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 | 289.2 | ||
Root | \(0.500000 + 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.289 |
Dual form | 1152.2.k.f.865.2 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | −0.778017 | − | 0.628243i | \(-0.783774\pi\) |
0.628243 | + | 0.778017i | \(0.283774\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.55765i | 1.72263i | 0.508072 | + | 0.861314i | \(0.330358\pi\) | ||||
−0.508072 | + | 0.861314i | \(0.669642\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.47363 | − | 2.47363i | 0.745826 | − | 0.745826i | −0.227866 | − | 0.973692i | \(-0.573175\pi\) |
0.973692 | + | 0.227866i | \(0.0731749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0594122 | + | 0.0594122i | 0.0164780 | + | 0.0164780i | 0.715298 | − | 0.698820i | \(-0.246291\pi\) |
−0.698820 | + | 0.715298i | \(0.746291\pi\) | |||||||
\(14\) | 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 | 0.936754 | − | 0.349989i | \(-0.113815\pi\) |
−0.349989 | + | 0.936754i | \(0.613815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 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 | 0.0403780 | − | 0.999184i | \(-0.487144\pi\) |
−0.999184 | + | 0.0403780i | \(0.987144\pi\) | |||||||
\(30\) | 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 | −0.968822 | − | 0.247756i | \(-0.920307\pi\) |
0.247756 | + | 0.968822i | \(0.420307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.27391i | 1.44834i | 0.689620 | + | 0.724171i | \(0.257777\pi\) | ||||
−0.689620 | + | 0.724171i | \(0.742223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61040 | + | 1.61040i | −0.245583 | + | 0.245583i | −0.819155 | − | 0.573572i | \(-0.805557\pi\) |
0.573572 | + | 0.819155i | \(0.305557\pi\) | |||||||
\(44\) | 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 | −0.740189 | − | 0.672399i | \(-0.765264\pi\) |
0.672399 | + | 0.740189i | \(0.265264\pi\) | |||||||
\(54\) | 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 | −0.917800 | − | 0.397044i | \(-0.870036\pi\) |
0.397044 | + | 0.917800i | \(0.370036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.72922 | − | 2.72922i | −0.349441 | − | 0.349441i | 0.510460 | − | 0.859901i | \(-0.329475\pi\) |
−0.859901 | + | 0.510460i | \(0.829475\pi\) | |||||||
\(62\) | 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 | 0.899072 | − | 0.437800i | \(-0.144242\pi\) |
−0.437800 | + | 0.899072i | \(0.644242\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.11529i | 1.08179i | 0.841091 | + | 0.540893i | \(0.181914\pi\) | ||||
−0.841091 | + | 0.540893i | \(0.818086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.541560i | − | 0.0633848i | −0.999498 | − | 0.0316924i | \(-0.989910\pi\) | ||
0.999498 | − | 0.0316924i | \(-0.0100897\pi\) | |||||||
\(74\) | 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 | 0.982660 | + | 0.185415i | \(0.0593628\pi\) |
0.185415 | + | 0.982660i | \(0.440637\pi\) | |||||||
\(84\) | 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 | \(-0.716930\pi\) | ||
0.629964 | − | 0.776625i | \(-0.283070\pi\) | |||||||
\(90\) | 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 | −0.729320 | − | 0.684173i | \(-0.760164\pi\) |
0.684173 | + | 0.729320i | \(0.260164\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.33686i | − | 0.131724i | −0.997829 | − | 0.0658622i | \(-0.979020\pi\) | ||
0.997829 | − | 0.0658622i | \(-0.0209798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.06255 | + | 6.06255i | −0.586088 | + | 0.586088i | −0.936570 | − | 0.350481i | \(-0.886018\pi\) |
0.350481 | + | 0.936570i | \(0.386018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.71627 | − | 5.71627i | −0.547519 | − | 0.547519i | 0.378203 | − | 0.925722i | \(-0.376542\pi\) |
−0.925722 | + | 0.378203i | \(0.876542\pi\) | |||||||
\(110\) | 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 | 0.608461 | − | 0.793584i | \(-0.291787\pi\) |
−0.793584 | + | 0.608461i | \(0.791787\pi\) | |||||||
\(132\) | 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 | \(0.0461127\pi\) | ||||
−0.989525 | + | 0.144361i | \(0.953887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.88118 | − | 5.88118i | 0.498835 | − | 0.498835i | −0.412240 | − | 0.911075i | \(-0.635254\pi\) |
0.911075 | + | 0.412240i | \(0.135254\pi\) | |||||||
\(140\) | 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 | −0.985899 | − | 0.167342i | \(-0.946482\pi\) |
0.167342 | + | 0.985899i | \(0.446482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.97685i | − | 0.811905i | −0.913894 | − | 0.405952i | \(-0.866940\pi\) | ||
0.913894 | − | 0.405952i | \(-0.133060\pi\) | |||||||
\(152\) | 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 | 0.934877 | + | 0.354971i | \(0.115509\pi\) |
0.354971 | + | 0.934877i | \(0.384491\pi\) | |||||||
\(158\) | 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 | 0.349214 | − | 0.937043i | \(-0.386449\pi\) |
−0.937043 | + | 0.349214i | \(0.886449\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.83822i | − | 0.451775i | −0.974153 | − | 0.225888i | \(-0.927472\pi\) | ||
0.974153 | − | 0.225888i | \(-0.0725282\pi\) | |||||||
\(168\) | 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 | 0.555734 | − | 0.831360i | \(-0.312437\pi\) |
−0.831360 | + | 0.555734i | \(0.812437\pi\) | |||||||
\(174\) | 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 | 0.269212 | − | 0.963081i | \(-0.413237\pi\) |
−0.963081 | + | 0.269212i | \(0.913237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.8316 | − | 10.8316i | 0.805104 | − | 0.805104i | −0.178785 | − | 0.983888i | \(-0.557217\pi\) |
0.983888 | + | 0.178785i | \(0.0572165\pi\) | |||||||
\(182\) | 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 | −0.388014 | − | 0.921654i | \(-0.626839\pi\) |
0.921654 | + | 0.388014i | \(0.126839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.68000i | 0.260868i | 0.991457 | + | 0.130434i | \(0.0416371\pi\) | ||||
−0.991457 | + | 0.130434i | \(0.958363\pi\) | |||||||
\(200\) | 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 | 0.963677 | − | 0.267069i | \(-0.0860551\pi\) |
−0.267069 | + | 0.963677i | \(0.586055\pi\) | |||||||
\(212\) | 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 | 0.259445 | − | 0.965758i | \(-0.416460\pi\) |
−0.965758 | + | 0.259445i | \(0.916460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1712 | − | 20.1712i | 1.33295 | − | 1.33295i | 0.430229 | − | 0.902720i | \(-0.358433\pi\) |
0.902720 | − | 0.430229i | \(-0.141567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.5702i | − | 0.889014i | −0.895775 | − | 0.444507i | \(-0.853379\pi\) | ||
0.895775 | − | 0.444507i | \(-0.146621\pi\) | |||||||
\(234\) | 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 | −0.999985 | − | 0.00541463i | \(-0.998276\pi\) |
0.00541463 | + | 0.999985i | \(0.498276\pi\) | |||||||
\(252\) | 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 | \(0.134715\pi\) | ||||
−0.911772 | + | 0.410697i | \(0.865285\pi\) | |||||||
\(264\) | 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 | 0.255257 | − | 0.966873i | \(-0.417840\pi\) |
−0.966873 | + | 0.255257i | \(0.917840\pi\) | |||||||
\(270\) | 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 | −0.296949 | − | 0.954893i | \(-0.595969\pi\) |
0.954893 | + | 0.296949i | \(0.0959690\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8910i | 1.36556i | 0.730624 | + | 0.682780i | \(0.239229\pi\) | ||||
−0.730624 | + | 0.682780i | \(0.760771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.48528 | − | 4.48528i | 0.266622 | − | 0.266622i | −0.561115 | − | 0.827738i | \(-0.689628\pi\) |
0.827738 | + | 0.561115i | \(0.189628\pi\) | |||||||
\(284\) | 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 | 0.313636 | − | 0.949543i | \(-0.398453\pi\) |
0.949543 | − | 0.313636i | \(-0.101547\pi\) | |||||||
\(294\) | 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 | 0.271253 | − | 0.962508i | \(-0.412562\pi\) |
−0.962508 | + | 0.271253i | \(0.912562\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 26.8651i | − | 1.52338i | −0.647943 | − | 0.761689i | \(-0.724370\pi\) | ||
0.647943 | − | 0.761689i | \(-0.275630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6890i | 1.11289i | 0.830885 | + | 0.556445i | \(0.187835\pi\) | ||||
−0.830885 | + | 0.556445i | \(0.812165\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.3447 | + | 21.3447i | 1.19884 | + | 1.19884i | 0.974515 | + | 0.224323i | \(0.0720171\pi\) |
0.224323 | + | 0.974515i | \(0.427983\pi\) | |||||||
\(318\) | 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 | −0.176690 | − | 0.984266i | \(-0.556539\pi\) |
0.984266 | + | 0.176690i | \(0.0565391\pi\) | |||||||
\(332\) | 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 | −0.351067 | − | 0.936350i | \(-0.614181\pi\) |
0.936350 | + | 0.351067i | \(0.114181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0563 | − | 20.0563i | −1.07359 | − | 1.07359i | −0.997068 | − | 0.0765186i | \(-0.975620\pi\) |
−0.0765186 | − | 0.997068i | \(-0.524380\pi\) | |||||||
\(350\) | 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 | \(0.344786\pi\) | ||||
−0.468522 | + | 0.883452i | \(0.655214\pi\) | |||||||
\(360\) | 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 | −0.999836 | − | 0.0181339i | \(-0.994227\pi\) |
0.0181339 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(374\) | 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 | −0.751306 | − | 0.659954i | \(-0.770576\pi\) |
0.659954 | + | 0.751306i | \(0.270576\pi\) | |||||||
\(380\) | 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 | −0.938565 | − | 0.345103i | \(-0.887844\pi\) |
0.345103 | + | 0.938565i | \(0.387844\pi\) | |||||||
\(390\) | 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 | 0.896689 | − | 0.442661i | \(-0.145965\pi\) |
−0.442661 | + | 0.896689i | \(0.645965\pi\) | |||||||
\(398\) | 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 | \(-0.785629\pi\) | ||
0.781665 | − | 0.623699i | \(-0.214371\pi\) | |||||||
\(410\) | 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 | 0.507392 | − | 0.861716i | \(-0.330610\pi\) |
−0.861716 | + | 0.507392i | \(0.830610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.39550 | + | 2.39550i | −0.116749 | + | 0.116749i | −0.763068 | − | 0.646318i | \(-0.776308\pi\) |
0.646318 | + | 0.763068i | \(0.276308\pi\) | |||||||
\(422\) | 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 | \(0.250239\pi\) | ||||
−0.706576 | + | 0.707637i | \(0.749761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3056 | + | 10.3056i | −0.489633 | + | 0.489633i | −0.908190 | − | 0.418557i | \(-0.862536\pi\) |
0.418557 | + | 0.908190i | \(0.362536\pi\) | |||||||
\(444\) | 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 | \(-0.932464\pi\) | ||
0.977576 | − | 0.210584i | \(-0.0675364\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.6218 | + | 14.6218i | 0.681004 | + | 0.681004i | 0.960226 | − | 0.279223i | \(-0.0900767\pi\) |
−0.279223 | + | 0.960226i | \(0.590077\pi\) | |||||||
\(462\) | 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 | 0.995725 | + | 0.0923633i | \(0.0294421\pi\) |
0.0923633 | + | 0.995725i | \(0.470558\pi\) | |||||||
\(468\) | 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 | \(0.295418\pi\) | ||||
−0.599369 | + | 0.800473i | \(0.704582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8910 | − | 12.8910i | 0.581761 | − | 0.581761i | −0.353626 | − | 0.935387i | \(-0.615051\pi\) |
0.935387 | + | 0.353626i | \(0.115051\pi\) | |||||||
\(492\) | 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 | 0.951470 | − | 0.307742i | \(-0.0995734\pi\) |
−0.307742 | + | 0.951470i | \(0.599573\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 30.2969i | − | 1.35087i | −0.737420 | − | 0.675435i | \(-0.763956\pi\) | ||
0.737420 | − | 0.675435i | \(-0.236044\pi\) | |||||||
\(504\) | 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 | 0.901611 | − | 0.432548i | \(-0.142385\pi\) |
−0.432548 | + | 0.901611i | \(0.642385\pi\) | |||||||
\(510\) | 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 | \(-0.816320\pi\) | ||
0.838078 | − | 0.545551i | \(-0.183680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9008 | + | 12.9008i | −0.564112 | + | 0.564112i | −0.930473 | − | 0.366361i | \(-0.880604\pi\) |
0.366361 | + | 0.930473i | \(0.380604\pi\) | |||||||
\(524\) | 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 | 0.195023 | − | 0.980799i | \(-0.437522\pi\) |
−0.980799 | + | 0.195023i | \(0.937522\pi\) | |||||||
\(542\) | 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 | 0.936896 | − | 0.349609i | \(-0.113685\pi\) |
−0.349609 | + | 0.936896i | \(0.613685\pi\) | |||||||
\(548\) | 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 | −0.982808 | − | 0.184631i | \(-0.940891\pi\) |
−0.184631 | − | 0.982808i | \(-0.559109\pi\) | |||||||
\(558\) | 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 | 0.988646 | − | 0.150263i | \(-0.0480121\pi\) |
−0.150263 | + | 0.988646i | \(0.548012\pi\) | |||||||
\(564\) | 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 | \(-0.908784\pi\) | ||
0.959221 | − | 0.282658i | \(-0.0912163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8284 | + | 14.8284i | −0.620550 | + | 0.620550i | −0.945672 | − | 0.325122i | \(-0.894595\pi\) |
0.325122 | + | 0.945672i | \(0.394595\pi\) | |||||||
\(572\) | 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 | −0.262232 | − | 0.965005i | \(-0.584459\pi\) |
0.965005 | + | 0.262232i | \(0.0844585\pi\) | |||||||
\(588\) | 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 | \(-0.958055\pi\) | ||
0.991330 | − | 0.131394i | \(-0.0419453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.45844i | 0.141073i | 0.997509 | + | 0.0705364i | \(0.0224711\pi\) | ||||
−0.997509 | + | 0.0705364i | \(0.977529\pi\) | |||||||
\(602\) | 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 | −0.755881 | − | 0.654709i | \(-0.772791\pi\) |
0.654709 | + | 0.755881i | \(0.272791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.9098i | 0.922315i | 0.887318 | + | 0.461157i | \(0.152566\pi\) | ||||
−0.887318 | + | 0.461157i | \(0.847434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.6104 | + | 28.6104i | −1.14995 | + | 1.14995i | −0.163386 | + | 0.986562i | \(0.552242\pi\) |
−0.986562 | + | 0.163386i | \(0.947758\pi\) | |||||||
\(620\) | 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 | \(0.0714659\pi\) | ||||
−0.974902 | + | 0.222635i | \(0.928534\pi\) | |||||||
\(632\) | 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 | 0.258491 | − | 0.966014i | \(-0.416775\pi\) |
−0.966014 | + | 0.258491i | \(0.916775\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.72999i | − | 0.264583i | −0.991211 | − | 0.132292i | \(-0.957766\pi\) | ||
0.991211 | − | 0.132292i | \(-0.0422335\pi\) | |||||||
\(648\) | 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 | 0.999699 | + | 0.0245347i | \(0.00781042\pi\) |
0.0245347 | + | 0.999699i | \(0.492190\pi\) | |||||||
\(654\) | 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 | 0.380449 | − | 0.924802i | \(-0.375770\pi\) |
−0.924802 | + | 0.380449i | \(0.875770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.9241 | + | 11.9241i | −0.463794 | + | 0.463794i | −0.899897 | − | 0.436103i | \(-0.856358\pi\) |
0.436103 | + | 0.899897i | \(0.356358\pi\) | |||||||
\(662\) | 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 | −0.698456 | − | 0.715653i | \(-0.746129\pi\) |
0.715653 | + | 0.698456i | \(0.246129\pi\) | |||||||
\(678\) | 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 | −0.620567 | − | 0.784153i | \(-0.713098\pi\) |
0.784153 | + | 0.620567i | \(0.213098\pi\) | |||||||
\(684\) | 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 | 0.977012 | − | 0.213185i | \(-0.0683836\pi\) |
−0.213185 | + | 0.977012i | \(0.568384\pi\) | |||||||
\(692\) | 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 | 0.481746 | − | 0.876311i | \(-0.340003\pi\) |
−0.876311 | + | 0.481746i | \(0.840003\pi\) | |||||||
\(702\) | 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 | −0.941459 | − | 0.337127i | \(-0.890545\pi\) |
0.337127 | + | 0.941459i | \(0.390545\pi\) | |||||||
\(710\) | 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 | \(-0.724033\pi\) | ||
0.647135 | − | 0.762375i | \(-0.275967\pi\) | |||||||
\(728\) | 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 | 0.704404 | − | 0.709799i | \(-0.251214\pi\) |
−0.709799 | + | 0.704404i | \(0.751214\pi\) | |||||||
\(734\) | 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 | 0.678833 | − | 0.734293i | \(-0.262486\pi\) |
−0.734293 | + | 0.678833i | \(0.762486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.5175i | 1.48644i | 0.669046 | + | 0.743221i | \(0.266703\pi\) | ||||
−0.669046 | + | 0.743221i | \(0.733297\pi\) | |||||||
\(744\) | 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 | −0.557572 | − | 0.830128i | \(-0.688267\pi\) |
0.830128 | + | 0.557572i | \(0.188267\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.8182i | 1.55216i | 0.630635 | + | 0.776079i | \(0.282794\pi\) | ||||
−0.630635 | + | 0.776079i | \(0.717206\pi\) | |||||||
\(762\) | 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 | −0.986510 | − | 0.163701i | \(-0.947657\pi\) |
0.163701 | + | 0.986510i | \(0.447657\pi\) | |||||||
\(774\) | 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 | 0.793759 | − | 0.608232i | \(-0.208121\pi\) |
−0.608232 | + | 0.793759i | \(0.708121\pi\) | |||||||
\(788\) | 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 | 0.941028 | − | 0.338330i | \(-0.109862\pi\) |
−0.338330 | + | 0.941028i | \(0.609862\pi\) | |||||||
\(798\) | 0 | 0 |