Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6480,2,Mod(1,6480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6480.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6480.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: | \(51.7430605098\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6480.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.514137 | 0.194325 | 0.0971627 | − | 0.995269i | \(-0.469023\pi\) | ||||
0.0971627 | + | 0.995269i | \(0.469023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.32088 | 1.00128 | 0.500642 | − | 0.865654i | \(-0.333097\pi\) | ||||
0.500642 | + | 0.865654i | \(0.333097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.32088 | −0.366347 | −0.183174 | − | 0.983081i | \(-0.558637\pi\) | ||||
−0.183174 | + | 0.983081i | \(0.558637\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.32088 | −0.805433 | −0.402716 | − | 0.915325i | \(-0.631934\pi\) | ||||
−0.402716 | + | 0.915325i | \(0.631934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.32088 | 0.303032 | 0.151516 | − | 0.988455i | \(-0.451585\pi\) | ||||
0.151516 | + | 0.988455i | \(0.451585\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.12763 | −0.860671 | −0.430335 | − | 0.902669i | \(-0.641605\pi\) | ||||
−0.430335 | + | 0.902669i | \(0.641605\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.38650 | −0.257467 | −0.128734 | − | 0.991679i | \(-0.541091\pi\) | ||||
−0.128734 | + | 0.991679i | \(0.541091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.73566 | −1.56897 | −0.784486 | − | 0.620147i | \(-0.787073\pi\) | ||||
−0.784486 | + | 0.620147i | \(0.787073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.514137 | 0.0869050 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.292611 | 0.0481049 | 0.0240524 | − | 0.999711i | \(-0.492343\pi\) | ||||
0.0240524 | + | 0.999711i | \(0.492343\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.3492 | −1.77244 | −0.886220 | − | 0.463264i | \(-0.846678\pi\) | ||||
−0.886220 | + | 0.463264i | \(0.846678\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3492 | −1.57823 | −0.789116 | − | 0.614244i | \(-0.789461\pi\) | ||||
−0.789116 | + | 0.614244i | \(0.789461\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.86330 | 0.709385 | 0.354692 | − | 0.934983i | \(-0.384586\pi\) | ||||
0.354692 | + | 0.934983i | \(0.384586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.73566 | −0.962238 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.02827 | −0.690687 | −0.345343 | − | 0.938476i | \(-0.612238\pi\) | ||||
−0.345343 | + | 0.938476i | \(0.612238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.32088 | 0.447788 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.02827 | 0.654625 | 0.327313 | − | 0.944916i | \(-0.393857\pi\) | ||||
0.327313 | + | 0.944916i | \(0.393857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.34916 | 0.940963 | 0.470482 | − | 0.882410i | \(-0.344080\pi\) | ||||
0.470482 | + | 0.882410i | \(0.344080\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.32088 | −0.163836 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.44852 | −1.15432 | −0.577160 | − | 0.816631i | \(-0.695839\pi\) | ||||
−0.577160 | + | 0.816631i | \(0.695839\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.99093 | −1.06703 | −0.533513 | − | 0.845792i | \(-0.679129\pi\) | ||||
−0.533513 | + | 0.845792i | \(0.679129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.05655 | 0.708865 | 0.354433 | − | 0.935082i | \(-0.384674\pi\) | ||||
0.354433 | + | 0.935082i | \(0.384674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.70739 | 0.194575 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.05655 | 0.906432 | 0.453216 | − | 0.891401i | \(-0.350277\pi\) | ||||
0.453216 | + | 0.891401i | \(0.350277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.54241 | −0.169302 | −0.0846508 | − | 0.996411i | \(-0.526977\pi\) | ||||
−0.0846508 | + | 0.996411i | \(0.526977\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.32088 | −0.360200 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.679116 | −0.0711906 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.32088 | 0.135520 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.2553 | −1.24433 | −0.622167 | − | 0.782885i | \(-0.713747\pi\) | ||||
−0.622167 | + | 0.782885i | \(0.713747\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6700 | 1.16121 | 0.580606 | − | 0.814184i | \(-0.302816\pi\) | ||||
0.580606 | + | 0.814184i | \(0.302816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.292611 | −0.0288318 | −0.0144159 | − | 0.999896i | \(-0.504589\pi\) | ||||
−0.0144159 | + | 0.999896i | \(0.504589\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.87237 | −0.181009 | −0.0905043 | − | 0.995896i | \(-0.528848\pi\) | ||||
−0.0905043 | + | 0.995896i | \(0.528848\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.54787 | 0.531390 | 0.265695 | − | 0.964057i | \(-0.414399\pi\) | ||||
0.265695 | + | 0.964057i | \(0.414399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.80128 | 0.733883 | 0.366942 | − | 0.930244i | \(-0.380405\pi\) | ||||
0.366942 | + | 0.930244i | \(0.380405\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.12763 | −0.384904 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.70739 | −0.156516 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0282739 | 0.00257035 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8916 | −1.58762 | −0.793810 | − | 0.608166i | \(-0.791906\pi\) | ||||
−0.793810 | + | 0.608166i | \(0.791906\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.679116 | 0.0588868 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.67004 | 0.484424 | 0.242212 | − | 0.970223i | \(-0.422127\pi\) | ||||
0.242212 | + | 0.970223i | \(0.422127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.38650 | −0.366818 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.38650 | −0.115143 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6610 | 1.44684 | 0.723422 | − | 0.690407i | \(-0.242568\pi\) | ||||
0.723422 | + | 0.690407i | \(0.242568\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.26434 | −0.102890 | −0.0514451 | − | 0.998676i | \(-0.516383\pi\) | ||||
−0.0514451 | + | 0.998676i | \(0.516383\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.73566 | −0.701665 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.6700 | −1.25061 | −0.625303 | − | 0.780382i | \(-0.715025\pi\) | ||||
−0.625303 | + | 0.780382i | \(0.715025\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.12217 | −0.167250 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7074 | −1.23030 | −0.615149 | − | 0.788411i | \(-0.710904\pi\) | ||||
−0.615149 | + | 0.788411i | \(0.710904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.16498 | −0.477060 | −0.238530 | − | 0.971135i | \(-0.576666\pi\) | ||||
−0.238530 | + | 0.971135i | \(0.576666\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2553 | −0.865790 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.58522 | 0.652722 | 0.326361 | − | 0.945245i | \(-0.394177\pi\) | ||||
0.326361 | + | 0.945245i | \(0.394177\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.514137 | 0.0388651 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.06562 | 0.0796482 | 0.0398241 | − | 0.999207i | \(-0.487320\pi\) | ||||
0.0398241 | + | 0.999207i | \(0.487320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6700 | −0.941757 | −0.470878 | − | 0.882198i | \(-0.656063\pi\) | ||||
−0.470878 | + | 0.882198i | \(0.656063\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.292611 | 0.0215132 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0283 | −0.806467 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9344 | 1.22533 | 0.612664 | − | 0.790343i | \(-0.290098\pi\) | ||||
0.612664 | + | 0.790343i | \(0.290098\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.7175 | 1.92317 | 0.961585 | − | 0.274509i | \(-0.0885153\pi\) | ||||
0.961585 | + | 0.274509i | \(0.0885153\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.2553 | −1.01565 | −0.507823 | − | 0.861462i | \(-0.669550\pi\) | ||||
−0.507823 | + | 0.861462i | \(0.669550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.6610 | 1.74817 | 0.874085 | − | 0.485773i | \(-0.161462\pi\) | ||||
0.874085 | + | 0.485773i | \(0.161462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.712853 | −0.0500325 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3492 | −0.792660 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.38650 | 0.303421 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.37743 | 0.370198 | 0.185099 | − | 0.982720i | \(-0.440739\pi\) | ||||
0.185099 | + | 0.982720i | \(0.440739\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.3492 | −0.705807 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.49133 | −0.304891 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.38650 | 0.295068 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.66458 | −0.580223 | −0.290112 | − | 0.956993i | \(-0.593692\pi\) | ||||
−0.290112 | + | 0.956993i | \(0.593692\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.32088 | −0.220415 | −0.110207 | − | 0.993909i | \(-0.535152\pi\) | ||||
−0.110207 | + | 0.993909i | \(0.535152\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.3118 | −1.67265 | −0.836326 | − | 0.548233i | \(-0.815301\pi\) | ||||
−0.836326 | + | 0.548233i | \(0.815301\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.6327 | 1.81028 | 0.905139 | − | 0.425116i | \(-0.139767\pi\) | ||||
0.905139 | + | 0.425116i | \(0.139767\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.86330 | 0.317246 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.19872 | 0.271592 | 0.135796 | − | 0.990737i | \(-0.456641\pi\) | ||||
0.135796 | + | 0.990737i | \(0.456641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.60442 | 0.232181 | 0.116091 | − | 0.993239i | \(-0.462964\pi\) | ||||
0.116091 | + | 0.993239i | \(0.462964\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.73566 | −0.430326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.74474 | −0.111015 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.87783 | 0.434125 | 0.217062 | − | 0.976158i | \(-0.430352\pi\) | ||||
0.217062 | + | 0.976158i | \(0.430352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.7074 | −0.861776 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.0000 | −1.12281 | −0.561405 | − | 0.827541i | \(-0.689739\pi\) | ||||
−0.561405 | + | 0.827541i | \(0.689739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.150442 | 0.00934801 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.23606 | −0.384532 | −0.192266 | − | 0.981343i | \(-0.561584\pi\) | ||||
−0.192266 | + | 0.981343i | \(0.561584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.02827 | −0.308884 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.92345 | 0.605044 | 0.302522 | − | 0.953142i | \(-0.402172\pi\) | ||||
0.302522 | + | 0.953142i | \(0.402172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.60442 | −0.401190 | −0.200595 | − | 0.979674i | \(-0.564288\pi\) | ||||
−0.200595 | + | 0.979674i | \(0.564288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.32088 | 0.200257 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.6610 | 1.36157 | 0.680783 | − | 0.732485i | \(-0.261640\pi\) | ||||
0.680783 | + | 0.732485i | \(0.261640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.5479 | −0.927508 | −0.463754 | − | 0.885964i | \(-0.653498\pi\) | ||||
−0.463754 | + | 0.885964i | \(0.653498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.645378 | −0.0383637 | −0.0191819 | − | 0.999816i | \(-0.506106\pi\) | ||||
−0.0191819 | + | 0.999816i | \(0.506106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.83502 | −0.344430 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.97173 | −0.351278 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.37743 | −0.0804704 | −0.0402352 | − | 0.999190i | \(-0.512811\pi\) | ||||
−0.0402352 | + | 0.999190i | \(0.512811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.02827 | 0.292757 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.45213 | 0.315305 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.32088 | −0.306691 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.34916 | 0.420812 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.98546 | 0.455754 | 0.227877 | − | 0.973690i | \(-0.426822\pi\) | ||||
0.227877 | + | 0.973690i | \(0.426822\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.63270 | −0.546220 | −0.273110 | − | 0.961983i | \(-0.588052\pi\) | ||||
−0.273110 | + | 0.961983i | \(0.588052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.5369 | −1.38691 | −0.693455 | − | 0.720500i | \(-0.743912\pi\) | ||||
−0.693455 | + | 0.720500i | \(0.743912\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.3492 | −1.14292 | −0.571461 | − | 0.820629i | \(-0.693623\pi\) | ||||
−0.571461 | + | 0.820629i | \(0.693623\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.60442 | −0.257798 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.38650 | −0.244072 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.32088 | −0.0732695 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.50040 | 0.137851 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4431 | −0.903792 | −0.451896 | − | 0.892071i | \(-0.649252\pi\) | ||||
−0.451896 | + | 0.892071i | \(0.649252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.44852 | −0.516228 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.89703 | 0.266758 | 0.133379 | − | 0.991065i | \(-0.457417\pi\) | ||||
0.133379 | + | 0.991065i | \(0.457417\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.0101 | −1.57099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.06201 | −0.381313 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.2745 | −1.19576 | −0.597878 | − | 0.801587i | \(-0.703989\pi\) | ||||
−0.597878 | + | 0.801587i | \(0.703989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.94345 | −0.157559 | −0.0787797 | − | 0.996892i | \(-0.525102\pi\) | ||||
−0.0787797 | + | 0.996892i | \(0.525102\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8296 | 1.00220 | 0.501098 | − | 0.865390i | \(-0.332930\pi\) | ||||
0.501098 | + | 0.865390i | \(0.332930\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.99093 | −0.477189 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.8770 | 1.68241 | 0.841203 | − | 0.540720i | \(-0.181848\pi\) | ||||
0.841203 | + | 0.540720i | \(0.181848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2553 | −0.908172 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.05655 | 0.317014 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3492 | 0.957818 | 0.478909 | − | 0.877864i | \(-0.341032\pi\) | ||||
0.478909 | + | 0.877864i | \(0.341032\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.58522 | −0.134218 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.19872 | −0.113845 | −0.0569226 | − | 0.998379i | \(-0.518129\pi\) | ||||
−0.0569226 | + | 0.998379i | \(0.518129\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.83141 | 0.0943226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.4713 | −0.794709 | −0.397354 | − | 0.917665i | \(-0.630072\pi\) | ||||
−0.397354 | + | 0.917665i | \(0.630072\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.70739 | −0.393829 | −0.196915 | − | 0.980421i | \(-0.563092\pi\) | ||||
−0.196915 | + | 0.980421i | \(0.563092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.70739 | 0.0870166 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.6327 | −1.24893 | −0.624464 | − | 0.781054i | \(-0.714682\pi\) | ||||
−0.624464 | + | 0.781054i | \(0.714682\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7074 | 0.693212 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.05655 | 0.405369 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.77301 | −0.339928 | −0.169964 | − | 0.985450i | \(-0.554365\pi\) | ||||
−0.169964 | + | 0.985450i | \(0.554365\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.4996 | −0.923826 | −0.461913 | − | 0.886925i | \(-0.652837\pi\) | ||||
−0.461913 | + | 0.886925i | \(0.652837\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5388 | 0.574789 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.971726 | 0.0481667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.4148 | −0.663318 | −0.331659 | − | 0.943399i | \(-0.607608\pi\) | ||||
−0.331659 | + | 0.943399i | \(0.607608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.58522 | 0.127210 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.54241 | −0.0757140 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.1150 | 1.61777 | 0.808886 | − | 0.587966i | \(-0.200071\pi\) | ||||
0.808886 | + | 0.587966i | \(0.200071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6983 | −0.716352 | −0.358176 | − | 0.933654i | \(-0.616601\pi\) | ||||
−0.358176 | + | 0.933654i | \(0.616601\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.32088 | −0.161087 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.77847 | 0.182853 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.7549 | 1.57775 | 0.788873 | − | 0.614556i | \(-0.210665\pi\) | ||||
0.788873 | + | 0.614556i | \(0.210665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.8314 | −0.568581 | −0.284291 | − | 0.958738i | \(-0.591758\pi\) | ||||
−0.284291 | + | 0.958738i | \(0.591758\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.45213 | −0.260811 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.31181 | −0.396701 | −0.198351 | − | 0.980131i | \(-0.563558\pi\) | ||||
−0.198351 | + | 0.980131i | \(0.563558\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.1751 | 1.38615 | 0.693076 | − | 0.720865i | \(-0.256255\pi\) | ||||
0.693076 | + | 0.720865i | \(0.256255\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | −0.142214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9717 | 0.895331 | 0.447666 | − | 0.894201i | \(-0.352256\pi\) | ||||
0.447666 | + | 0.894201i | \(0.352256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.6892 | −1.77472 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.679116 | −0.0318374 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.2353 | −1.08690 | −0.543450 | − | 0.839442i | \(-0.682882\pi\) | ||||
−0.543450 | + | 0.839442i | \(0.682882\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.42571 | 0.206126 | 0.103063 | − | 0.994675i | \(-0.467136\pi\) | ||||
0.103063 | + | 0.994675i | \(0.467136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.5087 | 0.906645 | 0.453322 | − | 0.891347i | \(-0.350239\pi\) | ||||
0.453322 | + | 0.891347i | \(0.350239\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.5935 | 1.13805 | 0.569026 | − | 0.822320i | \(-0.307321\pi\) | ||||
0.569026 | + | 0.822320i | \(0.307321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.85783 | −0.224314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.3684 | −1.58026 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.32088 | 0.0606063 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.7549 | −1.49661 | −0.748304 | − | 0.663356i | \(-0.769132\pi\) | ||||
−0.748304 | + | 0.663356i | \(0.769132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.386505 | −0.0176231 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.2553 | −0.556483 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.03735 | 0.273578 | 0.136789 | − | 0.990600i | \(-0.456322\pi\) | ||||
0.136789 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.4431 | −0.651806 | −0.325903 | − | 0.945403i | \(-0.605668\pi\) | ||||
−0.325903 | + | 0.945403i | \(0.605668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.60442 | 0.207373 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.62257 | −0.207351 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.9717 | −0.938823 | −0.469412 | − | 0.882979i | \(-0.655534\pi\) | ||||
−0.469412 | + | 0.882979i | \(0.655534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.31728 | 0.237086 | 0.118543 | − | 0.992949i | \(-0.462178\pi\) | ||||
0.118543 | + | 0.992949i | \(0.462178\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.6700 | 0.519310 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.2270 | 0.807897 | 0.403949 | − | 0.914782i | \(-0.367637\pi\) | ||||
0.403949 | + | 0.914782i | \(0.367637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.11389 | 0.137751 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.292611 | −0.0128940 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.1504 | 0.710296 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.1232 | 1.75783 | 0.878915 | − | 0.476978i | \(-0.158268\pi\) | ||||
0.878915 | + | 0.476978i | \(0.158268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.9873 | −0.830257 | −0.415129 | − | 0.909763i | \(-0.636263\pi\) | ||||
−0.415129 | + | 0.909763i | \(0.636263\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.0101 | 1.26370 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.96265 | −0.259246 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.9909 | 0.649329 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.87237 | −0.0809495 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.3684 | −0.963473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5279 | 0.710589 | 0.355294 | − | 0.934754i | \(-0.384381\pi\) | ||||
0.355294 | + | 0.934754i | \(0.384381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.54787 | 0.237645 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6737 | −0.755671 | −0.377835 | − | 0.925873i | \(-0.623331\pi\) | ||||
−0.377835 | + | 0.925873i | \(0.623331\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.83141 | −0.0780208 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.14217 | 0.176143 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.3401 | 0.734723 | 0.367362 | − | 0.930078i | \(-0.380261\pi\) | ||||
0.367362 | + | 0.930078i | \(0.380261\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6700 | 0.578181 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.9945 | −0.547654 | −0.273827 | − | 0.961779i | \(-0.588290\pi\) | ||||
−0.273827 | + | 0.961779i | \(0.588290\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.80128 | 0.328202 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6802 | −0.699269 | −0.349635 | − | 0.936886i | \(-0.613694\pi\) | ||||
−0.349635 | + | 0.936886i | \(0.613694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.12763 | −0.172134 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.5953 | −0.982287 | −0.491144 | − | 0.871079i | \(-0.663421\pi\) | ||||
−0.491144 | + | 0.871079i | \(0.663421\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.793010 | −0.0328996 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.6983 | −0.691574 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.1276 | −1.16095 | −0.580476 | − | 0.814277i | \(-0.697133\pi\) | ||||
−0.580476 | + | 0.814277i | \(0.697133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.5388 | −0.475448 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.17872 | −0.376925 | −0.188462 | − | 0.982080i | \(-0.560350\pi\) | ||||
−0.188462 | + | 0.982080i | \(0.560350\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.70739 | −0.0699961 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.4713 | 1.28588 | 0.642942 | − | 0.765915i | \(-0.277714\pi\) | ||||
0.642942 | + | 0.765915i | \(0.277714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.2654 | −1.19376 | −0.596880 | − | 0.802330i | \(-0.703593\pi\) | ||||
−0.596880 | + | 0.802330i | \(0.703593\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0282739 | 0.00114950 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.2034 | 1.79416 | 0.897080 | − | 0.441868i | \(-0.145684\pi\) | ||||
0.897080 | + | 0.441868i | \(0.145684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.42385 | −0.259881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.1715 | −1.42056 | −0.710282 | − | 0.703918i | \(-0.751432\pi\) | ||||
−0.710282 | + | 0.703918i | \(0.751432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.42571 | −0.298948 | −0.149474 | − | 0.988766i | \(-0.547758\pi\) | ||||
−0.149474 | + | 0.988766i | \(0.547758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.54787 | −0.343568 | −0.171784 | − | 0.985135i | \(-0.554953\pi\) | ||||
−0.171784 | + | 0.985135i | \(0.554953\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.54241 | −0.0617954 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.971726 | −0.0387453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.36836 | 0.0942829 | 0.0471415 | − | 0.998888i | \(-0.484989\pi\) | ||||
0.0471415 | + | 0.998888i | \(0.484989\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.8916 | −0.710005 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.89703 | 0.352513 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.133096 | −0.00525698 | −0.00262849 | − | 0.999997i | \(-0.500837\pi\) | ||||
−0.00262849 | + | 0.999997i | \(0.500837\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.6464 | 0.893088 | 0.446544 | − | 0.894762i | \(-0.352655\pi\) | ||||
0.446544 | + | 0.894762i | \(0.352655\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.3912 | −1.82383 | −0.911913 | − | 0.410385i | \(-0.865394\pi\) | ||||
−0.911913 | + | 0.410385i | \(0.865394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.6983 | 0.655466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.4057 | 1.42467 | 0.712333 | − | 0.701842i | \(-0.247639\pi\) | ||||
0.712333 | + | 0.701842i | \(0.247639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.1414 | −0.745642 | −0.372821 | − | 0.927903i | \(-0.621609\pi\) | ||||
−0.372821 | + | 0.927903i | \(0.621609\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.9072 | 1.55221 | 0.776104 | − | 0.630605i | \(-0.217193\pi\) | ||||
0.776104 | + | 0.630605i | \(0.217193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.679116 | 0.0263350 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.72298 | 0.221595 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.4057 | 0.942172 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.6508 | 0.911673 | 0.455836 | − | 0.890064i | \(-0.349340\pi\) | ||||
0.455836 | + | 0.890064i | \(0.349340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.8031 | −0.568931 | −0.284465 | − | 0.958686i | \(-0.591816\pi\) | ||||
−0.284465 | + | 0.958686i | \(0.591816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.30088 | −0.241806 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.95252 | 0.189503 | 0.0947515 | − | 0.995501i | \(-0.469794\pi\) | ||||
0.0947515 | + | 0.995501i | \(0.469794\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.67004 | 0.216641 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.64177 | 0.253031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.2088 | 0.730739 | 0.365369 | − | 0.930863i | \(-0.380943\pi\) | ||||
0.365369 | + | 0.930863i | \(0.380943\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.00000 | −0.303457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.6892 | 1.42758 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.3492 | −1.10850 | −0.554251 | − | 0.832349i | \(-0.686995\pi\) | ||||
−0.554251 | + | 0.832349i | \(0.686995\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.386505 | 0.0145773 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.7266 | 1.45441 | 0.727204 | − | 0.686422i | \(-0.240820\pi\) | ||||
0.727204 | + | 0.686422i | \(0.240820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.0576 | 1.35037 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.38650 | −0.164046 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.0848 | 0.562569 | 0.281284 | − | 0.959624i | \(-0.409240\pi\) | ||||
0.281284 | + | 0.959624i | \(0.409240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.150442 | −0.00560275 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.38650 | −0.0514935 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.3455 | −0.457871 | −0.228936 | − | 0.973442i | \(-0.573525\pi\) | ||||
−0.228936 | + | 0.973442i | \(0.573525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.3684 | 1.27116 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.3774 | −1.15580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.7266 | −1.09351 | −0.546755 | − | 0.837293i | \(-0.684137\pi\) | ||||
−0.546755 | + | 0.837293i | \(0.684137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.3648 | −1.77433 | −0.887165 | − | 0.461452i | \(-0.847329\pi\) | ||||
−0.887165 | + | 0.461452i | \(0.847329\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.6610 | 0.647048 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.962653 | −0.0351746 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.8205 | 1.16115 | 0.580573 | − | 0.814208i | \(-0.302829\pi\) | ||||
0.580573 | + | 0.814208i | \(0.302829\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.26434 | −0.0460139 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.94531 | 0.179740 | 0.0898701 | − | 0.995953i | \(-0.471355\pi\) | ||||
0.0898701 | + | 0.995953i | \(0.471355\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.4249 | 1.28415 | 0.642076 | − | 0.766641i | \(-0.278073\pi\) | ||||
0.642076 | + | 0.766641i | \(0.278073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.85237 | 0.103263 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.64177 | −0.239820 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.4249 | 1.78231 | 0.891154 | − | 0.453701i | \(-0.149897\pi\) | ||||
0.891154 | + | 0.453701i | \(0.149897\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.6599 | 0.455345 | 0.227673 | − | 0.973738i | \(-0.426888\pi\) | ||||
0.227673 | + | 0.973738i | \(0.426888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.73566 | −0.313794 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.9909 | −0.537106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.8578 | −1.06840 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.6700 | −0.559288 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.9344 | −1.10269 | −0.551346 | − | 0.834277i | \(-0.685885\pi\) | ||||
−0.551346 | + | 0.834277i | \(0.685885\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.01093 | 0.142612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.70739 | −0.344720 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.5935 | −1.08368 | −0.541839 | − | 0.840483i | \(-0.682272\pi\) | ||||
−0.541839 | + | 0.840483i | \(0.682272\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.1504 | −0.571362 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.1131 | 0.709776 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.12217 | −0.0747966 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.89703 | −0.101854 | −0.0509271 | − | 0.998702i | \(-0.516218\pi\) | ||||
−0.0509271 | + | 0.998702i | \(0.516218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.8861 | 0.522722 | 0.261361 | − | 0.965241i | \(-0.415829\pi\) | ||||
0.261361 | + | 0.965241i | \(0.415829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.7074 | −0.550206 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.6700 | −0.478254 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.95173 | −0.312417 | −0.156209 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156209 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.99454 | −0.104383 | −0.0521915 | − | 0.998637i | \(-0.516621\pi\) | ||||
−0.0521915 | + | 0.998637i | \(0.516621\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.9663 | −1.11158 | −0.555788 | − | 0.831324i | \(-0.687583\pi\) | ||||
−0.555788 | + | 0.831324i | \(0.687583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.7458 | 0.789994 | 0.394997 | − | 0.918682i | \(-0.370746\pi\) | ||||
0.394997 | + | 0.918682i | \(0.370746\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.3684 | 0.775018 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.16498 | −0.213348 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.2643 | 0.803174 | 0.401587 | − | 0.915821i | \(-0.368459\pi\) | ||||
0.401587 | + | 0.915821i | \(0.368459\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0776 | −0.933710 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.2553 | −0.387193 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0145366 | 0.000499485 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.20779 | −0.0414025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9909 | 0.376322 | 0.188161 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188161 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.1504 | −0.551689 | −0.275844 | − | 0.961202i | \(-0.588957\pi\) | ||||
−0.275844 | + | 0.961202i | \(0.588957\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.5188 | −0.973049 | −0.486524 | − | 0.873667i | \(-0.661736\pi\) | ||||
−0.486524 | + | 0.873667i | \(0.661736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.2890 | −0.418322 | −0.209161 | − | 0.977881i | \(-0.567073\pi\) | ||||
−0.209161 | + | 0.977881i | \(0.567073\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.58522 | 0.291906 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.7549 | 0.907597 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4804 | 0.422882 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.514137 | 0.0173810 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.7002 | −1.34058 | −0.670290 | − | 0.742099i | \(-0.733830\pi\) | ||||
−0.670290 | + | 0.742099i | \(0.733830\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.1040 | 1.08161 | 0.540806 | − | 0.841147i | \(-0.318119\pi\) | ||||
0.540806 | + | 0.841147i | \(0.318119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5051 | −0.454482 | −0.227241 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227241 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.1222 | −1.17929 | −0.589643 | − | 0.807664i | \(-0.700732\pi\) | ||||
−0.589643 | + | 0.807664i | \(0.700732\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.19872 | −0.308515 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.42385 | 0.214966 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.06562 | 0.0356198 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.1120 | 0.403959 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6983 | 0.556302 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.6700 | −0.421166 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.1186 | −0.502004 | −0.251002 | − | 0.967987i | \(-0.580760\pi\) | ||||
−0.251002 | + | 0.967987i | \(0.580760\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.5561 | −1.74126 | −0.870631 | − | 0.491936i | \(-0.836289\pi\) | ||||
−0.870631 | + | 0.491936i | \(0.836289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.12217 | −0.169519 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.08482 | 0.101870 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.5489 | 1.79940 | 0.899702 | − | 0.436505i | \(-0.143784\pi\) | ||||
0.899702 | + | 0.436505i | \(0.143784\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.8760 | 0.390903 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.292611 | 0.00962098 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.3793 | 0.668623 | 0.334311 | − | 0.942463i | \(-0.391496\pi\) | ||||
0.334311 | + | 0.942463i | \(0.391496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.89703 | −0.291588 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.0283 | −0.360663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.1979 | 1.60723 | 0.803613 | − | 0.595152i | \(-0.202908\pi\) | ||||
0.803613 | + | 0.595152i | \(0.202908\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.2371 | −0.757508 | −0.378754 | − | 0.925497i | \(-0.623647\pi\) | ||||
−0.378754 | + | 0.925497i | \(0.623647\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.8452 | 1.52549 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.1642 | −1.20767 | −0.603837 | − | 0.797108i | \(-0.706362\pi\) | ||||
−0.603837 | + | 0.797108i | \(0.706362\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | −0.259691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.5761 | −0.763706 | −0.381853 | − | 0.924223i | \(-0.624714\pi\) | ||||
−0.381853 | + | 0.924223i | \(0.624714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.9344 | 0.547984 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.91518 | 0.0941360 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.3118 | 1.46167 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.7175 | 0.860067 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.38290 | −0.269576 | −0.134788 | − | 0.990874i | \(-0.543035\pi\) | ||||
−0.134788 | + | 0.990874i | \(0.543035\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2078 | −0.423858 | −0.211929 | − | 0.977285i | \(-0.567975\pi\) | ||||
−0.211929 | + | 0.977285i | \(0.567975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.11310 | −0.131860 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.3310 | −0.458490 | −0.229245 | − | 0.973369i | \(-0.573626\pi\) | ||||
−0.229245 | + | 0.973369i | \(0.573626\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.96265 | −0.318408 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.3082 | 1.03047 | 0.515236 | − | 0.857048i | \(-0.327704\pi\) | ||||
0.515236 | + | 0.857048i | \(0.327704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.2553 | −0.454210 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.7175 | 1.35834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.6700 | 1.26016 | 0.630080 | − | 0.776530i | \(-0.283022\pi\) | ||||
0.630080 | + | 0.776530i | \(0.283022\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.6610 | 0.781805 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.6874 | 1.22524 | 0.612621 | − | 0.790377i | \(-0.290115\pi\) | ||||
0.612621 | + | 0.790377i | \(0.290115\pi\) | |||||||
\(998\) | 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 | 6480.2.a.bv.1.3 | 3 | ||
3.2 | odd | 2 | 6480.2.a.bs.1.3 | 3 | |||
4.3 | odd | 2 | 405.2.a.j.1.3 | 3 | |||
9.2 | odd | 6 | 2160.2.q.k.1441.1 | 6 | |||
9.4 | even | 3 | 720.2.q.i.241.1 | 6 | |||
9.5 | odd | 6 | 2160.2.q.k.721.1 | 6 | |||
9.7 | even | 3 | 720.2.q.i.481.1 | 6 | |||
12.11 | even | 2 | 405.2.a.i.1.1 | 3 | |||
20.3 | even | 4 | 2025.2.b.l.649.1 | 6 | |||
20.7 | even | 4 | 2025.2.b.l.649.6 | 6 | |||
20.19 | odd | 2 | 2025.2.a.n.1.1 | 3 | |||
36.7 | odd | 6 | 45.2.e.b.31.1 | yes | 6 | ||
36.11 | even | 6 | 135.2.e.b.91.3 | 6 | |||
36.23 | even | 6 | 135.2.e.b.46.3 | 6 | |||
36.31 | odd | 6 | 45.2.e.b.16.1 | ✓ | 6 | ||
60.23 | odd | 4 | 2025.2.b.m.649.6 | 6 | |||
60.47 | odd | 4 | 2025.2.b.m.649.1 | 6 | |||
60.59 | even | 2 | 2025.2.a.o.1.3 | 3 | |||
180.7 | even | 12 | 225.2.k.b.49.6 | 12 | |||
180.23 | odd | 12 | 675.2.k.b.424.1 | 12 | |||
180.43 | even | 12 | 225.2.k.b.49.1 | 12 | |||
180.47 | odd | 12 | 675.2.k.b.199.1 | 12 | |||
180.59 | even | 6 | 675.2.e.b.451.1 | 6 | |||
180.67 | even | 12 | 225.2.k.b.124.1 | 12 | |||
180.79 | odd | 6 | 225.2.e.b.76.3 | 6 | |||
180.83 | odd | 12 | 675.2.k.b.199.6 | 12 | |||
180.103 | even | 12 | 225.2.k.b.124.6 | 12 | |||
180.119 | even | 6 | 675.2.e.b.226.1 | 6 | |||
180.139 | odd | 6 | 225.2.e.b.151.3 | 6 | |||
180.167 | odd | 12 | 675.2.k.b.424.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.1 | ✓ | 6 | 36.31 | odd | 6 | ||
45.2.e.b.31.1 | yes | 6 | 36.7 | odd | 6 | ||
135.2.e.b.46.3 | 6 | 36.23 | even | 6 | |||
135.2.e.b.91.3 | 6 | 36.11 | even | 6 | |||
225.2.e.b.76.3 | 6 | 180.79 | odd | 6 | |||
225.2.e.b.151.3 | 6 | 180.139 | odd | 6 | |||
225.2.k.b.49.1 | 12 | 180.43 | even | 12 | |||
225.2.k.b.49.6 | 12 | 180.7 | even | 12 | |||
225.2.k.b.124.1 | 12 | 180.67 | even | 12 | |||
225.2.k.b.124.6 | 12 | 180.103 | even | 12 | |||
405.2.a.i.1.1 | 3 | 12.11 | even | 2 | |||
405.2.a.j.1.3 | 3 | 4.3 | odd | 2 | |||
675.2.e.b.226.1 | 6 | 180.119 | even | 6 | |||
675.2.e.b.451.1 | 6 | 180.59 | even | 6 | |||
675.2.k.b.199.1 | 12 | 180.47 | odd | 12 | |||
675.2.k.b.199.6 | 12 | 180.83 | odd | 12 | |||
675.2.k.b.424.1 | 12 | 180.23 | odd | 12 | |||
675.2.k.b.424.6 | 12 | 180.167 | odd | 12 | |||
720.2.q.i.241.1 | 6 | 9.4 | even | 3 | |||
720.2.q.i.481.1 | 6 | 9.7 | even | 3 | |||
2025.2.a.n.1.1 | 3 | 20.19 | odd | 2 | |||
2025.2.a.o.1.3 | 3 | 60.59 | even | 2 | |||
2025.2.b.l.649.1 | 6 | 20.3 | even | 4 | |||
2025.2.b.l.649.6 | 6 | 20.7 | even | 4 | |||
2025.2.b.m.649.1 | 6 | 60.47 | odd | 4 | |||
2025.2.b.m.649.6 | 6 | 60.23 | odd | 4 | |||
2160.2.q.k.721.1 | 6 | 9.5 | odd | 6 | |||
2160.2.q.k.1441.1 | 6 | 9.2 | odd | 6 | |||
6480.2.a.bs.1.3 | 3 | 3.2 | odd | 2 | |||
6480.2.a.bv.1.3 | 3 | 1.1 | even | 1 | trivial |