 | −0.538723 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.12494 | 0.208495 | 0.104248 | − | 0.994551i | \(-0.466757\pi\) | ||||
0.104248 | + | 0.994551i | \(0.466757\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0575 | −0.409969 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.4439 | −0.660350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.14637 | −0.174578 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.5296 | 1.20388 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.58715 | 0.189096 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.1323 | −0.443952 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3503 | −0.754715 | −0.377357 | − | 0.926068i | \(-0.623167\pi\) | ||||
−0.377357 | + | 0.926068i | \(0.623167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.2995 | 0.650955 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.70306 | 0.192141 | 0.0960705 | − | 0.995375i | \(-0.469373\pi\) | ||||
0.0960705 | + | 0.995375i | \(0.469373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.29694 | 0.279214 | 0.139607 | − | 0.990207i | \(-0.455416\pi\) | ||||
0.139607 | + | 0.990207i | \(0.455416\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.3650 | 0.684561 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.4783 | −0.855479 | −0.427740 | − | 0.903902i | \(-0.640690\pi\) | ||||
−0.427740 | + | 0.903902i | \(0.640690\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.14637 | 0.172604 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.538405 | −0.0180373 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.0073 | 0.368347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.7894 | −0.728338 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.5132 | 0.351027 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −50.3797 | −1.68026 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.945597 | 0.0315024 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.4966 | 0.915031 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.39312 | 0.146032 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.9964 | 1.32806 | 0.664029 | − | 0.747706i | \(-0.268845\pi\) | ||||
0.664029 | + | 0.747706i | \(0.268845\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.0147 | 0.597510 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.3864 | 0.642300 | 0.321150 | − | 0.947028i | \(-0.395931\pi\) | ||||
0.321150 | + | 0.947028i | \(0.395931\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.356541 | −0.0117998 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.6461 | 0.980071 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.9284 | 0.393910 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.1213 | −1.25751 | −0.628754 | − | 0.777605i | \(-0.716435\pi\) | ||||
−0.628754 | + | 0.777605i | \(0.716435\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.3931 | 0.671976 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.8421 | 0.850602 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.6644 | −0.778081 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.3272 | 0.667631 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.8500 | −0.552832 | −0.276416 | − | 0.961038i | \(-0.589147\pi\) | ||||
−0.276416 | + | 0.961038i | \(0.589147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.17513 | −0.136835 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.2959 | −0.762672 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.321500 | 0.0105142 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.4973 | −1.29032 | −0.645159 | − | 0.764048i | \(-0.723209\pi\) | ||||
−0.645159 | + | 0.764048i | \(0.723209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.0000 | 1.30535 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.9718 | 1.82463 | 0.912315 | − | 0.409489i | \(-0.134293\pi\) | ||||
0.912315 | + | 0.409489i | \(0.134293\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.4998 | −0.537306 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 60.0294 | 1.95276 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5725 | 0.441046 | 0.220523 | − | 0.975382i | \(-0.429224\pi\) | ||||
0.220523 | + | 0.975382i | \(0.429224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.4637 | −1.15120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.5917 | −0.473169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.0246 | 0.843018 | 0.421509 | − | 0.906824i | \(-0.361501\pi\) | ||||
0.421509 | + | 0.906824i | \(0.361501\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.8971 | −0.999807 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.43550 | −0.111054 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.9431 | −1.09608 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.6560 | 1.18245 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.1495 | −0.455961 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.5970 | 0.952762 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0277 | 0.418942 | 0.209471 | − | 0.977815i | \(-0.432826\pi\) | ||||
0.209471 | + | 0.977815i | \(0.432826\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.225327 | −0.00723854 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.6148 | −1.94522 | −0.972612 | − | 0.232437i | \(-0.925330\pi\) | ||||
−0.972612 | + | 0.232437i | \(0.925330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0502 | 0.418370 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.2302 | −0.519781 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −62.1396 | −1.98802 | −0.994012 | − | 0.109275i | \(-0.965147\pi\) | ||||
−0.994012 | + | 0.109275i | \(0.965147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.16779 | −0.133203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8666 | 0.442728 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.37842 | −0.203440 | −0.101720 | − | 0.994813i | \(-0.532435\pi\) | ||||
−0.101720 | + | 0.994813i | \(0.532435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 91.3582 | 2.91092 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.1825 | 1.34268 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.7005 | 0.912624 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.1249 | 0.448694 | 0.224347 | − | 0.974509i | \(-0.427975\pi\) | ||||
0.224347 | + | 0.974509i | \(0.427975\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.1625 | −0.671572 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −61.3906 | −1.94621 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1568 | −0.416682 | −0.208341 | − | 0.978056i | \(-0.566806\pi\) | ||||
−0.208341 | + | 0.978056i | \(0.566806\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.5855 | 0.651295 |
(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 | 4864.2.a.bh.1.2 | 3 | ||
4.3 | odd | 2 | 4864.2.a.bb.1.2 | 3 | |||
8.3 | odd | 2 | 4864.2.a.bg.1.2 | 3 | |||
8.5 | even | 2 | 4864.2.a.ba.1.2 | 3 | |||
16.3 | odd | 4 | 2432.2.c.e.1217.3 | ✓ | 6 | ||
16.5 | even | 4 | 2432.2.c.h.1217.3 | yes | 6 | ||
16.11 | odd | 4 | 2432.2.c.e.1217.4 | yes | 6 | ||
16.13 | even | 4 | 2432.2.c.h.1217.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.e.1217.3 | ✓ | 6 | 16.3 | odd | 4 | ||
2432.2.c.e.1217.4 | yes | 6 | 16.11 | odd | 4 | ||
2432.2.c.h.1217.3 | yes | 6 | 16.5 | even | 4 | ||
2432.2.c.h.1217.4 | yes | 6 | 16.13 | even | 4 | ||
4864.2.a.ba.1.2 | 3 | 8.5 | even | 2 | |||
4864.2.a.bb.1.2 | 3 | 4.3 | odd | 2 | |||
4864.2.a.bg.1.2 | 3 | 8.3 | odd | 2 | |||
4864.2.a.bh.1.2 | 3 | 1.1 | even | 1 | trivial |