Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(289,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.k (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 865.2 | ||
Root | \(0.500000 - 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.865 |
Dual form | 1152.2.k.f.289.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.334904 | − | 0.334904i | −0.149774 | − | 0.149774i | 0.628243 | − | 0.778017i | \(-0.283774\pi\) |
−0.778017 | + | 0.628243i | \(0.783774\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.55765i | − | 1.72263i | −0.508072 | − | 0.861314i | \(-0.669642\pi\) | ||
0.508072 | − | 0.861314i | \(-0.330358\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.47363 | + | 2.47363i | 0.745826 | + | 0.745826i | 0.973692 | − | 0.227866i | \(-0.0731749\pi\) |
−0.227866 | + | 0.973692i | \(0.573175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0594122 | − | 0.0594122i | 0.0164780 | − | 0.0164780i | −0.698820 | − | 0.715298i | \(-0.746291\pi\) |
0.715298 | + | 0.698820i | \(0.246291\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.61706 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.55765 | − | 2.55765i | 0.586765 | − | 0.586765i | −0.349989 | − | 0.936754i | \(-0.613815\pi\) |
0.936754 | + | 0.349989i | \(0.113815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.82843i | − | 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.77568i | − | 0.955136i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.16333 | + | 5.16333i | −0.958807 | + | 0.958807i | −0.999184 | − | 0.0403780i | \(-0.987144\pi\) |
0.0403780 | + | 0.999184i | \(0.487144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.557647 | 0.100156 | 0.0500782 | − | 0.998745i | \(-0.484053\pi\) | ||||
0.0500782 | + | 0.998745i | \(0.484053\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.52637 | + | 1.52637i | −0.258004 | + | 0.258004i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.38607 | − | 4.38607i | −0.721066 | − | 0.721066i | 0.247756 | − | 0.968822i | \(-0.420307\pi\) |
−0.968822 | + | 0.247756i | \(0.920307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.27391i | − | 1.44834i | −0.689620 | − | 0.724171i | \(-0.742223\pi\) | ||
0.689620 | − | 0.724171i | \(-0.257777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61040 | − | 1.61040i | −0.245583 | − | 0.245583i | 0.573572 | − | 0.819155i | \(-0.305557\pi\) |
−0.819155 | + | 0.573572i | \(0.805557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.7721 | −1.96745 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.493523 | − | 0.493523i | −0.0677906 | − | 0.0677906i | 0.672399 | − | 0.740189i | \(-0.265264\pi\) |
−0.740189 | + | 0.672399i | \(0.765264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.65685i | − | 0.223410i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | − | 4.00000i | −0.520756 | − | 0.520756i | 0.397044 | − | 0.917800i | \(-0.370036\pi\) |
−0.917800 | + | 0.397044i | \(0.870036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.72922 | + | 2.72922i | −0.349441 | + | 0.349441i | −0.859901 | − | 0.510460i | \(-0.829475\pi\) |
0.510460 | + | 0.859901i | \(0.329475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0397948 | −0.00493593 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.77568 | − | 3.77568i | 0.461273 | − | 0.461273i | −0.437800 | − | 0.899072i | \(-0.644242\pi\) |
0.899072 | + | 0.437800i | \(0.144242\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.11529i | − | 1.08179i | −0.841091 | − | 0.540893i | \(-0.818086\pi\) | ||
0.841091 | − | 0.540893i | \(-0.181914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.541560i | 0.0633848i | 0.999498 | + | 0.0316924i | \(0.0100897\pi\) | ||||
−0.999498 | + | 0.0316924i | \(0.989910\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.2739 | − | 11.2739i | 1.28478 | − | 1.28478i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9937 | 1.23689 | 0.618445 | − | 0.785828i | \(-0.287763\pi\) | ||||
0.618445 | + | 0.785828i | \(0.287763\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.6417 | − | 10.6417i | 1.16807 | − | 1.16807i | 0.185415 | − | 0.982660i | \(-0.440637\pi\) |
0.982660 | − | 0.185415i | \(-0.0593628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21137 | + | 1.21137i | 0.131391 | + | 0.131391i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6533i | 1.55325i | 0.629964 | + | 0.776625i | \(0.283070\pi\) | ||||
−0.629964 | + | 0.776625i | \(0.716930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.270780 | − | 0.270780i | −0.0283854 | − | 0.0283854i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.71313 | −0.175764 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.31724 | 0.438349 | 0.219175 | − | 0.975686i | \(-0.429664\pi\) | ||||
0.219175 | + | 0.975686i | \(0.429664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.453728 | − | 0.453728i | −0.0451477 | − | 0.0451477i | 0.684173 | − | 0.729320i | \(-0.260164\pi\) |
−0.729320 | + | 0.684173i | \(0.760164\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.33686i | 0.131724i | 0.997829 | + | 0.0658622i | \(0.0209798\pi\) | ||||
−0.997829 | + | 0.0658622i | \(0.979020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.06255 | − | 6.06255i | −0.586088 | − | 0.586088i | 0.350481 | − | 0.936570i | \(-0.386018\pi\) |
−0.936570 | + | 0.350481i | \(0.886018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.71627 | + | 5.71627i | −0.547519 | + | 0.547519i | −0.925722 | − | 0.378203i | \(-0.876542\pi\) |
0.378203 | + | 0.925722i | \(0.376542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.55136 | 0.898516 | 0.449258 | − | 0.893402i | \(-0.351688\pi\) | ||||
0.449258 | + | 0.893402i | \(0.351688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.947252 | + | 0.947252i | −0.0883317 | + | 0.0883317i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.4853i | 1.51120i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.23765i | 0.112514i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.27391 | + | 3.27391i | −0.292828 | + | 0.292828i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.09921 | −0.452481 | −0.226241 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226241 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.11882 | + | 2.11882i | −0.185123 | + | 0.185123i | −0.793584 | − | 0.608461i | \(-0.791787\pi\) |
0.608461 | + | 0.793584i | \(0.291787\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.6569 | − | 11.6569i | −1.01078 | − | 1.01078i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.37941i | − | 0.288723i | −0.989525 | − | 0.144361i | \(-0.953887\pi\) | ||
0.989525 | − | 0.144361i | \(-0.0461127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.88118 | + | 5.88118i | 0.498835 | + | 0.498835i | 0.911075 | − | 0.412240i | \(-0.135254\pi\) |
−0.412240 | + | 0.911075i | \(0.635254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.293927 | 0.0245794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.45844 | 0.287208 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.99176 | − | 9.99176i | −0.818557 | − | 0.818557i | 0.167342 | − | 0.985899i | \(-0.446482\pi\) |
−0.985899 | + | 0.167342i | \(0.946482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.97685i | 0.811905i | 0.913894 | + | 0.405952i | \(0.133060\pi\) | ||||
−0.913894 | + | 0.405952i | \(0.866940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.186758 | − | 0.186758i | −0.0150008 | − | 0.0150008i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1618 | − | 16.1618i | 1.28985 | − | 1.28985i | 0.354971 | − | 0.934877i | \(-0.384491\pi\) |
0.934877 | − | 0.354971i | \(-0.115509\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.8910 | −1.01595 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.50490 | + | 7.50490i | −0.587829 | + | 0.587829i | −0.937043 | − | 0.349214i | \(-0.886449\pi\) |
0.349214 | + | 0.937043i | \(0.386449\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.83822i | 0.451775i | 0.974153 | + | 0.225888i | \(0.0725282\pi\) | ||||
−0.974153 | + | 0.225888i | \(0.927472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9929i | 0.999457i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.62530 | + | 3.62530i | −0.275627 | + | 0.275627i | −0.831360 | − | 0.555734i | \(-0.812437\pi\) |
0.555734 | + | 0.831360i | \(0.312437\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.7659 | −1.64534 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.28334 | + | 9.28334i | −0.693869 | + | 0.693869i | −0.963081 | − | 0.269212i | \(-0.913237\pi\) |
0.269212 | + | 0.963081i | \(0.413237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.8316 | + | 10.8316i | 0.805104 | + | 0.805104i | 0.983888 | − | 0.178785i | \(-0.0572165\pi\) |
−0.178785 | + | 0.983888i | \(0.557217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.93783i | 0.215993i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.94725 | − | 8.94725i | −0.654288 | − | 0.654288i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.63001 | −0.624446 | −0.312223 | − | 0.950009i | \(-0.601074\pi\) | ||||
−0.312223 | + | 0.950009i | \(0.601074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4514 | 0.824288 | 0.412144 | − | 0.911119i | \(-0.364780\pi\) | ||||
0.412144 | + | 0.911119i | \(0.364780\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.48999 | + | 7.48999i | 0.533640 | + | 0.533640i | 0.921654 | − | 0.388014i | \(-0.126839\pi\) |
−0.388014 | + | 0.921654i | \(0.626839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.68000i | − | 0.260868i | −0.991457 | − | 0.130434i | \(-0.958363\pi\) | ||
0.991457 | − | 0.130434i | \(-0.0416371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.5326 | + | 23.5326i | 1.65167 | + | 1.65167i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.10587 | + | 3.10587i | −0.216923 | + | 0.216923i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.6533 | 0.875249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1188 | − | 10.1188i | 0.696609 | − | 0.696609i | −0.267069 | − | 0.963677i | \(-0.586055\pi\) |
0.963677 | + | 0.267069i | \(0.0860551\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.07866i | 0.0735637i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.54156i | − | 0.172532i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.214897 | + | 0.214897i | −0.0144556 | + | 0.0144556i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.86156 | 0.325554 | 0.162777 | − | 0.986663i | \(-0.447955\pi\) | ||||
0.162777 | + | 0.986663i | \(0.447955\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.6417 | + | 10.6417i | −0.706312 | + | 0.706312i | −0.965758 | − | 0.259445i | \(-0.916460\pi\) |
0.259445 | + | 0.965758i | \(0.416460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1712 | + | 20.1712i | 1.33295 | + | 1.33295i | 0.902720 | + | 0.430229i | \(0.141567\pi\) |
0.430229 | + | 0.902720i | \(0.358433\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5702i | 0.889014i | 0.895775 | + | 0.444507i | \(0.146621\pi\) | ||||
−0.895775 | + | 0.444507i | \(0.853379\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.947252 | − | 0.947252i | −0.0617919 | − | 0.0617919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3629 | 1.89933 | 0.949665 | − | 0.313267i | \(-0.101424\pi\) | ||||
0.949665 | + | 0.313267i | \(0.101424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.0063 | 1.54638 | 0.773190 | − | 0.634175i | \(-0.218660\pi\) | ||||
0.773190 | + | 0.634175i | \(0.218660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.61235 | + | 4.61235i | 0.294672 | + | 0.294672i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.303911i | − | 0.0193374i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.7570 | − | 15.7570i | −0.994571 | − | 0.994571i | 0.00541463 | − | 0.999985i | \(-0.498276\pi\) |
−0.999985 | + | 0.00541463i | \(0.998276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.99647 | − | 6.99647i | 0.439864 | − | 0.439864i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.66038 | −0.540220 | −0.270110 | − | 0.962829i | \(-0.587060\pi\) | ||||
−0.270110 | + | 0.962829i | \(0.587060\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.9902 | + | 19.9902i | −1.24213 | + | 1.24213i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 13.3208i | − | 0.821394i | −0.911772 | − | 0.410697i | \(-0.865285\pi\) | ||
0.911772 | − | 0.410697i | \(-0.134715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.330566i | 0.0203065i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.6714 | + | 11.6714i | −0.711616 | + | 0.711616i | −0.966873 | − | 0.255257i | \(-0.917840\pi\) |
0.255257 | + | 0.966873i | \(0.417840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9769 | 1.33500 | 0.667499 | − | 0.744610i | \(-0.267365\pi\) | ||||
0.667499 | + | 0.744610i | \(0.267365\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.8132 | − | 11.8132i | 0.712365 | − | 0.712365i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.9504 | + | 10.9504i | 0.657945 | + | 0.657945i | 0.954893 | − | 0.296949i | \(-0.0959690\pi\) |
−0.296949 | + | 0.954893i | \(0.595969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.8910i | − | 1.36556i | −0.730624 | − | 0.682780i | \(-0.760771\pi\) | ||
0.730624 | − | 0.682780i | \(-0.239229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.48528 | + | 4.48528i | 0.266622 | + | 0.266622i | 0.827738 | − | 0.561115i | \(-0.189628\pi\) |
−0.561115 | + | 0.827738i | \(0.689628\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −42.2672 | −2.49496 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.91688 | −0.230405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6221 | + | 21.6221i | 1.26318 | + | 1.26318i | 0.949543 | + | 0.313636i | \(0.101547\pi\) |
0.313636 | + | 0.949543i | \(0.398453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.67923i | 0.155991i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.168043 | − | 0.168043i | −0.00971818 | − | 0.00971818i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.33962 | + | 7.33962i | −0.423048 | + | 0.423048i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.82805 | 0.104674 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.1118 | + | 12.1118i | −0.691255 | + | 0.691255i | −0.962508 | − | 0.271253i | \(-0.912562\pi\) |
0.271253 | + | 0.962508i | \(0.412562\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.8651i | 1.52338i | 0.647943 | + | 0.761689i | \(0.275630\pi\) | ||||
−0.647943 | + | 0.761689i | \(0.724370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.6890i | − | 1.11289i | −0.830885 | − | 0.556445i | \(-0.812165\pi\) | ||
0.830885 | − | 0.556445i | \(-0.187835\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.3447 | − | 21.3447i | 1.19884 | − | 1.19884i | 0.224323 | − | 0.974515i | \(-0.427983\pi\) |
0.974515 | − | 0.224323i | \(-0.0720171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.5443 | −1.43021 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.25116 | + | 9.25116i | −0.514748 | + | 0.514748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.283734 | − | 0.283734i | −0.0157387 | − | 0.0157387i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.8910i | − | 0.710702i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6926 | + | 14.6926i | 0.807576 | + | 0.807576i | 0.984266 | − | 0.176690i | \(-0.0565391\pi\) |
−0.176690 | + | 0.984266i | \(0.556539\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.52898 | −0.138173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0098 | −1.25342 | −0.626712 | − | 0.779251i | \(-0.715600\pi\) | ||||
−0.626712 | + | 0.779251i | \(0.715600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.37941 | + | 1.37941i | 0.0746993 | + | 0.0746993i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 30.8651i | 1.66656i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.9026 | + | 10.9026i | 0.585284 | + | 0.585284i | 0.936350 | − | 0.351067i | \(-0.114181\pi\) |
−0.351067 | + | 0.936350i | \(0.614181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0563 | + | 20.0563i | −1.07359 | + | 1.07359i | −0.0765186 | + | 0.997068i | \(0.524380\pi\) |
−0.997068 | + | 0.0765186i | \(0.975620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.2117 | 0.649965 | 0.324983 | − | 0.945720i | \(-0.394642\pi\) | ||||
0.324983 | + | 0.945720i | \(0.394642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.05275 | + | 3.05275i | −0.162023 | + | 0.162023i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 33.4780i | − | 1.76690i | −0.468522 | − | 0.883452i | \(-0.655214\pi\) | ||
0.468522 | − | 0.883452i | \(-0.344786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.91688i | 0.311415i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.181370 | − | 0.181370i | 0.00949337 | − | 0.00949337i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.702379 | 0.0366639 | 0.0183319 | − | 0.999832i | \(-0.494164\pi\) | ||||
0.0183319 | + | 0.999832i | \(0.494164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.24930 | + | 2.24930i | −0.116778 | + | 0.116778i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.9598 | − | 18.9598i | −0.981702 | − | 0.981702i | 0.0181339 | − | 0.999836i | \(-0.494227\pi\) |
−0.999836 | + | 0.0181339i | \(0.994227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.613530i | 0.0315984i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.77844 | − | 1.77844i | −0.0913523 | − | 0.0913523i | 0.659954 | − | 0.751306i | \(-0.270576\pi\) |
−0.751306 | + | 0.659954i | \(0.770576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.4880 | 1.30238 | 0.651188 | − | 0.758916i | \(-0.274271\pi\) | ||||
0.651188 | + | 0.758916i | \(0.274271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.55136 | −0.384853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.7049 | − | 11.7049i | −0.593462 | − | 0.593462i | 0.345103 | − | 0.938565i | \(-0.387844\pi\) |
−0.938565 | + | 0.345103i | \(0.887844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2306i | 0.517383i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.68184 | − | 3.68184i | −0.185253 | − | 0.185253i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.04646 | − | 9.04646i | 0.454029 | − | 0.454029i | −0.442661 | − | 0.896689i | \(-0.645965\pi\) |
0.896689 | + | 0.442661i | \(0.145965\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0853 | 0.903137 | 0.451568 | − | 0.892237i | \(-0.350865\pi\) | ||||
0.451568 | + | 0.892237i | \(0.350865\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0331311 | − | 0.0331311i | 0.00165038 | − | 0.00165038i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 21.6990i | − | 1.07558i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.2271i | 1.24740i | 0.781665 | + | 0.623699i | \(0.214371\pi\) | ||||
−0.781665 | + | 0.623699i | \(0.785629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.2306 | + | 18.2306i | −0.897069 | + | 0.897069i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.12787 | −0.349894 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.25283 | + | 7.25283i | −0.354324 | + | 0.354324i | −0.861716 | − | 0.507392i | \(-0.830610\pi\) |
0.507392 | + | 0.861716i | \(0.330610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.39550 | − | 2.39550i | −0.116749 | − | 0.116749i | 0.646318 | − | 0.763068i | \(-0.276308\pi\) |
−0.763068 | + | 0.646318i | \(0.776308\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.2739i | 0.837908i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4388 | + | 12.4388i | 0.601957 | + | 0.601957i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.42454 | −0.213123 | −0.106561 | − | 0.994306i | \(-0.533984\pi\) | ||||
−0.106561 | + | 0.994306i | \(0.533984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.31371 | 0.351474 | 0.175737 | − | 0.984437i | \(-0.443769\pi\) | ||||
0.175737 | + | 0.984437i | \(0.443769\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.23412 | − | 7.23412i | −0.346055 | − | 0.346055i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 29.6533i | − | 1.41527i | −0.706576 | − | 0.707637i | \(-0.749761\pi\) | ||
0.706576 | − | 0.707637i | \(-0.250239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3056 | − | 10.3056i | −0.489633 | − | 0.489633i | 0.418557 | − | 0.908190i | \(-0.362536\pi\) |
−0.908190 | + | 0.418557i | \(0.862536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.90746 | − | 4.90746i | 0.232636 | − | 0.232636i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.48844 | 0.306208 | 0.153104 | − | 0.988210i | \(-0.451073\pi\) | ||||
0.153104 | + | 0.988210i | \(0.451073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.9402 | − | 22.9402i | 1.08021 | − | 1.08021i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.181370i | 0.00850278i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.00353i | 0.421167i | 0.977576 | + | 0.210584i | \(0.0675364\pi\) | ||||
−0.977576 | + | 0.210584i | \(0.932464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.6218 | − | 14.6218i | 0.681004 | − | 0.681004i | −0.279223 | − | 0.960226i | \(-0.590077\pi\) |
0.960226 | + | 0.279223i | \(0.0900767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6435 | 0.866437 | 0.433219 | − | 0.901289i | \(-0.357378\pi\) | ||||
0.433219 | + | 0.901289i | \(0.357378\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.5138 | − | 23.5138i | 1.08809 | − | 1.08809i | 0.0923633 | − | 0.995725i | \(-0.470558\pi\) |
0.995725 | − | 0.0923633i | \(-0.0294421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.2082 | − | 17.2082i | −0.794601 | − | 0.794601i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.96703i | − | 0.366325i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.2145 | − | 12.2145i | −0.560440 | − | 0.560440i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.08864 | −0.0497412 | −0.0248706 | − | 0.999691i | \(-0.507917\pi\) | ||||
−0.0248706 | + | 0.999691i | \(0.507917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.521173 | −0.0237634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.44586 | − | 1.44586i | −0.0656531 | − | 0.0656531i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 35.3298i | − | 1.60095i | −0.599369 | − | 0.800473i | \(-0.704582\pi\) | ||
0.599369 | − | 0.800473i | \(-0.295418\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8910 | + | 12.8910i | 0.581761 | + | 0.581761i | 0.935387 | − | 0.353626i | \(-0.115051\pi\) |
−0.353626 | + | 0.935387i | \(0.615051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.6761 | − | 18.6761i | 0.841128 | − | 0.841128i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −41.5443 | −1.86352 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.3798 | − | 14.3798i | 0.643728 | − | 0.643728i | −0.307742 | − | 0.951470i | \(-0.599573\pi\) |
0.951470 | + | 0.307742i | \(0.0995734\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.2969i | 1.35087i | 0.737420 | + | 0.675435i | \(0.236044\pi\) | ||||
−0.737420 | + | 0.675435i | \(0.763956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.303911i | 0.0135239i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5825 | − | 10.5825i | 0.469063 | − | 0.469063i | −0.432548 | − | 0.901611i | \(-0.642385\pi\) |
0.901611 | + | 0.432548i | \(0.142385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.46824 | 0.109188 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.447718 | − | 0.447718i | 0.0197288 | − | 0.0197288i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.99647 | + | 6.99647i | 0.307704 | + | 0.307704i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.9049i | 1.09110i | 0.838078 | + | 0.545551i | \(0.183680\pi\) | ||||
−0.838078 | + | 0.545551i | \(0.816320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9008 | − | 12.9008i | −0.564112 | − | 0.564112i | 0.366361 | − | 0.930473i | \(-0.380604\pi\) |
−0.930473 | + | 0.366361i | \(0.880604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.01704 | −0.0878638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.550984 | − | 0.550984i | −0.0238657 | − | 0.0238657i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.06074i | 0.175561i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.0671 | − | 34.0671i | −1.46738 | − | 1.46738i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.2767 | + | 18.2767i | −0.785776 | + | 0.785776i | −0.980799 | − | 0.195023i | \(-0.937522\pi\) |
0.195023 | + | 0.980799i | \(0.437522\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.82880 | 0.164008 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.7355 | − | 13.7355i | 0.587287 | − | 0.587287i | −0.349609 | − | 0.936896i | \(-0.613685\pi\) |
0.936896 | + | 0.349609i | \(0.113685\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.4120i | 1.12519i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 50.1055i | − | 2.13070i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.5525 | + | 27.5525i | −1.16744 | + | 1.16744i | −0.184631 | + | 0.982808i | \(0.559109\pi\) |
−0.982808 | + | 0.184631i | \(0.940891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.191354 | −0.00809342 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.8928 | − | 19.8928i | 0.838383 | − | 0.838383i | −0.150263 | − | 0.988646i | \(-0.548012\pi\) |
0.988646 | + | 0.150263i | \(0.0480121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.19879 | − | 3.19879i | −0.134574 | − | 0.134574i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.4849i | 0.565317i | 0.959221 | + | 0.282658i | \(0.0912163\pi\) | ||||
−0.959221 | + | 0.282658i | \(0.908784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8284 | − | 14.8284i | −0.620550 | − | 0.620550i | 0.325122 | − | 0.945672i | \(-0.394595\pi\) |
−0.945672 | + | 0.325122i | \(0.894595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5077 | −0.563308 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6176 | −0.483648 | −0.241824 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241824 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −48.5010 | − | 48.5010i | −2.01216 | − | 2.01216i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.44158i | − | 0.101120i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.0268 | + | 17.0268i | 0.702773 | + | 0.702773i | 0.965005 | − | 0.262232i | \(-0.0844585\pi\) |
−0.262232 | + | 0.965005i | \(0.584459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.42627 | − | 1.42627i | 0.0587682 | − | 0.0587682i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −41.5372 | −1.70573 | −0.852865 | − | 0.522132i | \(-0.825137\pi\) | ||||
−0.852865 | + | 0.522132i | \(0.825137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52099 | − | 5.52099i | 0.226338 | − | 0.226338i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.43160i | 0.262788i | 0.991330 | + | 0.131394i | \(0.0419453\pi\) | ||||
−0.991330 | + | 0.131394i | \(0.958055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.45844i | − | 0.141073i | −0.997509 | − | 0.0705364i | \(-0.977529\pi\) | ||
0.997509 | − | 0.0705364i | \(-0.0224711\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.414494 | − | 0.414494i | 0.0168516 | − | 0.0168516i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.1019 | 1.22180 | 0.610900 | − | 0.791708i | \(-0.290808\pi\) | ||||
0.610900 | + | 0.791708i | \(0.290808\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.168043 | − | 0.168043i | 0.00679829 | − | 0.00679829i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.50490 | − | 2.50490i | −0.101172 | − | 0.101172i | 0.654709 | − | 0.755881i | \(-0.272791\pi\) |
−0.755881 | + | 0.654709i | \(0.772791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.9098i | − | 0.922315i | −0.887318 | − | 0.461157i | \(-0.847434\pi\) | ||
0.887318 | − | 0.461157i | \(-0.152566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.6104 | − | 28.6104i | −1.14995 | − | 1.14995i | −0.986562 | − | 0.163386i | \(-0.947758\pi\) |
−0.163386 | − | 0.986562i | \(-0.552242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 66.7847 | 2.67567 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.6855 | −0.867420 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8647 | + | 15.8647i | 0.632567 | + | 0.632567i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.1851i | − | 0.445270i | −0.974902 | − | 0.222635i | \(-0.928534\pi\) | ||
0.974902 | − | 0.222635i | \(-0.0714659\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.70774 | + | 1.70774i | 0.0677698 | + | 0.0677698i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.818234 | + | 0.818234i | −0.0324196 | + | 0.0324196i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.69312 | 0.264362 | 0.132181 | − | 0.991226i | \(-0.457802\pi\) | ||||
0.132181 | + | 0.991226i | \(0.457802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.9410 | + | 17.9410i | −0.707522 | + | 0.707522i | −0.966014 | − | 0.258491i | \(-0.916775\pi\) |
0.258491 | + | 0.966014i | \(0.416775\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.72999i | 0.264583i | 0.991211 | + | 0.132292i | \(0.0422335\pi\) | ||||
−0.991211 | + | 0.132292i | \(0.957766\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.7890i | − | 0.776786i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.1731 | − | 26.1731i | 1.02423 | − | 1.02423i | 0.0245347 | − | 0.999699i | \(-0.492190\pi\) |
0.999699 | − | 0.0245347i | \(-0.00781042\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.41921 | 0.0554529 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.9741 | + | 13.9741i | −0.544353 | + | 0.544353i | −0.924802 | − | 0.380449i | \(-0.875770\pi\) |
0.380449 | + | 0.924802i | \(0.375770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.9241 | − | 11.9241i | −0.463794 | − | 0.463794i | 0.436103 | − | 0.899897i | \(-0.356358\pi\) |
−0.899897 | + | 0.436103i | \(0.856358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.80785i | 0.302776i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6041 | + | 14.6041i | 0.565473 | + | 0.565473i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.5021 | −0.521244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.3066 | −1.43807 | −0.719033 | − | 0.694976i | \(-0.755415\pi\) | ||||
−0.719033 | + | 0.694976i | \(0.755415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.447461 | + | 0.447461i | 0.0171973 | + | 0.0171973i | 0.715653 | − | 0.698456i | \(-0.246129\pi\) |
−0.698456 | + | 0.715653i | \(0.746129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 19.6764i | − | 0.755113i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.27521 | + | 4.27521i | 0.163586 | + | 0.163586i | 0.784153 | − | 0.620567i | \(-0.213098\pi\) |
−0.620567 | + | 0.784153i | \(0.713098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.13178 | + | 1.13178i | −0.0432430 | + | 0.0432430i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0586426 | −0.00223410 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0786 | − | 20.0786i | 0.763827 | − | 0.763827i | −0.213185 | − | 0.977012i | \(-0.568384\pi\) |
0.977012 | + | 0.213185i | \(0.0683836\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.93926i | − | 0.149425i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.5443i | 1.27058i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.4467 | + | 10.4467i | −0.394565 | + | 0.394565i | −0.876311 | − | 0.481746i | \(-0.840003\pi\) |
0.481746 | + | 0.876311i | \(0.340003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.4361 | −0.846192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.06793 | + | 2.06793i | −0.0777727 | + | 0.0777727i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0916 | − | 16.0916i | −0.604332 | − | 0.604332i | 0.337127 | − | 0.941459i | \(-0.390545\pi\) |
−0.941459 | + | 0.337127i | \(0.890545\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.57726i | − | 0.0590690i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0984373 | − | 0.0984373i | −0.00368135 | − | 0.00368135i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9957 | −1.15594 | −0.577972 | − | 0.816057i | \(-0.696156\pi\) | ||||
−0.577972 | + | 0.816057i | \(0.696156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.09292 | 0.226912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.6584 | + | 24.6584i | 0.915790 | + | 0.915790i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1117i | 1.52475i | 0.647135 | + | 0.762375i | \(0.275967\pi\) | ||||
−0.647135 | + | 0.762375i | \(0.724033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.82490 | + | 5.82490i | 0.215442 | + | 0.215442i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.146061 | + | 0.146061i | −0.00539490 | + | 0.00539490i | −0.709799 | − | 0.704404i | \(-0.751214\pi\) |
0.704404 | + | 0.709799i | \(0.251214\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.6792 | 0.688058 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.50766 | + | 1.50766i | −0.0554601 | + | 0.0554601i | −0.734293 | − | 0.678833i | \(-0.762486\pi\) |
0.678833 | + | 0.734293i | \(0.262486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40.5175i | − | 1.48644i | −0.669046 | − | 0.743221i | \(-0.733297\pi\) | ||
0.669046 | − | 0.743221i | \(-0.266703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.69256i | 0.245196i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.6309 | + | 27.6309i | −1.00961 | + | 1.00961i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5843 | 0.459208 | 0.229604 | − | 0.973284i | \(-0.426257\pi\) | ||||
0.229604 | + | 0.973284i | \(0.426257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.34129 | − | 3.34129i | 0.121602 | − | 0.121602i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.49900 | + | 7.49900i | 0.272556 | + | 0.272556i | 0.830128 | − | 0.557572i | \(-0.188267\pi\) |
−0.557572 | + | 0.830128i | \(0.688267\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 42.8182i | − | 1.55216i | −0.630635 | − | 0.776079i | \(-0.717206\pi\) | ||
0.630635 | − | 0.776079i | \(-0.282794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.0527 | + | 26.0527i | 0.943172 | + | 0.943172i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.475298 | −0.0171620 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.7455 | 0.459614 | 0.229807 | − | 0.973236i | \(-0.426190\pi\) | ||||
0.229807 | + | 0.973236i | \(0.426190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.8765 | − | 22.8765i | −0.822809 | − | 0.822809i | 0.163701 | − | 0.986510i | \(-0.447657\pi\) |
−0.986510 | + | 0.163701i | \(0.947657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.66314i | − | 0.0956630i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.7194 | − | 23.7194i | −0.849836 | − | 0.849836i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.5478 | − | 22.5478i | 0.806825 | − | 0.806825i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.8253 | −0.386370 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.20470 | − | 5.20470i | 0.185528 | − | 0.185528i | −0.608232 | − | 0.793759i | \(-0.708121\pi\) |
0.793759 | + | 0.608232i | \(0.208121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 43.5317i | − | 1.54781i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.324298i | 0.0115162i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.0149 | − | 17.0149i | 0.602698 | − | 0.602698i | −0.338330 | − | 0.941028i | \(-0.609862\pi\) |
0.941028 | + | 0.338330i | \(0.109862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.2306 | −0.361932 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.33962 | + | 1.33962i | −0.0472740 | + | 0.0472740i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.31724 | + | 4.31724i | 0.152163 | + | 0.152163i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 7.83586i | − | 0.275494i | −0.990467 | − | 0.137747i | \(-0.956014\pi\) | ||
0.990467 | − | 0.137747i | \(-0.0439861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.3396 | + | 32.3396i | 1.13560 | + | 1.13560i | 0.989230 | + | 0.146366i | \(0.0467578\pi\) |
0.146366 | + | 0.989230i | \(0.453242\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.02684 | 0.176083 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.23765 | −0.288199 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.3541 | + | 19.3541i | 0.675464 | + | 0.675464i | 0.958970 | − | 0.283507i | \(-0.0914978\pi\) |
−0.283507 | + | 0.958970i | \(0.591498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 28.8560i | − | 1.00586i | −0.864328 | − | 0.502929i | \(-0.832256\pi\) | ||
0.864328 | − | 0.502929i | \(-0.167744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.1984 | + | 10.1984i | 0.354634 | + | 0.354634i | 0.861830 | − | 0.507197i | \(-0.169318\pi\) |
−0.507197 | + | 0.861830i | \(0.669318\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.3794 | + | 15.3794i | −0.534148 | + | 0.534148i | −0.921804 | − | 0.387656i | \(-0.873285\pi\) |
0.387656 | + | 0.921804i | \(0.373285\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 49.8147 | 1.72598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.95524 | − | 1.95524i | 0.0676640 | − | 0.0676640i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 44.4557i | − | 1.53478i | −0.641181 | − | 0.767390i | \(-0.721555\pi\) | ||
0.641181 | − | 0.767390i | \(-0.278445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 24.3200i | − | 0.838620i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.35139 | − | 4.35139i | 0.149692 | − | 0.149692i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.64077 | 0.193819 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.4057 | + | 12.4057i | −0.425262 | + | 0.425262i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7131 | + | 11.7131i | 0.401049 | + | 0.401049i | 0.878603 | − | 0.477553i | \(-0.158476\pi\) |
−0.477553 | + | 0.878603i | \(0.658476\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0888i | 0.652062i | 0.945359 | + | 0.326031i | \(0.105711\pi\) | ||||
−0.945359 | + | 0.326031i | \(0.894289\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1323 | − | 38.1323i | −1.30106 | − | 1.30106i | −0.927679 | − | 0.373379i | \(-0.878199\pi\) |
−0.373379 | − | 0.927679i | \(-0.621801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.64533 | 0.124089 | 0.0620443 | − | 0.998073i | \(-0.480238\pi\) | ||||
0.0620443 | + | 0.998073i | \(0.480238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.42826 | 0.0825632 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.1943 | + | 27.1943i | 0.922504 | + | 0.922504i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.448643i | − | 0.0152017i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.9213 | + | 14.9213i | 0.504433 | + | 0.504433i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.0563 | + | 40.0563i | −1.35260 | + | 1.35260i | −0.469866 | + | 0.882738i | \(0.655698\pi\) |
−0.882738 | + | 0.469866i | \(0.844302\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.0118 | 0.674214 | 0.337107 | − | 0.941466i | \(-0.390552\pi\) | ||||
0.337107 | + | 0.941466i | \(0.390552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.6273 | + | 10.6273i | −0.357636 | + | 0.357636i | −0.862941 | − | 0.505305i | \(-0.831380\pi\) |
0.505305 | + | 0.862941i | \(0.331380\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.1180i | 0.876958i | 0.898742 | + | 0.438479i | \(0.144483\pi\) | ||||
−0.898742 | + | 0.438479i | \(0.855517\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.2404i | 0.779458i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.23412 | − | 7.23412i | 0.242081 | − | 0.242081i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.21805 | 0.207847 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.87932 | + | 2.87932i | −0.0960306 | + | 0.0960306i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.78510 | + | 1.78510i | 0.0594704 | + | 0.0594704i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 7.25507i | − | 0.241167i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.2378 | + | 36.2378i | 1.20326 | + | 1.20326i | 0.973170 | + | 0.230087i | \(0.0739010\pi\) |
0.230087 | + | 0.973170i | \(0.426099\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0535 | −0.697533 | −0.348767 | − | 0.937210i | \(-0.613399\pi\) | ||||
−0.348767 | + | 0.937210i | \(0.613399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.6470 | 1.74236 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.65685 | + | 9.65685i | 0.318897 | + | 0.318897i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.8839i | 0.589937i | 0.955507 | + | 0.294968i | \(0.0953091\pi\) | ||||
−0.955507 | + | 0.294968i | \(0.904691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.541560 | − | 0.541560i | −0.0178257 | − | 0.0178257i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.9465 | + | 20.9465i | −0.688716 | + | 0.688716i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.2774 | −0.337192 | −0.168596 | − | 0.985685i | \(-0.553923\pi\) | ||||
−0.168596 | + | 0.985685i | \(0.553923\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.2243 | + | 35.2243i | −1.15443 | + | 1.15443i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.99294i | 0.195990i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5780i | 0.443574i | 0.975095 | + | 0.221787i | \(0.0711890\pi\) | ||||
−0.975095 | + | 0.221787i | \(0.928811\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.95902 | + | 3.95902i | −0.129060 | + | 0.129060i | −0.768686 | − | 0.639626i | \(-0.779089\pi\) |
0.639626 | + | 0.768686i | \(0.279089\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.2306 | −0.854186 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.1708 | − | 33.1708i | 1.07791 | − | 1.07791i | 0.0812084 | − | 0.996697i | \(-0.474122\pi\) |
0.996697 | − | 0.0812084i | \(-0.0258779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0321752 | + | 0.0321752i | 0.00104445 | + | 0.00104445i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.59115i | − | 0.181115i | −0.995891 | − | 0.0905576i | \(-0.971135\pi\) | ||
0.995891 | − | 0.0905576i | \(-0.0288649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.89023 | + | 2.89023i | 0.0935255 | + | 0.0935255i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.4022 | −0.497362 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6890 | −0.989969 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.83511 | − | 3.83511i | −0.123457 | − | 0.123457i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.7561i | 0.989048i | 0.869164 | + | 0.494524i | \(0.164658\pi\) | ||||
−0.869164 | + | 0.494524i | \(0.835342\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.03756 | − | 8.03756i | −0.257938 | − | 0.257938i | 0.566277 | − | 0.824215i | \(-0.308383\pi\) |
−0.824215 | + | 0.566277i | \(0.808383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.8043 | − | 26.8043i | 0.859307 | − | 0.859307i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.8323 | −0.730471 | −0.365235 | − | 0.930915i | \(-0.619012\pi\) | ||||
−0.365235 | + | 0.930915i | \(0.619012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.2468 | + | 36.2468i | −1.15845 | + | 1.15845i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.3557i | 1.47852i | 0.673422 | + | 0.739258i | \(0.264824\pi\) | ||||
−0.673422 | + | 0.739258i | \(0.735176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 5.01686i | − | 0.159850i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.55489 | + | 4.55489i | −0.144837 | + | 0.144837i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.43683 | −0.109175 | −0.0545873 | − | 0.998509i | \(-0.517384\pi\) | ||||
−0.0545873 | + | 0.998509i | \(0.517384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.23245 | + | 1.23245i | −0.0390712 | + | 0.0390712i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.9430 | + | 21.9430i | 0.694940 | + | 0.694940i | 0.963315 | − | 0.268374i | \(-0.0864864\pi\) |
−0.268374 | + | 0.963315i | \(0.586486\pi\) | |||||||
\(998\) | 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 | 1152.2.k.f.865.2 | 8 | ||
3.2 | odd | 2 | 384.2.j.a.97.2 | 8 | |||
4.3 | odd | 2 | 1152.2.k.c.865.2 | 8 | |||
8.3 | odd | 2 | 144.2.k.b.37.1 | 8 | |||
8.5 | even | 2 | 576.2.k.b.433.3 | 8 | |||
12.11 | even | 2 | 384.2.j.b.97.4 | 8 | |||
16.3 | odd | 4 | 1152.2.k.c.289.2 | 8 | |||
16.5 | even | 4 | 576.2.k.b.145.3 | 8 | |||
16.11 | odd | 4 | 144.2.k.b.109.1 | 8 | |||
16.13 | even | 4 | inner | 1152.2.k.f.289.2 | 8 | ||
24.5 | odd | 2 | 192.2.j.a.49.3 | 8 | |||
24.11 | even | 2 | 48.2.j.a.37.4 | yes | 8 | ||
32.3 | odd | 8 | 9216.2.a.y.1.3 | 4 | |||
32.13 | even | 8 | 9216.2.a.bn.1.2 | 4 | |||
32.19 | odd | 8 | 9216.2.a.bo.1.2 | 4 | |||
32.29 | even | 8 | 9216.2.a.x.1.3 | 4 | |||
48.5 | odd | 4 | 192.2.j.a.145.3 | 8 | |||
48.11 | even | 4 | 48.2.j.a.13.4 | ✓ | 8 | ||
48.29 | odd | 4 | 384.2.j.a.289.2 | 8 | |||
48.35 | even | 4 | 384.2.j.b.289.4 | 8 | |||
96.5 | odd | 8 | 3072.2.d.i.1537.3 | 8 | |||
96.11 | even | 8 | 3072.2.d.f.1537.2 | 8 | |||
96.29 | odd | 8 | 3072.2.a.n.1.2 | 4 | |||
96.35 | even | 8 | 3072.2.a.t.1.2 | 4 | |||
96.53 | odd | 8 | 3072.2.d.i.1537.6 | 8 | |||
96.59 | even | 8 | 3072.2.d.f.1537.7 | 8 | |||
96.77 | odd | 8 | 3072.2.a.o.1.3 | 4 | |||
96.83 | even | 8 | 3072.2.a.i.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.4 | ✓ | 8 | 48.11 | even | 4 | ||
48.2.j.a.37.4 | yes | 8 | 24.11 | even | 2 | ||
144.2.k.b.37.1 | 8 | 8.3 | odd | 2 | |||
144.2.k.b.109.1 | 8 | 16.11 | odd | 4 | |||
192.2.j.a.49.3 | 8 | 24.5 | odd | 2 | |||
192.2.j.a.145.3 | 8 | 48.5 | odd | 4 | |||
384.2.j.a.97.2 | 8 | 3.2 | odd | 2 | |||
384.2.j.a.289.2 | 8 | 48.29 | odd | 4 | |||
384.2.j.b.97.4 | 8 | 12.11 | even | 2 | |||
384.2.j.b.289.4 | 8 | 48.35 | even | 4 | |||
576.2.k.b.145.3 | 8 | 16.5 | even | 4 | |||
576.2.k.b.433.3 | 8 | 8.5 | even | 2 | |||
1152.2.k.c.289.2 | 8 | 16.3 | odd | 4 | |||
1152.2.k.c.865.2 | 8 | 4.3 | odd | 2 | |||
1152.2.k.f.289.2 | 8 | 16.13 | even | 4 | inner | ||
1152.2.k.f.865.2 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.a.i.1.3 | 4 | 96.83 | even | 8 | |||
3072.2.a.n.1.2 | 4 | 96.29 | odd | 8 | |||
3072.2.a.o.1.3 | 4 | 96.77 | odd | 8 | |||
3072.2.a.t.1.2 | 4 | 96.35 | even | 8 | |||
3072.2.d.f.1537.2 | 8 | 96.11 | even | 8 | |||
3072.2.d.f.1537.7 | 8 | 96.59 | even | 8 | |||
3072.2.d.i.1537.3 | 8 | 96.5 | odd | 8 | |||
3072.2.d.i.1537.6 | 8 | 96.53 | odd | 8 | |||
9216.2.a.x.1.3 | 4 | 32.29 | even | 8 | |||
9216.2.a.y.1.3 | 4 | 32.3 | odd | 8 | |||
9216.2.a.bn.1.2 | 4 | 32.13 | even | 8 | |||
9216.2.a.bo.1.2 | 4 | 32.19 | odd | 8 |