Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1932) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.30278 | −0.582619 | −0.291309 | − | 0.956629i | \(-0.594091\pi\) | ||||
−0.291309 | + | 0.956629i | \(0.594091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.60555 | −1.08711 | −0.543557 | − | 0.839372i | \(-0.682923\pi\) | ||||
−0.543557 | + | 0.839372i | \(0.682923\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.30278 | −1.19338 | −0.596688 | − | 0.802474i | \(-0.703517\pi\) | ||||
−0.596688 | + | 0.802474i | \(0.703517\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.30278 | −0.336375 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.394449 | 0.0904927 | 0.0452464 | − | 0.998976i | \(-0.485593\pi\) | ||||
0.0452464 | + | 0.998976i | \(0.485593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.30278 | −0.660555 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.60555 | −0.627646 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.30278 | 0.220209 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.21110 | 1.02110 | 0.510549 | − | 0.859848i | \(-0.329442\pi\) | ||||
0.510549 | + | 0.859848i | \(0.329442\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.30278 | −0.688996 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.60555 | 0.250745 | 0.125372 | − | 0.992110i | \(-0.459987\pi\) | ||||
0.125372 | + | 0.992110i | \(0.459987\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.90833 | −0.443516 | −0.221758 | − | 0.975102i | \(-0.571179\pi\) | ||||
−0.221758 | + | 0.975102i | \(0.571179\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.30278 | −0.194206 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.39445 | 0.495131 | 0.247566 | − | 0.968871i | \(-0.420369\pi\) | ||||
0.247566 | + | 0.968871i | \(0.420369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.09167 | 0.287313 | 0.143657 | − | 0.989628i | \(-0.454114\pi\) | ||||
0.143657 | + | 0.989628i | \(0.454114\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.69722 | 0.633374 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.394449 | 0.0522460 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0916731 | −0.0119348 | −0.00596741 | − | 0.999982i | \(-0.501899\pi\) | ||||
−0.00596741 | + | 0.999982i | \(0.501899\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.51388 | −1.21813 | −0.609064 | − | 0.793121i | \(-0.708455\pi\) | ||||
−0.609064 | + | 0.793121i | \(0.708455\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.60555 | 0.695283 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.1194 | 1.84713 | 0.923566 | − | 0.383439i | \(-0.125260\pi\) | ||||
0.923566 | + | 0.383439i | \(0.125260\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.09167 | 0.129558 | 0.0647789 | − | 0.997900i | \(-0.479366\pi\) | ||||
0.0647789 | + | 0.997900i | \(0.479366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.8167 | −1.26599 | −0.632997 | − | 0.774154i | \(-0.718175\pi\) | ||||
−0.632997 | + | 0.774154i | \(0.718175\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.30278 | −0.381372 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.60555 | 0.410891 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6056 | 1.53074 | 0.765372 | − | 0.643588i | \(-0.222555\pi\) | ||||
0.765372 | + | 0.643588i | \(0.222555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.60555 | 0.834818 | 0.417409 | − | 0.908719i | \(-0.362938\pi\) | ||||
0.417409 | + | 0.908719i | \(0.362938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.90833 | 0.423918 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.302776 | −0.0320942 | −0.0160471 | − | 0.999871i | \(-0.505108\pi\) | ||||
−0.0160471 | + | 0.999871i | \(0.505108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.30278 | 0.451053 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.513878 | −0.0527228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0000 | −1.11688 | −0.558440 | − | 0.829545i | \(-0.688600\pi\) | ||||
−0.558440 | + | 0.829545i | \(0.688600\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.60555 | −0.362372 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.51388 | 0.847163 | 0.423581 | − | 0.905858i | \(-0.360773\pi\) | ||||
0.423581 | + | 0.905858i | \(0.360773\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0000 | 1.57653 | 0.788263 | − | 0.615338i | \(-0.210980\pi\) | ||||
0.788263 | + | 0.615338i | \(0.210980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.30278 | 0.127138 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.51388 | 0.533047 | 0.266523 | − | 0.963828i | \(-0.414125\pi\) | ||||
0.266523 | + | 0.963828i | \(0.414125\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0916731 | −0.00878069 | −0.00439034 | − | 0.999990i | \(-0.501397\pi\) | ||||
−0.00439034 | + | 0.999990i | \(0.501397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.21110 | 0.589532 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.5139 | −1.36535 | −0.682675 | − | 0.730722i | \(-0.739184\pi\) | ||||
−0.682675 | + | 0.730722i | \(0.739184\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.30278 | −0.121484 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.30278 | −0.397792 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | 0.275010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.60555 | 0.144768 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8167 | 0.967471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.302776 | 0.0268670 | 0.0134335 | − | 0.999910i | \(-0.495724\pi\) | ||||
0.0134335 | + | 0.999910i | \(0.495724\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.90833 | −0.256064 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.8167 | 1.46928 | 0.734639 | − | 0.678458i | \(-0.237352\pi\) | ||||
0.734639 | + | 0.678458i | \(0.237352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.394449 | −0.0342030 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.30278 | −0.112125 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.0278 | 1.71109 | 0.855543 | − | 0.517731i | \(-0.173223\pi\) | ||||
0.855543 | + | 0.517731i | \(0.173223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.69722 | 0.568051 | 0.284026 | − | 0.958817i | \(-0.408330\pi\) | ||||
0.284026 | + | 0.958817i | \(0.408330\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.39445 | 0.285864 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.5139 | 1.29734 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.30278 | −0.108190 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.81665 | −0.148826 | −0.0744130 | − | 0.997228i | \(-0.523708\pi\) | ||||
−0.0744130 | + | 0.997228i | \(0.523708\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.605551 | −0.0492791 | −0.0246395 | − | 0.999696i | \(-0.507844\pi\) | ||||
−0.0246395 | + | 0.999696i | \(0.507844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.30278 | 0.104641 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0278 | −1.03973 | −0.519864 | − | 0.854249i | \(-0.674017\pi\) | ||||
−0.519864 | + | 0.854249i | \(0.674017\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.09167 | 0.165880 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.48612 | 0.429706 | 0.214853 | − | 0.976646i | \(-0.431073\pi\) | ||||
0.214853 | + | 0.976646i | \(0.431073\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.69722 | 0.365678 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.81665 | −0.372724 | −0.186362 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186362 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.51388 | 0.424144 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.394449 | 0.0301642 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0278 | 1.37062 | 0.685312 | − | 0.728249i | \(-0.259666\pi\) | ||||
0.685312 | + | 0.728249i | \(0.259666\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.30278 | 0.249666 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0916731 | −0.00689057 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.90833 | −0.740583 | −0.370292 | − | 0.928916i | \(-0.620742\pi\) | ||||
−0.370292 | + | 0.928916i | \(0.620742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.4222 | 1.44364 | 0.721821 | − | 0.692080i | \(-0.243306\pi\) | ||||
0.721821 | + | 0.692080i | \(0.243306\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.51388 | −0.703286 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.09167 | −0.594912 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8167 | 0.790992 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.0278 | 1.08737 | 0.543685 | − | 0.839289i | \(-0.317029\pi\) | ||||
0.543685 | + | 0.839289i | \(0.317029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8167 | −0.850581 | −0.425291 | − | 0.905057i | \(-0.639828\pi\) | ||||
−0.425291 | + | 0.905057i | \(0.639828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.60555 | 0.401422 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.6972 | 1.40337 | 0.701685 | − | 0.712488i | \(-0.252432\pi\) | ||||
0.701685 | + | 0.712488i | \(0.252432\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.3028 | −1.65189 | −0.825945 | − | 0.563751i | \(-0.809358\pi\) | ||||
−0.825945 | + | 0.563751i | \(0.809358\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.1194 | 1.06644 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.00000 | −0.0701862 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.09167 | −0.146089 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.42221 | −0.0983760 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.39445 | 0.440212 | 0.220106 | − | 0.975476i | \(-0.429360\pi\) | ||||
0.220106 | + | 0.975476i | \(0.429360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.09167 | 0.0748002 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.78890 | 0.258401 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.00000 | 0.0678844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.8167 | −0.730922 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.9083 | 0.868308 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.48612 | 0.635238 | 0.317619 | − | 0.948218i | \(-0.397117\pi\) | ||||
0.317619 | + | 0.948218i | \(0.397117\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.30278 | −0.220185 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.3028 | −1.54666 | −0.773330 | − | 0.634004i | \(-0.781410\pi\) | ||||
−0.773330 | + | 0.634004i | \(0.781410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.3028 | −1.01124 | −0.505618 | − | 0.862757i | \(-0.668735\pi\) | ||||
−0.505618 | + | 0.862757i | \(0.668735\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.60555 | 0.237228 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.3305 | −1.20087 | −0.600437 | − | 0.799672i | \(-0.705006\pi\) | ||||
−0.600437 | + | 0.799672i | \(0.705006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.42221 | −0.288473 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.6056 | 0.883776 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3028 | −0.860485 | −0.430243 | − | 0.902713i | \(-0.641572\pi\) | ||||
−0.430243 | + | 0.902713i | \(0.641572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.2111 | 1.30191 | 0.650956 | − | 0.759116i | \(-0.274368\pi\) | ||||
0.650956 | + | 0.759116i | \(0.274368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.30278 | −0.0832313 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.69722 | −0.107992 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.60555 | 0.481982 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6056 | 0.669416 | 0.334708 | − | 0.942322i | \(-0.391362\pi\) | ||||
0.334708 | + | 0.942322i | \(0.391362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.60555 | −0.226679 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.90833 | 0.244749 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.0278 | −1.43643 | −0.718216 | − | 0.695820i | \(-0.755041\pi\) | ||||
−0.718216 | + | 0.695820i | \(0.755041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.21110 | −0.385939 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.6333 | 1.51895 | 0.759477 | − | 0.650534i | \(-0.225455\pi\) | ||||
0.759477 | + | 0.650534i | \(0.225455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.72498 | −0.167394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.302776 | −0.0185296 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.7250 | 1.50751 | 0.753754 | − | 0.657156i | \(-0.228241\pi\) | ||||
0.753754 | + | 0.657156i | \(0.228241\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8167 | −0.657065 | −0.328532 | − | 0.944493i | \(-0.606554\pi\) | ||||
−0.328532 | + | 0.944493i | \(0.606554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.30278 | 0.260416 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.9083 | 0.718099 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3305 | 1.40180 | 0.700898 | − | 0.713262i | \(-0.252783\pi\) | ||||
0.700898 | + | 0.713262i | \(0.252783\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.81665 | −0.227682 | −0.113841 | − | 0.993499i | \(-0.536316\pi\) | ||||
−0.113841 | + | 0.993499i | \(0.536316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.30278 | −0.552993 | −0.276496 | − | 0.961015i | \(-0.589173\pi\) | ||||
−0.276496 | + | 0.961015i | \(0.589173\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.513878 | −0.0304395 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.60555 | −0.0947727 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0000 | −0.644831 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.21110 | 0.0707534 | 0.0353767 | − | 0.999374i | \(-0.488737\pi\) | ||||
0.0353767 | + | 0.999374i | \(0.488737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.119429 | 0.00695345 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.60555 | −0.209215 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.30278 | −0.248836 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.90833 | 0.167633 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.51388 | 0.489110 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.3944 | 0.709704 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.4222 | 0.880192 | 0.440096 | − | 0.897951i | \(-0.354944\pi\) | ||||
0.440096 | + | 0.897951i | \(0.354944\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0000 | 0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.90833 | 0.278326 | 0.139163 | − | 0.990270i | \(-0.455559\pi\) | ||||
0.139163 | + | 0.990270i | \(0.455559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.7889 | −0.609825 | −0.304912 | − | 0.952380i | \(-0.598627\pi\) | ||||
−0.304912 | + | 0.952380i | \(0.598627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.30278 | 0.0734031 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.30278 | −0.0731712 | −0.0365856 | − | 0.999331i | \(-0.511648\pi\) | ||||
−0.0365856 | + | 0.999331i | \(0.511648\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.60555 | −0.201872 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.51388 | 0.307755 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.18335 | −0.0658431 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.2111 | 0.788290 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.0916731 | −0.00506953 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.39445 | −0.187142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.78890 | −0.263222 | −0.131611 | − | 0.991301i | \(-0.542015\pi\) | ||||
−0.131611 | + | 0.991301i | \(0.542015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.21110 | 0.340366 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.6972 | −1.07617 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.51388 | −0.300360 | −0.150180 | − | 0.988659i | \(-0.547985\pi\) | ||||
−0.150180 | + | 0.988659i | \(0.547985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.5139 | −0.788286 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.60555 | 0.195252 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.30278 | −0.0701391 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.18335 | −0.385622 | −0.192811 | − | 0.981236i | \(-0.561760\pi\) | ||||
−0.192811 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.5139 | −1.20514 | −0.602570 | − | 0.798066i | \(-0.705857\pi\) | ||||
−0.602570 | + | 0.798066i | \(0.705857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.30278 | −0.229665 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.39445 | 0.233893 | 0.116946 | − | 0.993138i | \(-0.462689\pi\) | ||||
0.116946 | + | 0.993138i | \(0.462689\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.42221 | −0.0754828 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.00000 | 0.158777 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.9083 | 1.15628 | 0.578139 | − | 0.815939i | \(-0.303779\pi\) | ||||
0.578139 | + | 0.815939i | \(0.303779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8444 | −0.991811 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0917 | 0.737592 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.72498 | −0.142243 | −0.0711214 | − | 0.997468i | \(-0.522658\pi\) | ||||
−0.0711214 | + | 0.997468i | \(0.522658\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.60555 | 0.0835817 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.09167 | −0.108594 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.57779 | 0.133473 | 0.0667366 | − | 0.997771i | \(-0.478741\pi\) | ||||
0.0667366 | + | 0.997771i | \(0.478741\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.8167 | 0.558570 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.30278 | −0.221604 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.21110 | −0.473143 | −0.236571 | − | 0.971614i | \(-0.576024\pi\) | ||||
−0.236571 | + | 0.971614i | \(0.576024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.302776 | 0.0155117 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.02776 | −0.308004 | −0.154002 | − | 0.988071i | \(-0.549216\pi\) | ||||
−0.154002 | + | 0.988071i | \(0.549216\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.69722 | −0.239393 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.90833 | −0.147839 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.2111 | 1.53176 | 0.765882 | − | 0.642981i | \(-0.222303\pi\) | ||||
0.765882 | + | 0.642981i | \(0.222303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.00000 | −0.151717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.8167 | 0.848288 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.7250 | −0.891841 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.39445 | −0.170362 | −0.0851812 | − | 0.996365i | \(-0.527147\pi\) | ||||
−0.0851812 | + | 0.996365i | \(0.527147\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.394449 | −0.0197471 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4222 | 0.670273 | 0.335136 | − | 0.942170i | \(-0.391218\pi\) | ||||
0.335136 | + | 0.942170i | \(0.391218\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.30278 | 0.214337 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.30278 | −0.0647354 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.3944 | −1.11005 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.42221 | 0.367004 | 0.183502 | − | 0.983019i | \(-0.441257\pi\) | ||||
0.183502 | + | 0.983019i | \(0.441257\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.0278 | 0.987896 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0916731 | 0.00451094 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.90833 | −0.486381 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.69722 | 0.327964 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.51388 | 0.415930 | 0.207965 | − | 0.978136i | \(-0.433316\pi\) | ||||
0.207965 | + | 0.978136i | \(0.433316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.09167 | 0.0532049 | 0.0266024 | − | 0.999646i | \(-0.491531\pi\) | ||||
0.0266024 | + | 0.999646i | \(0.491531\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.39445 | 0.165044 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.90833 | 0.480624 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.51388 | 0.460409 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.5139 | 0.749017 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.9083 | 0.621772 | 0.310886 | − | 0.950447i | \(-0.399374\pi\) | ||||
0.310886 | + | 0.950447i | \(0.399374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.02776 | 0.0493908 | 0.0246954 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246954 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.30278 | −0.0624633 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.394449 | 0.0188690 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6333 | 0.507500 | 0.253750 | − | 0.967270i | \(-0.418336\pi\) | ||||
0.253750 | + | 0.967270i | \(0.418336\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.6333 | −0.932807 | −0.466403 | − | 0.884572i | \(-0.654450\pi\) | ||||
−0.466403 | + | 0.884572i | \(0.654450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.394449 | 0.0186987 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.81665 | −0.0859248 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1194 | 1.56300 | 0.781501 | − | 0.623904i | \(-0.214454\pi\) | ||||
0.781501 | + | 0.623904i | \(0.214454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.78890 | −0.272589 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.605551 | −0.0284513 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.60555 | −0.262792 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.7250 | 1.48403 | 0.742016 | − | 0.670382i | \(-0.233870\pi\) | ||||
0.742016 | + | 0.670382i | \(0.233870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.00000 | −0.140028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.5416 | −1.18959 | −0.594796 | − | 0.803876i | \(-0.702767\pi\) | ||||
−0.594796 | + | 0.803876i | \(0.702767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.7889 | −0.547877 | −0.273938 | − | 0.961747i | \(-0.588326\pi\) | ||||
−0.273938 | + | 0.961747i | \(0.588326\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.30278 | 0.0604148 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.3944 | 0.573547 | 0.286773 | − | 0.957998i | \(-0.407417\pi\) | ||||
0.286773 | + | 0.957998i | \(0.407417\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.1194 | −0.698150 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.0278 | −0.600287 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.4861 | 0.482152 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.30278 | −0.0597754 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.09167 | 0.0957711 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.4222 | −0.613276 | −0.306638 | − | 0.951826i | \(-0.599204\pi\) | ||||
−0.306638 | + | 0.951826i | \(0.599204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.7250 | −1.21855 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3305 | 0.650716 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.2111 | 1.55025 | 0.775127 | − | 0.631806i | \(-0.217686\pi\) | ||||
0.775127 | + | 0.631806i | \(0.217686\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.48612 | 0.248091 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.3305 | −1.23341 | −0.616705 | − | 0.787194i | \(-0.711533\pi\) | ||||
−0.616705 | + | 0.787194i | \(0.711533\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.00000 | −0.135113 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.69722 | 0.211125 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.09167 | −0.0489682 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5416 | 0.785271 | 0.392636 | − | 0.919694i | \(-0.371563\pi\) | ||||
0.392636 | + | 0.919694i | \(0.371563\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.81665 | −0.215192 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.6972 | 0.566141 | 0.283071 | − | 0.959099i | \(-0.408647\pi\) | ||||
0.283071 | + | 0.959099i | \(0.408647\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.0917 | −0.493573 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.51388 | 0.244880 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.60555 | −0.381434 | −0.190717 | − | 0.981645i | \(-0.561081\pi\) | ||||
−0.190717 | + | 0.981645i | \(0.561081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8167 | 0.478501 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.394449 | 0.0174153 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.8444 | −0.918514 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.2389 | −0.538264 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0278 | 0.791331 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.2111 | 1.71787 | 0.858935 | − | 0.512085i | \(-0.171127\pi\) | ||||
0.858935 | + | 0.512085i | \(0.171127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.00000 | −0.0874539 | −0.0437269 | − | 0.999044i | \(-0.513923\pi\) | ||||
−0.0437269 | + | 0.999044i | \(0.513923\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.30278 | 0.144145 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | 0.130682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0916731 | −0.00397827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.90833 | −0.299233 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.18335 | −0.310563 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.90833 | −0.427576 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.60555 | −0.155302 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.60555 | −0.369982 | −0.184991 | − | 0.982740i | \(-0.559226\pi\) | ||||
−0.184991 | + | 0.982740i | \(0.559226\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.4222 | 0.833487 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.119429 | 0.00511580 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.5139 | −0.706082 | −0.353041 | − | 0.935608i | \(-0.614852\pi\) | ||||
−0.353041 | + | 0.935608i | \(0.614852\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.51388 | −0.406042 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.394449 | 0.0168041 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.6056 | −0.578567 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.09167 | −0.343472 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.4500 | 1.50206 | 0.751032 | − | 0.660266i | \(-0.229557\pi\) | ||||
0.751032 | + | 0.660266i | \(0.229557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5139 | 0.529281 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.8167 | 0.456679 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.1194 | 0.763643 | 0.381821 | − | 0.924236i | \(-0.375297\pi\) | ||||
0.381821 | + | 0.924236i | \(0.375297\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.9083 | 0.795479 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.00000 | −0.167689 | −0.0838444 | − | 0.996479i | \(-0.526720\pi\) | ||||
−0.0838444 | + | 0.996479i | \(0.526720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.816654 | 0.0341759 | 0.0170879 | − | 0.999854i | \(-0.494560\pi\) | ||||
0.0170879 | + | 0.999854i | \(0.494560\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.0278 | 0.627794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.30278 | −0.137735 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.6333 | 1.06713 | 0.533564 | − | 0.845760i | \(-0.320852\pi\) | ||||
0.533564 | + | 0.845760i | \(0.320852\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.8167 | −0.491083 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.60555 | −0.315531 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.54163 | −0.312343 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.60555 | 0.231761 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.30278 | −0.0950457 | −0.0475229 | − | 0.998870i | \(-0.515133\pi\) | ||||
−0.0475229 | + | 0.998870i | \(0.515133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.394449 | −0.0162530 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.6972 | 0.810236 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.0278 | −1.02777 | −0.513883 | − | 0.857860i | \(-0.671794\pi\) | ||||
−0.513883 | + | 0.857860i | \(0.671794\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.90833 | −0.160226 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.3028 | −0.953719 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.7250 | 0.601646 | 0.300823 | − | 0.953680i | \(-0.402739\pi\) | ||||
0.300823 | + | 0.953680i | \(0.402739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.9361 | 0.446092 | 0.223046 | − | 0.974808i | \(-0.428400\pi\) | ||||
0.223046 | + | 0.974808i | \(0.428400\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.1194 | 0.615711 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.60555 | −0.105931 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.1194 | −1.14133 | −0.570666 | − | 0.821182i | \(-0.693315\pi\) | ||||
−0.570666 | + | 0.821182i | \(0.693315\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.00000 | −0.0405220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.6056 | −0.590877 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.4500 | 0.825966 | 0.412983 | − | 0.910739i | \(-0.364487\pi\) | ||||
0.412983 | + | 0.910739i | \(0.364487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.09167 | −0.0843444 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.1194 | 0.729461 | 0.364730 | − | 0.931113i | \(-0.381161\pi\) | ||||
0.364730 | + | 0.931113i | \(0.381161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.33053 | 0.294639 | 0.147319 | − | 0.989089i | \(-0.452935\pi\) | ||||
0.147319 | + | 0.989089i | \(0.452935\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.302776 | 0.0121304 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.42221 | 0.0968882 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.42221 | −0.0567974 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.6333 | −0.742959 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.0000 | −0.995234 | −0.497617 | − | 0.867397i | \(-0.665792\pi\) | ||||
−0.497617 | + | 0.867397i | \(0.665792\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.39445 | 0.254157 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.394449 | −0.0156532 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.30278 | −0.170482 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.09167 | 0.0431859 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.1472 | −1.54622 | −0.773110 | − | 0.634271i | \(-0.781300\pi\) | ||||
−0.773110 | + | 0.634271i | \(0.781300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.2750 | 0.681260 | 0.340630 | − | 0.940197i | \(-0.389360\pi\) | ||||
0.340630 | + | 0.940197i | \(0.389360\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.78890 | 0.149188 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.9083 | 1.33307 | 0.666537 | − | 0.745472i | \(-0.267776\pi\) | ||||
0.666537 | + | 0.745472i | \(0.267776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.330532 | 0.0129745 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.00000 | 0.0391931 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.5139 | 0.411440 | 0.205720 | − | 0.978611i | \(-0.434046\pi\) | ||||
0.205720 | + | 0.978611i | \(0.434046\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.9083 | −0.856029 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.8167 | −0.421998 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.6056 | −1.07536 | −0.537680 | − | 0.843149i | \(-0.680699\pi\) | ||||
−0.537680 | + | 0.843149i | \(0.680699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.21110 | 0.241584 | 0.120792 | − | 0.992678i | \(-0.461457\pi\) | ||||
0.120792 | + | 0.992678i | \(0.461457\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9083 | 0.501318 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.513878 | 0.0199273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.48612 | 0.366755 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.3028 | 1.32424 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.4222 | −1.28833 | −0.644166 | − | 0.764886i | \(-0.722795\pi\) | ||||
−0.644166 | + | 0.764886i | \(0.722795\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.30278 | −0.127124 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.3028 | 1.31836 | 0.659181 | − | 0.751984i | \(-0.270903\pi\) | ||||
0.659181 | + | 0.751984i | \(0.270903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.0000 | 0.422141 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.3028 | −0.892964 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.3944 | 1.54565 | 0.772825 | − | 0.634619i | \(-0.218843\pi\) | ||||
0.772825 | + | 0.634619i | \(0.218843\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.0917 | −0.996912 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.3028 | −0.583837 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.00000 | −0.342873 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.9361 | −1.44316 | −0.721578 | − | 0.692333i | \(-0.756583\pi\) | ||||
−0.721578 | + | 0.692333i | \(0.756583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.60555 | 0.136964 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.72498 | −0.330957 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.81665 | −0.182444 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.3305 | −0.693324 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.1194 | 1.02429 | 0.512143 | − | 0.858900i | \(-0.328852\pi\) | ||||
0.512143 | + | 0.858900i | \(0.328852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.44996 | 0.0924020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.42221 | −0.166550 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.51388 | −0.320197 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9083 | 0.635006 | 0.317503 | − | 0.948257i | \(-0.397156\pi\) | ||||
0.317503 | + | 0.948257i | \(0.397156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6056 | 0.510248 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.00000 | −0.0374503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.2111 | −0.755852 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.3028 | −0.496801 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.0000 | 0.932343 | 0.466171 | − | 0.884694i | \(-0.345633\pi\) | ||||
0.466171 | + | 0.884694i | \(0.345633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.2111 | 0.751659 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.30278 | −0.122662 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.60555 | 0.133722 | 0.0668612 | − | 0.997762i | \(-0.478702\pi\) | ||||
0.0668612 | + | 0.997762i | \(0.478702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.72498 | 0.322705 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.0278 | −0.481191 | −0.240596 | − | 0.970625i | \(-0.577343\pi\) | ||||
−0.240596 | + | 0.970625i | \(0.577343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.30278 | −0.0480536 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −54.5139 | −2.00804 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.9722 | −0.513977 | −0.256989 | − | 0.966414i | \(-0.582730\pi\) | ||||
−0.256989 | + | 0.966414i | \(0.582730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.69722 | −0.0623491 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.7250 | −0.943758 | −0.471879 | − | 0.881663i | \(-0.656424\pi\) | ||||
−0.471879 | + | 0.881663i | \(0.656424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.36669 | 0.0867089 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.60555 | 0.278273 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.51388 | −0.201473 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4861 | −0.638078 | −0.319039 | − | 0.947742i | \(-0.603360\pi\) | ||||
−0.319039 | + | 0.947742i | \(0.603360\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.6056 | 0.386488 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.788897 | 0.0287109 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.4222 | −0.415147 | −0.207574 | − | 0.978219i | \(-0.566557\pi\) | ||||
−0.207574 | + | 0.978219i | \(0.566557\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.60555 | −0.130873 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.21110 | 0.0439024 | 0.0219512 | − | 0.999759i | \(-0.493012\pi\) | ||||
0.0219512 | + | 0.999759i | \(0.493012\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0916731 | 0.00331879 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.90833 | 0.141306 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.394449 | 0.0142427 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.6611 | 1.32203 | 0.661016 | − | 0.750372i | \(-0.270126\pi\) | ||||
0.661016 | + | 0.750372i | \(0.270126\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.0278 | −0.829324 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0278 | 0.432608 | 0.216304 | − | 0.976326i | \(-0.430600\pi\) | ||||
0.216304 | + | 0.976326i | \(0.430600\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.30278 | 0.118639 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.21110 | −0.222822 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.633308 | 0.0226906 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.93608 | −0.140844 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.9722 | 0.605765 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.3583 | −1.47426 | −0.737132 | − | 0.675749i | \(-0.763820\pi\) | ||||
−0.737132 | + | 0.675749i | \(0.763820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.6333 | 0.876969 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.5139 | 0.516054 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.9361 | 1.45368 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.72498 | −0.0966451 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.39445 | −0.261925 | −0.130962 | − | 0.991387i | \(-0.541807\pi\) | ||||
−0.130962 | + | 0.991387i | \(0.541807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.1833 | −0.360261 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.302776 | −0.0106981 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.0000 | 1.37628 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.30278 | 0.0459168 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.7250 | 0.870361 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.5416 | −1.63632 | −0.818158 | − | 0.574993i | \(-0.805005\pi\) | ||||
−0.818158 | + | 0.574993i | \(0.805005\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.2389 | 0.886256 | 0.443128 | − | 0.896458i | \(-0.353869\pi\) | ||||
0.443128 | + | 0.896458i | \(0.353869\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.8167 | −0.379357 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.14719 | −0.250355 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.14719 | −0.0401350 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.30278 | 0.150351 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.8167 | −0.482205 | −0.241102 | − | 0.970500i | \(-0.577509\pi\) | ||||
−0.241102 | + | 0.970500i | \(0.577509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.6695 | 0.406772 | 0.203386 | − | 0.979099i | \(-0.434805\pi\) | ||||
0.203386 | + | 0.979099i | \(0.434805\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.9083 | 0.414595 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.5416 | 0.679529 | 0.339765 | − | 0.940511i | \(-0.389653\pi\) | ||||
0.339765 | + | 0.940511i | \(0.389653\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.8444 | −1.31439 | −0.657195 | − | 0.753720i | \(-0.728257\pi\) | ||||
−0.657195 | + | 0.753720i | \(0.728257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.3305 | 0.809327 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.00000 | −0.103944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.27502 | 0.217156 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.3028 | −1.18426 | −0.592132 | − | 0.805841i | \(-0.701713\pi\) | ||||
−0.592132 | + | 0.805841i | \(0.701713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.81665 | −0.131453 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.18335 | −0.247115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.30278 | −0.319270 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.21110 | 0.212914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.183346 | 0.00627765 | 0.00313883 | − | 0.999995i | \(-0.499001\pi\) | ||||
0.00313883 | + | 0.999995i | \(0.499001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.513878 | −0.0175743 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.18335 | −0.142900 | −0.0714502 | − | 0.997444i | \(-0.522763\pi\) | ||||
−0.0714502 | + | 0.997444i | \(0.522763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.78890 | −0.163395 | −0.0816975 | − | 0.996657i | \(-0.526034\pi\) | ||||
−0.0816975 | + | 0.996657i | \(0.526034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.60555 | −0.0547170 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.6056 | 0.905663 | 0.452832 | − | 0.891596i | \(-0.350414\pi\) | ||||
0.452832 | + | 0.891596i | \(0.350414\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.4861 | −0.798552 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.0555 | −1.66409 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −65.0555 | −2.20432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.0000 | −0.372294 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.8167 | −0.365670 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.78890 | −0.0941744 | −0.0470872 | − | 0.998891i | \(-0.514994\pi\) | ||||
−0.0470872 | + | 0.998891i | \(0.514994\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.21110 | 0.0408495 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.6611 | −1.10038 | −0.550190 | − | 0.835040i | \(-0.685445\pi\) | ||||
−0.550190 | + | 0.835040i | \(0.685445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.1194 | 0.407851 | 0.203926 | − | 0.978986i | \(-0.434630\pi\) | ||||
0.203926 | + | 0.978986i | \(0.434630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.119429 | 0.00401458 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.5139 | −1.79682 | −0.898410 | − | 0.439158i | \(-0.855277\pi\) | ||||
−0.898410 | + | 0.439158i | \(0.855277\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.302776 | −0.0101548 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.60555 | −0.120791 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.33894 | 0.0448058 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.9083 | 0.431478 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.30278 | −0.143665 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00000 | −0.0333519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.27502 | −0.209051 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.90833 | 0.0967831 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.3028 | −0.841093 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7250 | 1.31905 | 0.659523 | − | 0.751684i | \(-0.270758\pi\) | ||||
0.659523 | + | 0.751684i | \(0.270758\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.51388 | 0.282388 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.39445 | 0.244989 | 0.122495 | − | 0.992469i | \(-0.460911\pi\) | ||||
0.122495 | + | 0.992469i | \(0.460911\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.4222 | −0.907543 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.3944 | 0.409748 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.8167 | −0.555335 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.2666 | 1.13035 | 0.565176 | − | 0.824971i | \(-0.308808\pi\) | ||||
0.565176 | + | 0.824971i | \(0.308808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.4222 | 0.508179 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.69722 | −0.154611 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.5139 | −0.674492 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.0000 | 0.525509 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.90833 | 0.128228 | 0.0641140 | − | 0.997943i | \(-0.479578\pi\) | ||||
0.0641140 | + | 0.997943i | \(0.479578\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.394449 | 0.0129275 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.90833 | 0.160691 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.0917 | −0.460847 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.8722 | −1.46591 | −0.732955 | − | 0.680277i | \(-0.761859\pi\) | ||||
−0.732955 | + | 0.680277i | \(0.761859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.7889 | −0.352082 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.84441 | 0.288320 | 0.144160 | − | 0.989554i | \(-0.453952\pi\) | ||||
0.144160 | + | 0.989554i | \(0.453952\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.60555 | 0.0522839 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.30278 | 0.0423793 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.5778 | 0.636193 | 0.318096 | − | 0.948058i | \(-0.396956\pi\) | ||||
0.318096 | + | 0.948058i | \(0.396956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.5416 | 1.51081 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.30278 | −0.0422454 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.33053 | 0.237459 | 0.118730 | − | 0.992927i | \(-0.462118\pi\) | ||||
0.118730 | + | 0.992927i | \(0.462118\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.5778 | −0.633523 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.60555 | −0.116551 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.0278 | −0.646730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.51388 | 0.177682 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.3944 | 0.495565 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.6333 | −1.59610 | −0.798050 | − | 0.602592i | \(-0.794135\pi\) | ||||
−0.798050 | + | 0.602592i | \(0.794135\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.18335 | −0.0380146 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.7250 | 1.75621 | 0.878104 | − | 0.478470i | \(-0.158808\pi\) | ||||
0.878104 | + | 0.478470i | \(0.158808\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.69722 | −0.214703 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.2111 | 0.455120 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.4861 | 0.911352 | 0.455676 | − | 0.890146i | \(-0.349398\pi\) | ||||
0.455676 | + | 0.890146i | \(0.349398\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.09167 | 0.0348900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.0916731 | −0.00292690 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.2389 | 1.57048 | 0.785238 | − | 0.619194i | \(-0.212541\pi\) | ||||
0.785238 | + | 0.619194i | \(0.212541\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.6611 | −0.817629 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.39445 | −0.108046 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.90833 | −0.0924794 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.3028 | −0.390811 | −0.195405 | − | 0.980723i | \(-0.562602\pi\) | ||||
−0.195405 | + | 0.980723i | \(0.562602\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.78890 | −0.151971 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.3583 | 0.962422 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.4222 | 1.31185 | 0.655927 | − | 0.754824i | \(-0.272278\pi\) | ||||
0.655927 | + | 0.754824i | \(0.272278\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.21110 | 0.196511 |
(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 | 7728.2.a.bk.1.1 | 2 | ||
4.3 | odd | 2 | 1932.2.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 5796.2.a.k.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.e.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
5796.2.a.k.1.2 | 2 | 12.11 | even | 2 | |||
7728.2.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial |