Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(1,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, 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("648.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.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: | \(5.17430605098\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
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 | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.267949 | −0.119831 | −0.0599153 | − | 0.998203i | \(-0.519083\pi\) | ||||
−0.0599153 | + | 0.998203i | \(0.519083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | −1.30931 | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.46410 | 1.23812 | 0.619060 | − | 0.785344i | \(-0.287514\pi\) | ||||
0.619060 | + | 0.785344i | \(0.287514\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.73205 | −1.39023 | −0.695113 | − | 0.718900i | \(-0.744646\pi\) | ||||
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.535898 | −0.122944 | −0.0614718 | − | 0.998109i | \(-0.519579\pi\) | ||||
−0.0614718 | + | 0.998109i | \(0.519579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.92820 | −1.86166 | −0.930830 | − | 0.365454i | \(-0.880914\pi\) | ||||
−0.930830 | + | 0.365454i | \(0.880914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92820 | −0.985641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.73205 | −1.43581 | −0.717903 | − | 0.696143i | \(-0.754898\pi\) | ||||
−0.717903 | + | 0.696143i | \(0.754898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.92820 | 0.525921 | 0.262960 | − | 0.964807i | \(-0.415301\pi\) | ||||
0.262960 | + | 0.964807i | \(0.415301\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.928203 | 0.156895 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.46410 | 1.06269 | 0.531346 | − | 0.847155i | \(-0.321686\pi\) | ||||
0.531346 | + | 0.847155i | \(0.321686\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.4641 | −1.74826 | −0.874130 | − | 0.485693i | \(-0.838567\pi\) | ||||
−0.874130 | + | 0.485693i | \(0.838567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.92820 | 1.01058 | 0.505291 | − | 0.862949i | \(-0.331385\pi\) | ||||
0.505291 | + | 0.862949i | \(0.331385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.92820 | −0.402220 | −0.201110 | − | 0.979569i | \(-0.564455\pi\) | ||||
−0.201110 | + | 0.979569i | \(0.564455\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.535898 | 0.0722605 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.53590 | 0.452725 | 0.226363 | − | 0.974043i | \(-0.427317\pi\) | ||||
0.226363 | + | 0.974043i | \(0.427317\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.19615 | −0.148364 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.46410 | −0.911885 | −0.455943 | − | 0.890009i | \(-0.650698\pi\) | ||||
−0.455943 | + | 0.890009i | \(0.650698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.92820 | 0.789542 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.46410 | 0.839777 | 0.419889 | − | 0.907576i | \(-0.362069\pi\) | ||||
0.419889 | + | 0.907576i | \(0.362069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.9282 | −1.19953 | −0.599763 | − | 0.800178i | \(-0.704739\pi\) | ||||
−0.599763 | + | 0.800178i | \(0.704739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.53590 | 0.166592 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.19615 | −0.550791 | −0.275396 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4641 | −1.62108 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.143594 | 0.0147324 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8564 | 1.60997 | 0.804987 | − | 0.593292i | \(-0.202172\pi\) | ||||
0.804987 | + | 0.593292i | \(0.202172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.92820 | −0.288524 | −0.144262 | − | 0.989539i | \(-0.546081\pi\) | ||||
−0.144262 | + | 0.989539i | \(0.546081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.9282 | 1.82986 | 0.914929 | − | 0.403614i | \(-0.132246\pi\) | ||||
0.914929 | + | 0.403614i | \(0.132246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.46410 | −0.236018 | −0.118009 | − | 0.993013i | \(-0.537651\pi\) | ||||
−0.118009 | + | 0.993013i | \(0.537651\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.73205 | −0.162938 | −0.0814688 | − | 0.996676i | \(-0.525961\pi\) | ||||
−0.0814688 | + | 0.996676i | \(0.525961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.39230 | 0.223084 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.8564 | 1.82023 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.66025 | 0.237940 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.46410 | 0.662332 | 0.331166 | − | 0.943573i | \(-0.392558\pi\) | ||||
0.331166 | + | 0.943573i | \(0.392558\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.9282 | 1.82851 | 0.914253 | − | 0.405144i | \(-0.132779\pi\) | ||||
0.914253 | + | 0.405144i | \(0.132779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.85641 | 0.160971 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.33975 | −0.285334 | −0.142667 | − | 0.989771i | \(-0.545568\pi\) | ||||
−0.142667 | + | 0.989771i | \(0.545568\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9282 | −1.60547 | −0.802735 | − | 0.596336i | \(-0.796622\pi\) | ||||
−0.802735 | + | 0.596336i | \(0.796622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.92820 | −0.746614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.07180 | 0.172053 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.2679 | 1.00503 | 0.502515 | − | 0.864569i | \(-0.332408\pi\) | ||||
0.502515 | + | 0.864569i | \(0.332408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.9282 | 1.21484 | 0.607420 | − | 0.794381i | \(-0.292205\pi\) | ||||
0.607420 | + | 0.794381i | \(0.292205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.784610 | −0.0630214 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3923 | −1.22844 | −0.614220 | − | 0.789135i | \(-0.710529\pi\) | ||||
−0.614220 | + | 0.789135i | \(0.710529\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.9282 | 2.43748 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.92820 | 0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.26795 | 0.324486 | 0.162243 | − | 0.986751i | \(-0.448127\pi\) | ||||
0.162243 | + | 0.986751i | \(0.448127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.0718 | 1.29051 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.92820 | −0.517838 | −0.258919 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.8564 | −1.47592 | −0.737958 | − | 0.674847i | \(-0.764210\pi\) | ||||
−0.737958 | + | 0.674847i | \(0.764210\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.73205 | −0.127343 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.4641 | 0.838338 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.85641 | 0.568470 | 0.284235 | − | 0.958755i | \(-0.408260\pi\) | ||||
0.284235 | + | 0.958755i | \(0.408260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.07180 | 0.293094 | 0.146547 | − | 0.989204i | \(-0.453184\pi\) | ||||
0.146547 | + | 0.989204i | \(0.453184\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.6603 | −1.04450 | −0.522250 | − | 0.852792i | \(-0.674907\pi\) | ||||
−0.522250 | + | 0.852792i | \(0.674907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.7846 | 1.87991 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.85641 | −0.129657 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.07180 | 0.0741377 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.32051 | 0.641650 | 0.320825 | − | 0.947138i | \(-0.396040\pi\) | ||||
0.320825 | + | 0.947138i | \(0.396040\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.07180 | 0.209495 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1436 | −0.688592 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.5885 | −1.72127 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.46410 | 0.499833 | 0.249917 | − | 0.968267i | \(-0.419597\pi\) | ||||
0.249917 | + | 0.968267i | \(0.419597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.7846 | −1.77776 | −0.888878 | − | 0.458143i | \(-0.848515\pi\) | ||||
−0.888878 | + | 0.458143i | \(0.848515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.4641 | −0.955815 | −0.477907 | − | 0.878410i | \(-0.658605\pi\) | ||||
−0.477907 | + | 0.878410i | \(0.658605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.26795 | −0.410627 | −0.205314 | − | 0.978696i | \(-0.565821\pi\) | ||||
−0.205314 | + | 0.978696i | \(0.565821\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.85641 | −0.121099 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.92820 | 0.189410 | 0.0947049 | − | 0.995505i | \(-0.469809\pi\) | ||||
0.0947049 | + | 0.995505i | \(0.469809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.9282 | −1.41252 | −0.706260 | − | 0.707953i | \(-0.749619\pi\) | ||||
−0.706260 | + | 0.707953i | \(0.749619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.33975 | −0.0855932 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.39230 | −0.152219 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0000 | −0.631194 | −0.315597 | − | 0.948893i | \(-0.602205\pi\) | ||||
−0.315597 | + | 0.948893i | \(0.602205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.8564 | 1.12262 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.0526 | −0.689440 | −0.344720 | − | 0.938706i | \(-0.612026\pi\) | ||||
−0.344720 | + | 0.938706i | \(0.612026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.3923 | −1.39139 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.7846 | 0.788333 | 0.394166 | − | 0.919039i | \(-0.371033\pi\) | ||||
0.394166 | + | 0.919039i | \(0.371033\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.784610 | 0.0481982 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.5167 | 1.49481 | 0.747404 | − | 0.664370i | \(-0.231300\pi\) | ||||
0.747404 | + | 0.664370i | \(0.231300\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4641 | 1.42534 | 0.712671 | − | 0.701498i | \(-0.247485\pi\) | ||||
0.712671 | + | 0.701498i | \(0.247485\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.85641 | 0.594364 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0000 | −0.841178 | −0.420589 | − | 0.907251i | \(-0.638177\pi\) | ||||
−0.420589 | + | 0.907251i | \(0.638177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.1244 | 1.20052 | 0.600259 | − | 0.799806i | \(-0.295064\pi\) | ||||
0.600259 | + | 0.799806i | \(0.295064\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.85641 | 0.585903 | 0.292951 | − | 0.956127i | \(-0.405363\pi\) | ||||
0.292951 | + | 0.956127i | \(0.405363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.0000 | −1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8564 | 0.932730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.1244 | −1.05884 | −0.529418 | − | 0.848361i | \(-0.677590\pi\) | ||||
−0.529418 | + | 0.848361i | \(0.677590\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.14359 | 0.124805 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −39.8564 | −2.30496 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.7128 | 2.28901 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.947441 | −0.0542503 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.07180 | −0.289463 | −0.144731 | − | 0.989471i | \(-0.546232\pi\) | ||||
−0.144731 | + | 0.989471i | \(0.546232\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7846 | −1.00525 | −0.502623 | − | 0.864506i | \(-0.667632\pi\) | ||||
−0.502623 | + | 0.864506i | \(0.667632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.26795 | −0.239712 | −0.119856 | − | 0.992791i | \(-0.538243\pi\) | ||||
−0.119856 | + | 0.992791i | \(0.538243\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.4641 | 0.865823 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.07180 | 0.170919 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.0000 | −1.22034 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.2487 | −1.55269 | −0.776345 | − | 0.630308i | \(-0.782928\pi\) | ||||
−0.776345 | + | 0.630308i | \(0.782928\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.00000 | 0.109272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.8564 | −1.08165 | −0.540824 | − | 0.841136i | \(-0.681887\pi\) | ||||
−0.540824 | + | 0.841136i | \(0.681887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.85641 | −0.317142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820 | 0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.0718 | −0.594365 | −0.297183 | − | 0.954821i | \(-0.596047\pi\) | ||||
−0.297183 | + | 0.954821i | \(0.596047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.8564 | −1.58910 | −0.794548 | − | 0.607201i | \(-0.792292\pi\) | ||||
−0.794548 | + | 0.607201i | \(0.792292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.535898 | −0.0284425 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.7846 | −1.41364 | −0.706819 | − | 0.707395i | \(-0.749870\pi\) | ||||
−0.706819 | + | 0.707395i | \(0.749870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7128 | −0.984885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.267949 | −0.0140251 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.07180 | 0.473544 | 0.236772 | − | 0.971565i | \(-0.423911\pi\) | ||||
0.236772 | + | 0.971565i | \(0.423911\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1436 | 0.526629 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.5167 | −1.77770 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7846 | 0.862167 | 0.431084 | − | 0.902312i | \(-0.358131\pi\) | ||||
0.431084 | + | 0.902312i | \(0.358131\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0000 | −0.919757 | −0.459879 | − | 0.887982i | \(-0.652107\pi\) | ||||
−0.459879 | + | 0.887982i | \(0.652107\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.85641 | −0.0946112 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0718 | −0.662766 | −0.331383 | − | 0.943496i | \(-0.607515\pi\) | ||||
−0.331383 | + | 0.943496i | \(0.607515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51.1769 | 2.58813 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.00000 | −0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.3923 | 1.07365 | 0.536825 | − | 0.843694i | \(-0.319624\pi\) | ||||
0.536825 | + | 0.843694i | \(0.319624\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.80385 | 0.339768 | 0.169884 | − | 0.985464i | \(-0.445661\pi\) | ||||
0.169884 | + | 0.985464i | \(0.445661\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0718 | 0.651153 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.9282 | −0.640827 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.07180 | 0.102444 | 0.0512219 | − | 0.998687i | \(-0.483688\pi\) | ||||
0.0512219 | + | 0.998687i | \(0.483688\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.7128 | 1.36366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.92820 | 0.143740 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.85641 | 0.0906914 | 0.0453457 | − | 0.998971i | \(-0.485561\pi\) | ||||
0.0453457 | + | 0.998971i | \(0.485561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.3923 | −0.847649 | −0.423825 | − | 0.905744i | \(-0.639313\pi\) | ||||
−0.423825 | + | 0.905744i | \(0.639313\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 28.2487 | 1.37026 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.2487 | −0.592757 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.0718 | 0.629646 | 0.314823 | − | 0.949150i | \(-0.398055\pi\) | ||||
0.314823 | + | 0.949150i | \(0.398055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.7846 | −0.662446 | −0.331223 | − | 0.943552i | \(-0.607461\pi\) | ||||
−0.331223 | + | 0.943552i | \(0.607461\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.78461 | 0.228879 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | −0.572729 | −0.286364 | − | 0.958121i | \(-0.592447\pi\) | ||||
−0.286364 | + | 0.958121i | \(0.592447\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.9282 | 0.709260 | 0.354630 | − | 0.935007i | \(-0.384607\pi\) | ||||
0.354630 | + | 0.935007i | \(0.384607\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.39230 | 0.0660016 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7846 | 0.603343 | 0.301672 | − | 0.953412i | \(-0.402455\pi\) | ||||
0.301672 | + | 0.953412i | \(0.402455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.8564 | −0.652473 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.14359 | 0.194255 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.0718 | −1.12603 | −0.563016 | − | 0.826446i | \(-0.690359\pi\) | ||||
−0.563016 | + | 0.826446i | \(0.690359\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.7846 | −0.781737 | −0.390869 | − | 0.920446i | \(-0.627825\pi\) | ||||
−0.390869 | + | 0.920446i | \(0.627825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.0000 | −1.85896 | −0.929479 | − | 0.368875i | \(-0.879743\pi\) | ||||
−0.929479 | + | 0.368875i | \(0.879743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.7128 | 0.727102 | 0.363551 | − | 0.931574i | \(-0.381564\pi\) | ||||
0.363551 | + | 0.931574i | \(0.381564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.8564 | 1.19394 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.9282 | 1.05424 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.64102 | 0.121178 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.8564 | 0.724498 | 0.362249 | − | 0.932081i | \(-0.382009\pi\) | ||||
0.362249 | + | 0.932081i | \(0.382009\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.8564 | 1.31574 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.24871 | −0.192924 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0718 | 0.954854 | 0.477427 | − | 0.878671i | \(-0.341569\pi\) | ||||
0.477427 | + | 0.878671i | \(0.341569\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.1436 | 0.728550 | 0.364275 | − | 0.931291i | \(-0.381317\pi\) | ||||
0.364275 | + | 0.931291i | \(0.381317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.3205 | 1.99610 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.92820 | −0.310772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.2487 | −1.08552 | −0.542761 | − | 0.839887i | \(-0.682621\pi\) | ||||
−0.542761 | + | 0.839887i | \(0.682621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.85641 | 0.0827731 | 0.0413865 | − | 0.999143i | \(-0.486822\pi\) | ||||
0.0413865 | + | 0.999143i | \(0.486822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.21539 | −0.143083 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.78461 | −0.389371 | −0.194685 | − | 0.980866i | \(-0.562369\pi\) | ||||
−0.194685 | + | 0.980866i | \(0.562369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.46410 | −0.153243 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.784610 | 0.0345740 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.8564 | −0.609404 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.7846 | −0.560104 | −0.280052 | − | 0.959985i | \(-0.590352\pi\) | ||||
−0.280052 | + | 0.959985i | \(0.590352\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.5359 | −1.24779 | −0.623894 | − | 0.781509i | \(-0.714450\pi\) | ||||
−0.623894 | + | 0.781509i | \(0.714450\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.7846 | −0.731149 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.7128 | 2.46577 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.9282 | 1.33965 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.07180 | −0.219273 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.0000 | −0.430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3923 | −0.575780 | −0.287890 | − | 0.957663i | \(-0.592954\pi\) | ||||
−0.287890 | + | 0.957663i | \(0.592954\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.660254 | 0.0282822 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.85641 | 0.421430 | 0.210715 | − | 0.977548i | \(-0.432421\pi\) | ||||
0.210715 | + | 0.977548i | \(0.432421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.14359 | 0.176523 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.8564 | −1.09953 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.5885 | −0.745247 | −0.372623 | − | 0.927983i | \(-0.621542\pi\) | ||||
−0.372623 | + | 0.927983i | \(0.621542\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −51.1769 | −2.16455 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.9282 | −0.629149 | −0.314574 | − | 0.949233i | \(-0.601862\pi\) | ||||
−0.314574 | + | 0.949233i | \(0.601862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.464102 | 0.0195249 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.4115 | 0.520319 | 0.260159 | − | 0.965566i | \(-0.416225\pi\) | ||||
0.260159 | + | 0.965566i | \(0.416225\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8564 | 0.579873 | 0.289936 | − | 0.957046i | \(-0.406366\pi\) | ||||
0.289936 | + | 0.957046i | \(0.406366\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.0000 | 1.83493 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.8564 | 1.03479 | 0.517393 | − | 0.855748i | \(-0.326903\pi\) | ||||
0.517393 | + | 0.855748i | \(0.326903\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.8564 | 1.57055 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.85641 | 0.242548 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.0000 | −1.07313 | −0.536567 | − | 0.843857i | \(-0.680279\pi\) | ||||
−0.536567 | + | 0.843857i | \(0.680279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.56922 | −0.0646586 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.5885 | 1.29718 | 0.648591 | − | 0.761137i | \(-0.275358\pi\) | ||||
0.648591 | + | 0.761137i | \(0.275358\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.32051 | −0.218120 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.07180 | 0.207228 | 0.103614 | − | 0.994618i | \(-0.466959\pi\) | ||||
0.103614 | + | 0.994618i | \(0.466959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.8564 | 0.850751 | 0.425375 | − | 0.905017i | \(-0.360142\pi\) | ||||
0.425375 | + | 0.905017i | \(0.360142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.87564 | 0.0762558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1769 | −0.940722 | −0.470361 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470361 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9282 | 1.25122 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.8564 | −0.963551 | −0.481776 | − | 0.876295i | \(-0.660008\pi\) | ||||
−0.481776 | + | 0.876295i | \(0.660008\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.4449 | 1.18541 | 0.592703 | − | 0.805421i | \(-0.298061\pi\) | ||||
0.592703 | + | 0.805421i | \(0.298061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.7846 | 1.47850 | 0.739249 | − | 0.673432i | \(-0.235181\pi\) | ||||
0.739249 | + | 0.673432i | \(0.235181\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.0000 | 0.721155 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.0526 | −1.47738 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.7846 | −1.14590 | −0.572949 | − | 0.819591i | \(-0.694201\pi\) | ||||
−0.572949 | + | 0.819591i | \(0.694201\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.00000 | −0.0793676 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3205 | 0.884371 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9808 | −0.868188 | −0.434094 | − | 0.900868i | \(-0.642931\pi\) | ||||
−0.434094 | + | 0.900868i | \(0.642931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.78461 | −0.346431 | −0.173216 | − | 0.984884i | \(-0.555416\pi\) | ||||
−0.173216 | + | 0.984884i | \(0.555416\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.7128 | 0.696363 | 0.348181 | − | 0.937427i | \(-0.386799\pi\) | ||||
0.348181 | + | 0.937427i | \(0.386799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.7846 | 1.28296 | 0.641480 | − | 0.767139i | \(-0.278321\pi\) | ||||
0.641480 | + | 0.767139i | \(0.278321\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.60770 | −0.219111 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.7846 | 1.51083 | 0.755417 | − | 0.655244i | \(-0.227434\pi\) | ||||
0.755417 | + | 0.655244i | \(0.227434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.32051 | 0.168048 | 0.0840241 | − | 0.996464i | \(-0.473223\pi\) | ||||
0.0840241 | + | 0.996464i | \(0.473223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.497423 | −0.0192892 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 69.0333 | 2.67298 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.07180 | −0.273004 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0718 | 0.465334 | 0.232667 | − | 0.972557i | \(-0.425255\pi\) | ||||
0.232667 | + | 0.972557i | \(0.425255\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.6410 | 1.48509 | 0.742547 | − | 0.669793i | \(-0.233617\pi\) | ||||
0.742547 | + | 0.669793i | \(0.233617\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54.9282 | −2.10795 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.9282 | −0.571212 | −0.285606 | − | 0.958347i | \(-0.592195\pi\) | ||||
−0.285606 | + | 0.958347i | \(0.592195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.894882 | 0.0341917 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.0718 | −0.497996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.3923 | −1.46051 | −0.730256 | − | 0.683174i | \(-0.760599\pi\) | ||||
−0.730256 | + | 0.683174i | \(0.760599\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.07180 | 0.192384 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.7128 | −1.50423 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.4449 | 0.885500 | 0.442750 | − | 0.896645i | \(-0.354003\pi\) | ||||
0.442750 | + | 0.896645i | \(0.354003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.46410 | −0.130651 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41.5692 | −1.56337 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.3205 | −0.462706 | −0.231353 | − | 0.972870i | \(-0.574315\pi\) | ||||
−0.231353 | + | 0.972870i | \(0.574315\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.1436 | −0.979085 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.39230 | 0.0894671 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.92820 | 0.183791 | 0.0918955 | − | 0.995769i | \(-0.470707\pi\) | ||||
0.0918955 | + | 0.995769i | \(0.470707\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.1436 | 0.377767 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.1051 | 1.41519 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1769 | 1.15629 | 0.578144 | − | 0.815935i | \(-0.303777\pi\) | ||||
0.578144 | + | 0.815935i | \(0.303777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 65.7128 | 2.43048 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.1436 | 0.448534 | 0.224267 | − | 0.974528i | \(-0.428001\pi\) | ||||
0.224267 | + | 0.974528i | \(0.428001\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.9282 | 0.549887 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.0000 | −1.03000 | −0.514998 | − | 0.857191i | \(-0.672207\pi\) | ||||
−0.514998 | + | 0.857191i | \(0.672207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.07180 | 0.332812 | 0.166406 | − | 0.986057i | \(-0.446784\pi\) | ||||
0.166406 | + | 0.986057i | \(0.446784\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.28719 | −0.120433 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −65.5692 | −2.39585 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.3205 | 0.632034 | 0.316017 | − | 0.948753i | \(-0.397654\pi\) | ||||
0.316017 | + | 0.948753i | \(0.397654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.00000 | −0.145575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.14359 | −0.295984 | −0.147992 | − | 0.988989i | \(-0.547281\pi\) | ||||
−0.147992 | + | 0.988989i | \(0.547281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.8038 | 1.40664 | 0.703319 | − | 0.710874i | \(-0.251700\pi\) | ||||
0.703319 | + | 0.710874i | \(0.251700\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.53590 | 0.309020 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.7128 | −1.28951 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.7846 | 1.14618 | 0.573091 | − | 0.819492i | \(-0.305744\pi\) | ||||
0.573091 | + | 0.819492i | \(0.305744\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.7321 | −1.14132 | −0.570661 | − | 0.821186i | \(-0.693313\pi\) | ||||
−0.570661 | + | 0.821186i | \(0.693313\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.4308 | −0.518369 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.71281 | −0.133025 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.12436 | 0.147205 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.5359 | 0.446857 | 0.223428 | − | 0.974720i | \(-0.428275\pi\) | ||||
0.223428 | + | 0.974720i | \(0.428275\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7846 | 0.560528 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −48.5167 | −1.71855 | −0.859274 | − | 0.511515i | \(-0.829084\pi\) | ||||
−0.859274 | + | 0.511515i | \(0.829084\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.7128 | −1.40494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.00000 | −0.0705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.28719 | −0.292085 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.2679 | −0.923532 | −0.461766 | − | 0.887002i | \(-0.652784\pi\) | ||||
−0.461766 | + | 0.887002i | \(0.652784\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.5692 | −1.74061 | −0.870305 | − | 0.492513i | \(-0.836079\pi\) | ||||
−0.870305 | + | 0.492513i | \(0.836079\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.14359 | 0.214937 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.6603 | 0.930449 | 0.465225 | − | 0.885193i | \(-0.345974\pi\) | ||||
0.465225 | + | 0.885193i | \(0.345974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | 0.697156 | 0.348578 | − | 0.937280i | \(-0.386665\pi\) | ||||
0.348578 | + | 0.937280i | \(0.386665\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.8564 | 0.551381 | 0.275691 | − | 0.961246i | \(-0.411093\pi\) | ||||
0.275691 | + | 0.961246i | \(0.411093\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.85641 | −0.133939 | −0.0669693 | − | 0.997755i | \(-0.521333\pi\) | ||||
−0.0669693 | + | 0.997755i | \(0.521333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.6603 | −0.993019 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.82309 | 0.166910 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.9282 | −1.27490 | −0.637452 | − | 0.770490i | \(-0.720011\pi\) | ||||
−0.637452 | + | 0.770490i | \(0.720011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.7846 | 1.06154 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.85641 | −0.0638623 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.2487 | 0.833196 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −57.7128 | −1.97837 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.58846 | 0.122579 | 0.0612897 | − | 0.998120i | \(-0.480479\pi\) | ||||
0.0612897 | + | 0.998120i | \(0.480479\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.85641 | 0.0633398 | 0.0316699 | − | 0.999498i | \(-0.489917\pi\) | ||||
0.0316699 | + | 0.999498i | \(0.489917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.0718 | −0.649212 | −0.324606 | − | 0.945849i | \(-0.605232\pi\) | ||||
−0.324606 | + | 0.945849i | \(0.605232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.14359 | −0.0388833 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.9282 | −0.506405 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.3205 | −1.12902 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.21539 | −0.311537 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.3205 | −0.483569 | −0.241785 | − | 0.970330i | \(-0.577733\pi\) | ||||
−0.241785 | + | 0.970330i | \(0.577733\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.6410 | 0.628032 | 0.314016 | − | 0.949418i | \(-0.398325\pi\) | ||||
0.314016 | + | 0.949418i | \(0.398325\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.9282 | 1.71387 | 0.856935 | − | 0.515424i | \(-0.172366\pi\) | ||||
0.856935 | + | 0.515424i | \(0.172366\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.6410 | 0.827364 | 0.413682 | − | 0.910421i | \(-0.364242\pi\) | ||||
0.413682 | + | 0.910421i | \(0.364242\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.8564 | −0.867196 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.71281 | −0.124245 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.85641 | 0.0620528 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.6410 | −0.755120 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.7846 | 0.559176 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.32051 | 0.176860 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.78461 | −0.158870 | −0.0794352 | − | 0.996840i | \(-0.525312\pi\) | ||||
−0.0794352 | + | 0.996840i | \(0.525312\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.7846 | −1.55004 | −0.775022 | − | 0.631935i | \(-0.782261\pi\) | ||||
−0.775022 | + | 0.631935i | \(0.782261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.8564 | 0.723341 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −72.4974 | −2.39408 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.1769 | 1.16038 | 0.580190 | − | 0.814481i | \(-0.302978\pi\) | ||||
0.580190 | + | 0.814481i | \(0.302978\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.92820 | 0.293875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.8564 | −1.04743 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.41154 | 0.144738 | 0.0723690 | − | 0.997378i | \(-0.476944\pi\) | ||||
0.0723690 | + | 0.997378i | \(0.476944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.67949 | −0.0878168 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.07180 | −0.100458 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.5692 | −1.65202 | −0.826012 | − | 0.563652i | \(-0.809396\pi\) | ||||
−0.826012 | + | 0.563652i | \(0.809396\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.1244 | 0.590837 | 0.295419 | − | 0.955368i | \(-0.404541\pi\) | ||||
0.295419 | + | 0.955368i | \(0.404541\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.8564 | −2.01432 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.9282 | 0.420110 | 0.210055 | − | 0.977690i | \(-0.432636\pi\) | ||||
0.210055 | + | 0.977690i | \(0.432636\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.46410 | 0.144911 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.9808 | −0.452881 | −0.226441 | − | 0.974025i | \(-0.572709\pi\) | ||||
−0.226441 | + | 0.974025i | \(0.572709\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.10512 | −0.0681200 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.5692 | 0.373590 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.4256 | −0.723407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.09103 | −0.0351216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.32051 | −0.299727 | −0.149864 | − | 0.988707i | \(-0.547883\pi\) | ||||
−0.149864 | + | 0.988707i | \(0.547883\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.928203 | −0.0297875 | −0.0148937 | − | 0.999889i | \(-0.504741\pi\) | ||||
−0.0148937 | + | 0.999889i | \(0.504741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 65.5692 | 2.10205 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.0718 | −0.546175 | −0.273088 | − | 0.961989i | \(-0.588045\pi\) | ||||
−0.273088 | + | 0.961989i | \(0.588045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3923 | 0.332140 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.0000 | −1.14822 | −0.574111 | − | 0.818778i | \(-0.694652\pi\) | ||||
−0.574111 | + | 0.818778i | \(0.694652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.92820 | 0.125163 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 102.354 | 3.25466 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.1051 | −1.46458 | −0.732289 | − | 0.680994i | \(-0.761548\pi\) | ||||
−0.732289 | + | 0.680994i | \(0.761548\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.07180 | −0.0339782 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.1769 | −1.52578 | −0.762889 | − | 0.646529i | \(-0.776220\pi\) | ||||
−0.762889 | + | 0.646529i | \(0.776220\pi\) | |||||||
\(998\) | 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 | 648.2.a.e.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 648.2.a.h.1.1 | yes | 2 | ||
4.3 | odd | 2 | 1296.2.a.m.1.2 | 2 | |||
8.3 | odd | 2 | 5184.2.a.bz.1.1 | 2 | |||
8.5 | even | 2 | 5184.2.a.cb.1.1 | 2 | |||
9.2 | odd | 6 | 648.2.i.i.433.2 | 4 | |||
9.4 | even | 3 | 648.2.i.j.217.1 | 4 | |||
9.5 | odd | 6 | 648.2.i.i.217.2 | 4 | |||
9.7 | even | 3 | 648.2.i.j.433.1 | 4 | |||
12.11 | even | 2 | 1296.2.a.q.1.1 | 2 | |||
24.5 | odd | 2 | 5184.2.a.bg.1.2 | 2 | |||
24.11 | even | 2 | 5184.2.a.bi.1.2 | 2 | |||
36.7 | odd | 6 | 1296.2.i.t.433.1 | 4 | |||
36.11 | even | 6 | 1296.2.i.r.433.2 | 4 | |||
36.23 | even | 6 | 1296.2.i.r.865.2 | 4 | |||
36.31 | odd | 6 | 1296.2.i.t.865.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.2.a.e.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
648.2.a.h.1.1 | yes | 2 | 3.2 | odd | 2 | ||
648.2.i.i.217.2 | 4 | 9.5 | odd | 6 | |||
648.2.i.i.433.2 | 4 | 9.2 | odd | 6 | |||
648.2.i.j.217.1 | 4 | 9.4 | even | 3 | |||
648.2.i.j.433.1 | 4 | 9.7 | even | 3 | |||
1296.2.a.m.1.2 | 2 | 4.3 | odd | 2 | |||
1296.2.a.q.1.1 | 2 | 12.11 | even | 2 | |||
1296.2.i.r.433.2 | 4 | 36.11 | even | 6 | |||
1296.2.i.r.865.2 | 4 | 36.23 | even | 6 | |||
1296.2.i.t.433.1 | 4 | 36.7 | odd | 6 | |||
1296.2.i.t.865.1 | 4 | 36.31 | odd | 6 | |||
5184.2.a.bg.1.2 | 2 | 24.5 | odd | 2 | |||
5184.2.a.bi.1.2 | 2 | 24.11 | even | 2 | |||
5184.2.a.bz.1.1 | 2 | 8.3 | odd | 2 | |||
5184.2.a.cb.1.1 | 2 | 8.5 | even | 2 |