Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(145,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, 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("576.145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.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: | \(4.59938315643\) |
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 | 145.1 | ||
Root | \(0.500000 - 0.0297061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.145 |
Dual form | 576.2.k.b.433.1 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(5\) | −1.74912 | + | 1.74912i | −0.782229 | + | 0.782229i | −0.980207 | − | 0.197977i | \(-0.936563\pi\) |
0.197977 | + | 0.980207i | \(0.436563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.55765i | − | 0.966700i | −0.875427 | − | 0.483350i | \(-0.839420\pi\) | ||
0.875427 | − | 0.483350i | \(-0.160580\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.473626 | − | 0.473626i | 0.142804 | − | 0.142804i | −0.632091 | − | 0.774894i | \(-0.717803\pi\) |
0.774894 | + | 0.632091i | \(0.217803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.88784 | + | 2.88784i | 0.800943 | + | 0.800943i | 0.983243 | − | 0.182300i | \(-0.0583543\pi\) |
−0.182300 | + | 0.983243i | \(0.558354\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.44549 | 1.56326 | 0.781630 | − | 0.623742i | \(-0.214389\pi\) | ||||
0.781630 | + | 0.623742i | \(0.214389\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.55765 | + | 4.55765i | 1.04560 | + | 1.04560i | 0.998910 | + | 0.0466864i | \(0.0148661\pi\) |
0.0466864 | + | 0.998910i | \(0.485134\pi\) | |||||||
\(20\) | 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 | ||||||||
\(25\) | − | 1.11882i | − | 0.223765i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.07931 | + | 3.07931i | 0.571813 | + | 0.571813i | 0.932635 | − | 0.360821i | \(-0.117504\pi\) |
−0.360821 | + | 0.932635i | \(0.617504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.55765 | −1.17779 | −0.588894 | − | 0.808210i | \(-0.700437\pi\) | ||||
−0.588894 | + | 0.808210i | \(0.700437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.47363 | + | 4.47363i | 0.756181 | + | 0.756181i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.72922 | + | 2.72922i | −0.448681 | + | 0.448681i | −0.894916 | − | 0.446235i | \(-0.852765\pi\) |
0.446235 | + | 0.894916i | \(0.352765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.788632i | − | 0.123164i | −0.998102 | − | 0.0615818i | \(-0.980385\pi\) | ||
0.998102 | − | 0.0615818i | \(-0.0196145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.389604 | − | 0.389604i | 0.0594141 | − | 0.0594141i | −0.676775 | − | 0.736190i | \(-0.736623\pi\) |
0.736190 | + | 0.676775i | \(0.236623\pi\) | |||||||
\(44\) | 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 | ||||||||
\(49\) | 0.458440 | 0.0654915 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.57754 | − | 2.57754i | 0.354053 | − | 0.354053i | −0.507562 | − | 0.861615i | \(-0.669453\pi\) |
0.861615 | + | 0.507562i | \(0.169453\pi\) | |||||||
\(54\) | 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 | \(-0.629964\pi\) |
0.917800 | + | 0.397044i | \(0.129964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.38607 | − | 4.38607i | −0.561579 | − | 0.561579i | 0.368177 | − | 0.929756i | \(-0.379982\pi\) |
−0.929756 | + | 0.368177i | \(0.879982\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.1023 | −1.25304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.11882 | + | 2.11882i | 0.258856 | + | 0.258856i | 0.824589 | − | 0.565733i | \(-0.191407\pi\) |
−0.565733 | + | 0.824589i | \(0.691407\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.11529i | − | 0.607074i | −0.952820 | − | 0.303537i | \(-0.901832\pi\) | ||
0.952820 | − | 0.303537i | \(-0.0981676\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.7721i | − | 1.72895i | −0.502676 | − | 0.864475i | \(-0.667651\pi\) | ||
0.502676 | − | 0.864475i | \(-0.332349\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.21137 | − | 1.21137i | −0.138048 | − | 0.138048i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.32000 | 0.711055 | 0.355528 | − | 0.934666i | \(-0.384301\pi\) | ||||
0.355528 | + | 0.934666i | \(0.384301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.641669 | + | 0.641669i | 0.0704323 | + | 0.0704323i | 0.741445 | − | 0.671013i | \(-0.234141\pi\) |
−0.671013 | + | 0.741445i | \(0.734141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2739 | + | 11.2739i | −1.22283 | + | 1.22283i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.31724i | − | 0.669626i | −0.942285 | − | 0.334813i | \(-0.891327\pi\) | ||
0.942285 | − | 0.334813i | \(-0.108673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.38607 | − | 7.38607i | 0.774271 | − | 0.774271i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.9437 | −1.63579 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.6533 | 1.28475 | 0.642375 | − | 0.766390i | \(-0.277949\pi\) | ||||
0.642375 | + | 0.766390i | \(0.277949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.52480 | + | 7.52480i | −0.748745 | + | 0.748745i | −0.974244 | − | 0.225498i | \(-0.927599\pi\) |
0.225498 | + | 0.974244i | \(0.427599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.33686i | 0.328790i | 0.986395 | + | 0.164395i | \(0.0525672\pi\) | ||||
−0.986395 | + | 0.164395i | \(0.947433\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0625 | + | 14.0625i | −1.35948 | + | 1.35948i | −0.484918 | + | 0.874560i | \(0.661151\pi\) |
−0.874560 | + | 0.484918i | \(0.838849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.76901 | + | 2.76901i | 0.265224 | + | 0.265224i | 0.827172 | − | 0.561949i | \(-0.189948\pi\) |
−0.561949 | + | 0.827172i | \(0.689948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.23765 | −0.210500 | −0.105250 | − | 0.994446i | \(-0.533564\pi\) | ||||
−0.105250 | + | 0.994446i | \(0.533564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.94725 | − | 4.94725i | −0.461334 | − | 0.461334i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 16.4853i | − | 1.51120i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5514i | 0.959214i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.78863 | − | 6.78863i | −0.607194 | − | 0.607194i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2145 | −1.08386 | −0.541931 | − | 0.840423i | \(-0.682307\pi\) | ||||
−0.541931 | + | 0.840423i | \(0.682307\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.77568 | − | 3.77568i | −0.329883 | − | 0.329883i | 0.522659 | − | 0.852542i | \(-0.324940\pi\) |
−0.852542 | + | 0.522659i | \(0.824940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6569 | − | 11.6569i | 1.01078 | − | 1.01078i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.10587i | 0.436224i | 0.975924 | + | 0.218112i | \(0.0699898\pi\) | ||||
−0.975924 | + | 0.218112i | \(0.930010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.7757 | + | 11.7757i | −0.998800 | + | 0.998800i | −0.999999 | − | 0.00119925i | \(-0.999618\pi\) |
0.00119925 | + | 0.999999i | \(0.499618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.73551 | 0.228755 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.7721 | −0.894578 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.90774 | − | 7.90774i | 0.647827 | − | 0.647827i | −0.304640 | − | 0.952467i | \(-0.598536\pi\) |
0.952467 | + | 0.304640i | \(0.0985363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.6506i | − | 1.19225i | −0.802893 | − | 0.596123i | \(-0.796707\pi\) | ||
0.802893 | − | 0.596123i | \(-0.203293\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.4701 | − | 11.4701i | 0.921300 | − | 0.921300i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.15196 | − | 3.15196i | −0.251553 | − | 0.251553i | 0.570054 | − | 0.821607i | \(-0.306922\pi\) |
−0.821607 | + | 0.570054i | \(0.806922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.23412 | 0.570128 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50490 | − | 5.50490i | −0.431177 | − | 0.431177i | 0.457852 | − | 0.889029i | \(-0.348619\pi\) |
−0.889029 | + | 0.457852i | \(0.848619\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.1814i | 1.56168i | 0.624730 | + | 0.780841i | \(0.285209\pi\) | ||||
−0.624730 | + | 0.780841i | \(0.714791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67923i | 0.283018i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.35322 | − | 4.35322i | −0.330969 | − | 0.330969i | 0.521985 | − | 0.852955i | \(-0.325192\pi\) |
−0.852955 | + | 0.521985i | \(0.825192\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.86156 | −0.216313 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.2833 | − | 13.2833i | −0.992843 | − | 0.992843i | 0.00713130 | − | 0.999975i | \(-0.497730\pi\) |
−0.999975 | + | 0.00713130i | \(0.997730\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.34628 | − | 6.34628i | 0.471715 | − | 0.471715i | −0.430754 | − | 0.902469i | \(-0.641752\pi\) |
0.902469 | + | 0.430754i | \(0.141752\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.54745i | − | 0.701943i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.05275 | − | 3.05275i | 0.223239 | − | 0.223239i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.60058 | 0.405243 | 0.202622 | − | 0.979257i | \(-0.435054\pi\) | ||||
0.202622 | + | 0.979257i | \(0.435054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.4514 | −1.40014 | −0.700071 | − | 0.714074i | \(-0.746848\pi\) | ||||
−0.700071 | + | 0.714074i | \(0.746848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.23793 | + | 1.23793i | −0.0881988 | + | 0.0881988i | −0.749830 | − | 0.661631i | \(-0.769865\pi\) |
0.661631 | + | 0.749830i | \(0.269865\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.993710i | − | 0.0704422i | −0.999380 | − | 0.0352211i | \(-0.988786\pi\) | ||
0.999380 | − | 0.0352211i | \(-0.0112135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.87579 | − | 7.87579i | 0.552772 | − | 0.552772i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.37941 | + | 1.37941i | 0.0963422 | + | 0.0963422i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.31724 | 0.298630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.22432 | − | 4.22432i | −0.290814 | − | 0.290814i | 0.546588 | − | 0.837402i | \(-0.315927\pi\) |
−0.837402 | + | 0.546588i | \(0.815927\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.36293i | 0.0929509i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.7721i | 1.13857i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.6135 | + | 18.6135i | 1.25208 | + | 1.25208i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.7659 | 1.59148 | 0.795740 | − | 0.605639i | \(-0.207082\pi\) | ||||
0.795740 | + | 0.605639i | \(0.207082\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.641669 | − | 0.641669i | −0.0425891 | − | 0.0425891i | 0.685492 | − | 0.728081i | \(-0.259587\pi\) |
−0.728081 | + | 0.685492i | \(0.759587\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.34275 | − | 5.34275i | 0.353059 | − | 0.353059i | −0.508188 | − | 0.861246i | \(-0.669684\pi\) |
0.861246 | + | 0.508188i | \(0.169684\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.2271i | 1.52166i | 0.648954 | + | 0.760828i | \(0.275207\pi\) | ||||
−0.648954 | + | 0.760828i | \(0.724793\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.94725 | + | 4.94725i | −0.322723 | + | 0.322723i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.9213 | 1.74140 | 0.870698 | − | 0.491817i | \(-0.163667\pi\) | ||||
0.870698 | + | 0.491817i | \(0.163667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3494 | −0.666664 | −0.333332 | − | 0.942809i | \(-0.608173\pi\) | ||||
−0.333332 | + | 0.942809i | \(0.608173\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.801866 | + | 0.801866i | −0.0512293 | + | 0.0512293i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.3235i | 1.67492i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.75696 | + | 9.75696i | −0.615854 | + | 0.615854i | −0.944465 | − | 0.328611i | \(-0.893419\pi\) |
0.328611 | + | 0.944465i | \(0.393419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.33962 | + | 1.33962i | 0.0842209 | + | 0.0842209i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.9965 | −1.06021 | −0.530105 | − | 0.847932i | \(-0.677848\pi\) | ||||
−0.530105 | + | 0.847932i | \(0.677848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.98038 | + | 6.98038i | 0.433740 | + | 0.433740i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.9929i | 1.84944i | 0.380643 | + | 0.924722i | \(0.375703\pi\) | ||||
−0.380643 | + | 0.924722i | \(0.624297\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.01686i | 0.553901i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.6003 | − | 20.6003i | −1.25602 | − | 1.25602i | −0.952976 | − | 0.303046i | \(-0.901996\pi\) |
−0.303046 | − | 0.952976i | \(-0.598004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.6506 | 1.61891 | 0.809453 | − | 0.587184i | \(-0.199764\pi\) | ||||
0.809453 | + | 0.587184i | \(0.199764\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.529904 | − | 0.529904i | −0.0319544 | − | 0.0319544i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.1220 | − | 12.1220i | 0.728338 | − | 0.728338i | −0.241951 | − | 0.970289i | \(-0.577787\pi\) |
0.970289 | + | 0.241951i | \(0.0777872\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.76588i | 0.164999i | 0.996591 | + | 0.0824993i | \(0.0262902\pi\) | ||||
−0.996591 | + | 0.0824993i | \(0.973710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.48528 | + | 4.48528i | −0.266622 | + | 0.266622i | −0.827738 | − | 0.561115i | \(-0.810372\pi\) |
0.561115 | + | 0.827738i | \(0.310372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.01704 | −0.119062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.5443 | 1.44378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.20793 | − | 8.20793i | 0.479512 | − | 0.479512i | −0.425463 | − | 0.904976i | \(-0.639889\pi\) |
0.904976 | + | 0.425463i | \(0.139889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.9929i | 0.814700i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.16804 | + | 8.16804i | −0.472370 | + | 0.472370i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.996470 | − | 0.996470i | −0.0574356 | − | 0.0574356i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.3435 | 0.878567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.4549 | − | 10.4549i | −0.596693 | − | 0.596693i | 0.342738 | − | 0.939431i | \(-0.388646\pi\) |
−0.939431 | + | 0.342738i | \(0.888646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 15.0761i | − | 0.854885i | −0.904043 | − | 0.427442i | \(-0.859415\pi\) | ||
0.904043 | − | 0.427442i | \(-0.140585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.0027i | − | 1.30019i | −0.759852 | − | 0.650096i | \(-0.774729\pi\) | ||
0.759852 | − | 0.650096i | \(-0.225271\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.75892 | + | 6.75892i | 0.379618 | + | 0.379618i | 0.870964 | − | 0.491346i | \(-0.163495\pi\) |
−0.491346 | + | 0.870964i | \(0.663495\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.91688 | 0.163314 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.3763 | + | 29.3763i | 1.63454 | + | 1.63454i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.23099 | − | 3.23099i | 0.179223 | − | 0.179223i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7.23412i | − | 0.398830i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.6631 | − | 19.6631i | 1.08078 | − | 1.08078i | 0.0843464 | − | 0.996436i | \(-0.473120\pi\) |
0.996436 | − | 0.0843464i | \(-0.0268802\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.41215 | −0.404969 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.00980 | 0.163954 | 0.0819771 | − | 0.996634i | \(-0.473877\pi\) | ||||
0.0819771 | + | 0.996634i | \(0.473877\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.10587 | + | 3.10587i | −0.168192 | + | 0.168192i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.0761i | − | 1.03001i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.27521 | − | 6.27521i | 0.336871 | − | 0.336871i | −0.518317 | − | 0.855188i | \(-0.673441\pi\) |
0.855188 | + | 0.518317i | \(0.173441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.74255 | − | 4.74255i | −0.253863 | − | 0.253863i | 0.568690 | − | 0.822552i | \(-0.307451\pi\) |
−0.822552 | + | 0.568690i | \(0.807451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.75882 | 0.466185 | 0.233093 | − | 0.972455i | \(-0.425116\pi\) | ||||
0.233093 | + | 0.972455i | \(0.425116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.94725 | + | 8.94725i | 0.474871 | + | 0.474871i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 32.7917i | − | 1.73068i | −0.501184 | − | 0.865341i | \(-0.667102\pi\) | ||
0.501184 | − | 0.865341i | \(-0.332898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5443i | 1.18654i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.8382 | + | 25.8382i | 1.35243 | + | 1.35243i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.6435 | −1.07758 | −0.538791 | − | 0.842439i | \(-0.681119\pi\) | ||||
−0.538791 | + | 0.842439i | \(0.681119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.59245 | − | 6.59245i | −0.342263 | − | 0.342263i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.6167 | + | 16.6167i | −0.860378 | + | 0.860378i | −0.991382 | − | 0.131004i | \(-0.958180\pi\) |
0.131004 | + | 0.991382i | \(0.458180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.7851i | 0.915979i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.77844 | + | 7.77844i | −0.399552 | + | 0.399552i | −0.878075 | − | 0.478523i | \(-0.841172\pi\) |
0.478523 | + | 0.878075i | \(0.341172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.2037 | −0.879070 | −0.439535 | − | 0.898225i | \(-0.644857\pi\) | ||||
−0.439535 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.23765 | 0.215971 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.8515 | − | 23.8515i | 1.20932 | − | 1.20932i | 0.238069 | − | 0.971248i | \(-0.423486\pi\) |
0.971248 | − | 0.238069i | \(-0.0765143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2306i | 0.921961i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.0544 | + | 11.0544i | −0.556208 | + | 0.556208i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2673 | − | 10.2673i | −0.515299 | − | 0.515299i | 0.400847 | − | 0.916145i | \(-0.368716\pi\) |
−0.916145 | + | 0.400847i | \(0.868716\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.2274 | −1.60936 | −0.804681 | − | 0.593708i | \(-0.797663\pi\) | ||||
−0.804681 | + | 0.593708i | \(0.797663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.9374 | − | 18.9374i | −0.943341 | − | 0.943341i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.58526i | 0.128146i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5702i | 0.572110i | 0.958213 | + | 0.286055i | \(0.0923440\pi\) | ||||
−0.958213 | + | 0.286055i | \(0.907656\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.2306 | − | 10.2306i | −0.503414 | − | 0.503414i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.24471 | −0.110188 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.74717 | + | 6.74717i | 0.329621 | + | 0.329621i | 0.852442 | − | 0.522822i | \(-0.175121\pi\) |
−0.522822 | + | 0.852442i | \(0.675121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.2239 | + | 17.2239i | −0.839443 | + | 0.839443i | −0.988785 | − | 0.149343i | \(-0.952284\pi\) |
0.149343 | + | 0.988785i | \(0.452284\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 7.21137i | − | 0.349803i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.2180 | + | 11.2180i | −0.542879 | + | 0.542879i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.7088 | 1.96087 | 0.980437 | − | 0.196832i | \(-0.0630654\pi\) | ||||
0.980437 | + | 0.196832i | \(0.0630654\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | −12.8910 | + | 12.8910i | −0.616659 | + | 0.616659i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 17.7122i | − | 0.845356i | −0.906280 | − | 0.422678i | \(-0.861090\pi\) | ||
0.906280 | − | 0.422678i | \(-0.138910\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6944 | − | 15.6944i | 0.745664 | − | 0.745664i | −0.227997 | − | 0.973662i | \(-0.573218\pi\) |
0.973662 | + | 0.227997i | \(0.0732178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.0496 | + | 11.0496i | 0.523801 | + | 0.523801i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.3400 | 1.33745 | 0.668723 | − | 0.743511i | \(-0.266841\pi\) | ||||
0.668723 | + | 0.743511i | \(0.266841\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.373517 | − | 0.373517i | −0.0175882 | − | 0.0175882i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.8382i | 1.21131i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.3396i | − | 0.811113i | −0.914070 | − | 0.405557i | \(-0.867078\pi\) | ||
0.914070 | − | 0.405557i | \(-0.132922\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.69284 | + | 1.69284i | 0.0788434 | + | 0.0788434i | 0.745429 | − | 0.666585i | \(-0.232245\pi\) |
−0.666585 | + | 0.745429i | \(0.732245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.70238 | −0.125590 | −0.0627951 | − | 0.998026i | \(-0.520001\pi\) | ||||
−0.0627951 | + | 0.998026i | \(0.520001\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1136 | − | 17.1136i | −0.791924 | − | 0.791924i | 0.189883 | − | 0.981807i | \(-0.439189\pi\) |
−0.981807 | + | 0.189883i | \(0.939189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.41921 | − | 5.41921i | 0.250236 | − | 0.250236i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.369053i | − | 0.0169691i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.09921 | − | 5.09921i | 0.233968 | − | 0.233968i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.2251 | −1.01549 | −0.507745 | − | 0.861508i | \(-0.669521\pi\) | ||||
−0.507745 | + | 0.861508i | \(0.669521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.7631 | −0.718735 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.1322 | + | 22.1322i | −1.00497 | + | 1.00497i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9839i | 0.633672i | 0.948480 | + | 0.316836i | \(0.102620\pi\) | ||||
−0.948480 | + | 0.316836i | \(0.897380\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.23412 | − | 7.23412i | 0.326471 | − | 0.326471i | −0.524772 | − | 0.851243i | \(-0.675849\pi\) |
0.851243 | + | 0.524772i | \(0.175849\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.8476 | + | 19.8476i | 0.893893 | + | 0.893893i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.0831 | −0.586858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.59078 | − | 2.59078i | −0.115979 | − | 0.115979i | 0.646735 | − | 0.762715i | \(-0.276134\pi\) |
−0.762715 | + | 0.646735i | \(0.776134\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 39.6443i | − | 1.76765i | −0.467817 | − | 0.883825i | \(-0.654959\pi\) | ||
0.467817 | − | 0.883825i | \(-0.345041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 26.3235i | − | 1.17138i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.2875 | − | 20.2875i | −0.899229 | − | 0.899229i | 0.0961393 | − | 0.995368i | \(-0.469351\pi\) |
−0.995368 | + | 0.0961393i | \(0.969351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.7819 | −1.67137 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.83655 | − | 5.83655i | −0.257189 | − | 0.257189i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.33962 | − | 1.33962i | 0.0589162 | − | 0.0589162i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 23.1784i | − | 1.01546i | −0.861515 | − | 0.507732i | \(-0.830484\pi\) | ||
0.861515 | − | 0.507732i | \(-0.169516\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.78550 | − | 5.78550i | 0.252982 | − | 0.252982i | −0.569210 | − | 0.822192i | \(-0.692751\pi\) |
0.822192 | + | 0.569210i | \(0.192751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.2672 | −1.84119 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.27744 | − | 2.27744i | 0.0986470 | − | 0.0986470i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 49.1941i | − | 2.12685i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.217129 | − | 0.217129i | 0.00935241 | − | 0.00935241i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.55175 | + | 4.55175i | 0.195695 | + | 0.195695i | 0.798152 | − | 0.602457i | \(-0.205811\pi\) |
−0.602457 | + | 0.798152i | \(0.705811\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.68667 | −0.414931 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.7355 | + | 27.7355i | 1.18588 | + | 1.18588i | 0.978195 | + | 0.207689i | \(0.0665942\pi\) |
0.207689 | + | 0.978195i | \(0.433406\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.0688i | 1.19577i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 16.1643i | − | 0.687377i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.17538 | + | 1.17538i | 0.0498026 | + | 0.0498026i | 0.731569 | − | 0.681767i | \(-0.238788\pi\) |
−0.681767 | + | 0.731569i | \(0.738788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.25023 | 0.0951745 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.7346 | − | 28.7346i | −1.21102 | − | 1.21102i | −0.970692 | − | 0.240326i | \(-0.922746\pi\) |
−0.240326 | − | 0.970692i | \(-0.577254\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.91391 | − | 3.91391i | 0.164659 | − | 0.164659i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 27.0004i | − | 1.13191i | −0.824435 | − | 0.565957i | \(-0.808507\pi\) | ||
0.824435 | − | 0.565957i | \(-0.191493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8284 | − | 14.8284i | 0.620550 | − | 0.620550i | −0.325122 | − | 0.945672i | \(-0.605405\pi\) |
0.945672 | + | 0.325122i | \(0.105405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.16451 | 0.131969 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6372 | −1.56686 | −0.783429 | − | 0.621481i | \(-0.786531\pi\) | ||||
−0.783429 | + | 0.621481i | \(0.786531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.64116 | − | 1.64116i | 0.0680869 | − | 0.0680869i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.44158i | − | 0.101120i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.2574 | + | 31.2574i | −1.29013 | + | 1.29013i | −0.355429 | + | 0.934703i | \(0.615665\pi\) |
−0.934703 | + | 0.355429i | \(0.884335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.8874 | − | 29.8874i | −1.23149 | − | 1.23149i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.59611 | 0.147675 | 0.0738373 | − | 0.997270i | \(-0.476475\pi\) | ||||
0.0738373 | + | 0.997270i | \(0.476475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.8347 | + | 28.8347i | 1.18211 | + | 1.18211i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.0296i | 0.900104i | 0.893002 | + | 0.450052i | \(0.148595\pi\) | ||||
−0.893002 | + | 0.450052i | \(0.851405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.7721i | − | 0.439405i | −0.975567 | − | 0.219703i | \(-0.929491\pi\) | ||
0.975567 | − | 0.219703i | \(-0.0705087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.4556 | − | 18.4556i | −0.750325 | − | 0.750325i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.47453 | −0.222204 | −0.111102 | − | 0.993809i | \(-0.535438\pi\) | ||||
−0.111102 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.16804 | + | 8.16804i | 0.330444 | + | 0.330444i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.5049 | + | 10.5049i | −0.424289 | + | 0.424289i | −0.886677 | − | 0.462389i | \(-0.846993\pi\) |
0.462389 | + | 0.886677i | \(0.346993\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.2235i | − | 0.894686i | −0.894363 | − | 0.447343i | \(-0.852370\pi\) | ||
0.894363 | − | 0.447343i | \(-0.147630\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.6398 | + | 11.6398i | −0.467843 | + | 0.467843i | −0.901215 | − | 0.433372i | \(-0.857324\pi\) |
0.433372 | + | 0.901215i | \(0.357324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.1573 | −0.647327 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.3424 | 1.17369 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.5912 | + | 17.5912i | −0.701405 | + | 0.701405i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.06977i | 0.162015i | 0.996713 | + | 0.0810075i | \(0.0258138\pi\) | ||||
−0.996713 | + | 0.0810075i | \(0.974186\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.3646 | − | 21.3646i | 0.847828 | − | 0.847828i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.32390 | + | 1.32390i | 0.0524549 | + | 0.0524549i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.41958 | 0.332553 | 0.166277 | − | 0.986079i | \(-0.446826\pi\) | ||||
0.166277 | + | 0.986079i | \(0.446826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.37275 | + | 7.37275i | 0.290753 | + | 0.290753i | 0.837378 | − | 0.546625i | \(-0.184088\pi\) |
−0.546625 | + | 0.837378i | \(0.684088\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 11.6132i | − | 0.456560i | −0.973595 | − | 0.228280i | \(-0.926690\pi\) | ||
0.973595 | − | 0.228280i | \(-0.0733102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.78901i | − | 0.148731i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.93049 | + | 1.93049i | 0.0755458 | + | 0.0755458i | 0.743870 | − | 0.668324i | \(-0.232988\pi\) |
−0.668324 | + | 0.743870i | \(0.732988\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.2082 | 0.516088 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.3102 | + | 22.3102i | 0.869081 | + | 0.869081i | 0.992371 | − | 0.123290i | \(-0.0393444\pi\) |
−0.123290 | + | 0.992371i | \(0.539344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7033 | − | 10.7033i | 0.416311 | − | 0.416311i | −0.467619 | − | 0.883930i | \(-0.654888\pi\) |
0.883930 | + | 0.467619i | \(0.154888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.7784i | 1.58132i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.70960 | + | 8.70960i | −0.337237 | + | 0.337237i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.15472 | −0.160391 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.6345 | −0.795401 | −0.397700 | − | 0.917515i | \(-0.630192\pi\) | ||||
−0.397700 | + | 0.917515i | \(0.630192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.8246 | + | 26.8246i | −1.03095 | + | 1.03095i | −0.0314484 | + | 0.999505i | \(0.510012\pi\) |
−0.999505 | + | 0.0314484i | \(0.989988\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 32.3627i | − | 1.24197i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.9026 | − | 12.9026i | 0.493705 | − | 0.493705i | −0.415766 | − | 0.909472i | \(-0.636487\pi\) |
0.909472 | + | 0.415766i | \(0.136487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.93077 | − | 8.93077i | −0.341227 | − | 0.341227i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.8871 | 0.567152 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3923 | + | 21.3923i | 0.813803 | + | 0.813803i | 0.985202 | − | 0.171399i | \(-0.0548286\pi\) |
−0.171399 | + | 0.985202i | \(0.554829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 41.1941i | − | 1.56258i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5.08312i | − | 0.192537i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2040 | − | 14.2040i | −0.536479 | − | 0.536479i | 0.386014 | − | 0.922493i | \(-0.373852\pi\) |
−0.922493 | + | 0.386014i | \(0.873852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.8776 | −0.938278 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.2458 | + | 19.2458i | 0.723812 | + | 0.723812i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.5474 | + | 29.5474i | −1.10968 | + | 1.10968i | −0.116485 | + | 0.993192i | \(0.537163\pi\) |
−0.993192 | + | 0.116485i | \(0.962837\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 18.5478i | − | 0.694622i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.78473 | + | 4.78473i | −0.178939 | + | 0.178939i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.3683 | 1.05796 | 0.528979 | − | 0.848635i | \(-0.322575\pi\) | ||||
0.528979 | + | 0.848635i | \(0.322575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.53450 | 0.317841 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.44521 | − | 3.44521i | 0.127952 | − | 0.127952i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.4843i | 0.759722i | 0.925044 | + | 0.379861i | \(0.124028\pi\) | ||||
−0.925044 | + | 0.379861i | \(0.875972\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.51119 | − | 2.51119i | 0.0928797 | − | 0.0928797i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.9961 | + | 33.9961i | 1.25567 | + | 1.25567i | 0.953138 | + | 0.302536i | \(0.0978331\pi\) |
0.302536 | + | 0.953138i | \(0.402167\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.00706 | 0.0739310 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.1645 | − | 15.1645i | −0.557836 | − | 0.557836i | 0.370855 | − | 0.928691i | \(-0.379065\pi\) |
−0.928691 | + | 0.370855i | \(0.879065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.17431i | − | 0.0797677i | −0.999204 | − | 0.0398839i | \(-0.987301\pi\) | ||
0.999204 | − | 0.0398839i | \(-0.0126988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.6631i | 1.01350i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.9670 | + | 35.9670i | 1.31421 | + | 1.31421i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.8980 | −1.09099 | −0.545497 | − | 0.838113i | \(-0.683659\pi\) | ||||
−0.545497 | + | 0.838113i | \(0.683659\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.6256 | + | 25.6256i | 0.932610 | + | 0.932610i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.3294 | + | 15.3294i | −0.557157 | + | 0.557157i | −0.928497 | − | 0.371340i | \(-0.878899\pi\) |
0.371340 | + | 0.928497i | \(0.378899\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.29449i | 0.155675i | 0.996966 | + | 0.0778375i | \(0.0248015\pi\) | ||||
−0.996966 | + | 0.0778375i | \(0.975198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.08216 | − | 7.08216i | 0.256392 | − | 0.256392i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.1027 | 0.834191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8819 | 1.22181 | 0.610907 | − | 0.791703i | \(-0.290805\pi\) | ||||
0.610907 | + | 0.791703i | \(0.290805\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.0230 | − | 35.0230i | 1.25969 | − | 1.25969i | 0.308450 | − | 0.951240i | \(-0.400190\pi\) |
0.951240 | − | 0.308450i | \(-0.0998104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.33686i | 0.263548i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.59431 | − | 3.59431i | 0.128779 | − | 0.128779i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.42274 | − | 2.42274i | −0.0866923 | − | 0.0866923i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0263 | 0.393545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1090 | − | 24.1090i | −0.859393 | − | 0.859393i | 0.131873 | − | 0.991267i | \(-0.457901\pi\) |
−0.991267 | + | 0.131873i | \(0.957901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.72312i | 0.203491i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.3326i | − | 0.899585i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.7722 | + | 28.7722i | 1.01917 | + | 1.01917i | 0.999813 | + | 0.0193524i | \(0.00616044\pi\) |
0.0193524 | + | 0.999813i | \(0.493840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.2306 | 0.644952 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.99647 | − | 6.99647i | −0.246900 | − | 0.246900i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.6533 | + | 12.6533i | −0.445971 | + | 0.445971i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9926i | 0.386478i | 0.981152 | + | 0.193239i | \(0.0618993\pi\) | ||||
−0.981152 | + | 0.193239i | \(0.938101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0259 | − | 15.0259i | 0.527630 | − | 0.527630i | −0.392235 | − | 0.919865i | \(-0.628298\pi\) |
0.919865 | + | 0.392235i | \(0.128298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.2574 | 0.674558 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.55136 | 0.124246 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2536 | − | 21.2536i | 0.741756 | − | 0.741756i | −0.231159 | − | 0.972916i | \(-0.574252\pi\) |
0.972916 | + | 0.231159i | \(0.0742519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.0851i | 1.92015i | 0.279751 | + | 0.960073i | \(0.409748\pi\) | ||||
−0.279751 | + | 0.960073i | \(0.590252\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.4290 | + | 24.4290i | −0.849480 | + | 0.849480i | −0.990068 | − | 0.140588i | \(-0.955101\pi\) |
0.140588 | + | 0.990068i | \(0.455101\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.9235 | − | 21.9235i | −0.761436 | − | 0.761436i | 0.215146 | − | 0.976582i | \(-0.430977\pi\) |
−0.976582 | + | 0.215146i | \(0.930977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.95487 | 0.102380 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.2996 | − | 35.2996i | −1.22159 | − | 1.22159i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.14195i | − | 0.177520i | −0.996053 | − | 0.0887599i | \(-0.971710\pi\) | ||
0.996053 | − | 0.0887599i | \(-0.0282904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 10.0357i | − | 0.346059i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.43541 | − | 6.43541i | −0.221385 | − | 0.221385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.9867 | 0.927272 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.71940 | − | 7.71940i | −0.264618 | − | 0.264618i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0857 | − | 13.0857i | 0.448046 | − | 0.448046i | −0.446659 | − | 0.894704i | \(-0.647386\pi\) |
0.894704 | + | 0.446659i | \(0.147386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.8878i | 0.781833i | 0.920426 | + | 0.390916i | \(0.127842\pi\) | ||||
−0.920426 | + | 0.390916i | \(0.872158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.1225 | − | 25.1225i | 0.857169 | − | 0.857169i | −0.133834 | − | 0.991004i | \(-0.542729\pi\) |
0.991004 | + | 0.133834i | \(0.0427290\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.9296 | −1.49538 | −0.747691 | − | 0.664047i | \(-0.768837\pi\) | ||||
−0.747691 | + | 0.664047i | \(0.768837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.2286 | 0.517788 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.99331 | − | 2.99331i | 0.101541 | − | 0.101541i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.2376i | 0.414657i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.3629 | + | 17.3629i | −0.586974 | + | 0.586974i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.2575 | + | 15.2575i | 0.515208 | + | 0.515208i | 0.916117 | − | 0.400910i | \(-0.131306\pi\) |
−0.400910 | + | 0.916117i | \(0.631306\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.6686 | −0.730035 | −0.365018 | − | 0.931001i | \(-0.618937\pi\) | ||||
−0.365018 | + | 0.931001i | \(0.618937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.0590385 | + | 0.0590385i | 0.00198680 | + | 0.00198680i | 0.708099 | − | 0.706113i | \(-0.249553\pi\) |
−0.706113 | + | 0.708099i | \(0.749553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.8043i | 1.03431i | 0.855892 | + | 0.517154i | \(0.173009\pi\) | ||||
−0.855892 | + | 0.517154i | \(0.826991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.2404i | 1.04777i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.8910 | + | 12.8910i | 0.431380 | + | 0.431380i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.4682 | 1.55326 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.1930 | − | 20.1930i | −0.673475 | − | 0.673475i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6135 | − | 16.6135i | 0.553477 | − | 0.553477i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.2008i | 0.737979i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.0170 | + | 35.0170i | −1.16272 | + | 1.16272i | −0.178844 | + | 0.983878i | \(0.557236\pi\) |
−0.983878 | + | 0.178844i | \(0.942764\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.0829331 | 0.00274770 | 0.00137385 | − | 0.999999i | \(-0.499563\pi\) | ||||
0.00137385 | + | 0.999999i | \(0.499563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.607822 | 0.0201160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.65685 | + | 9.65685i | −0.318897 | + | 0.318897i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 20.1161i | − | 0.663568i | −0.943355 | − | 0.331784i | \(-0.892350\pi\) | ||
0.943355 | − | 0.331784i | \(-0.107650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.7721 | − | 14.7721i | 0.486231 | − | 0.486231i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.05352 | + | 3.05352i | 0.100399 | + | 0.100399i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.55098 | −0.280549 | −0.140274 | − | 0.990113i | \(-0.544798\pi\) | ||||
−0.140274 | + | 0.990113i | \(0.544798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.08941 | + | 2.08941i | 0.0684776 | + | 0.0684776i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.6792i | 0.349248i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.5780i | 1.09695i | 0.836168 | + | 0.548473i | \(0.184791\pi\) | ||||
−0.836168 | + | 0.548473i | \(0.815209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.48463 | + | 8.48463i | 0.276591 | + | 0.276591i | 0.831747 | − | 0.555156i | \(-0.187341\pi\) |
−0.555156 | + | 0.831747i | \(0.687341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.23059 | 0.0726380 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.8571 | + | 17.8571i | 0.580277 | + | 0.580277i | 0.934979 | − | 0.354702i | \(-0.115418\pi\) |
−0.354702 | + | 0.934979i | \(0.615418\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.6596 | − | 42.6596i | 1.38479 | − | 1.38479i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.86469i | 0.125190i | 0.998039 | + | 0.0625948i | \(0.0199376\pi\) | ||||
−0.998039 | + | 0.0625948i | \(0.980062\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.79607 | + | 9.79607i | −0.316993 | + | 0.316993i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.0590 | 0.421698 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0027 | 0.387185 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 34.0228 | − | 34.0228i | 1.09523 | − | 1.09523i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 37.8714i | − | 1.21786i | −0.793224 | − | 0.608930i | \(-0.791599\pi\) | ||
0.793224 | − | 0.608930i | \(-0.208401\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.64873 | − | 2.64873i | 0.0850017 | − | 0.0850017i | −0.663327 | − | 0.748329i | \(-0.730856\pi\) |
0.748329 | + | 0.663327i | \(0.230856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.1180 | + | 30.1180i | 0.965540 | + | 0.965540i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.6530 | −0.564768 | −0.282384 | − | 0.959301i | \(-0.591125\pi\) | ||||
−0.282384 | + | 0.959301i | \(0.591125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.99201 | − | 2.99201i | −0.0956250 | − | 0.0956250i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.3557i | 0.713035i | 0.934289 | + | 0.356518i | \(0.116036\pi\) | ||||
−0.934289 | + | 0.356518i | \(0.883964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4.33057i | − | 0.137983i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.10197 | + | 1.10197i | 0.0350405 | + | 0.0350405i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.8769 | −0.567878 | −0.283939 | − | 0.958842i | \(-0.591641\pi\) | ||||
−0.283939 | + | 0.958842i | \(0.591641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.73812 | + | 1.73812i | 0.0551020 | + | 0.0551020i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.28610 | − | 4.28610i | 0.135742 | − | 0.135742i | −0.635971 | − | 0.771713i | \(-0.719400\pi\) |
0.771713 | + | 0.635971i | \(0.219400\pi\) | |||||||
\(998\) | 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 | 576.2.k.b.145.1 | 8 | ||
3.2 | odd | 2 | 192.2.j.a.145.4 | 8 | |||
4.3 | odd | 2 | 144.2.k.b.109.3 | 8 | |||
8.3 | odd | 2 | 1152.2.k.c.289.4 | 8 | |||
8.5 | even | 2 | 1152.2.k.f.289.4 | 8 | |||
12.11 | even | 2 | 48.2.j.a.13.2 | ✓ | 8 | ||
16.3 | odd | 4 | 1152.2.k.c.865.4 | 8 | |||
16.5 | even | 4 | inner | 576.2.k.b.433.1 | 8 | ||
16.11 | odd | 4 | 144.2.k.b.37.3 | 8 | |||
16.13 | even | 4 | 1152.2.k.f.865.4 | 8 | |||
24.5 | odd | 2 | 384.2.j.a.289.1 | 8 | |||
24.11 | even | 2 | 384.2.j.b.289.3 | 8 | |||
32.5 | even | 8 | 9216.2.a.x.1.2 | 4 | |||
32.11 | odd | 8 | 9216.2.a.bo.1.3 | 4 | |||
32.21 | even | 8 | 9216.2.a.bn.1.3 | 4 | |||
32.27 | odd | 8 | 9216.2.a.y.1.2 | 4 | |||
48.5 | odd | 4 | 192.2.j.a.49.4 | 8 | |||
48.11 | even | 4 | 48.2.j.a.37.2 | yes | 8 | ||
48.29 | odd | 4 | 384.2.j.a.97.1 | 8 | |||
48.35 | even | 4 | 384.2.j.b.97.3 | 8 | |||
96.5 | odd | 8 | 3072.2.a.n.1.3 | 4 | |||
96.11 | even | 8 | 3072.2.a.i.1.2 | 4 | |||
96.29 | odd | 8 | 3072.2.d.i.1537.7 | 8 | |||
96.35 | even | 8 | 3072.2.d.f.1537.3 | 8 | |||
96.53 | odd | 8 | 3072.2.a.o.1.2 | 4 | |||
96.59 | even | 8 | 3072.2.a.t.1.3 | 4 | |||
96.77 | odd | 8 | 3072.2.d.i.1537.2 | 8 | |||
96.83 | even | 8 | 3072.2.d.f.1537.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.2 | ✓ | 8 | 12.11 | even | 2 | ||
48.2.j.a.37.2 | yes | 8 | 48.11 | even | 4 | ||
144.2.k.b.37.3 | 8 | 16.11 | odd | 4 | |||
144.2.k.b.109.3 | 8 | 4.3 | odd | 2 | |||
192.2.j.a.49.4 | 8 | 48.5 | odd | 4 | |||
192.2.j.a.145.4 | 8 | 3.2 | odd | 2 | |||
384.2.j.a.97.1 | 8 | 48.29 | odd | 4 | |||
384.2.j.a.289.1 | 8 | 24.5 | odd | 2 | |||
384.2.j.b.97.3 | 8 | 48.35 | even | 4 | |||
384.2.j.b.289.3 | 8 | 24.11 | even | 2 | |||
576.2.k.b.145.1 | 8 | 1.1 | even | 1 | trivial | ||
576.2.k.b.433.1 | 8 | 16.5 | even | 4 | inner | ||
1152.2.k.c.289.4 | 8 | 8.3 | odd | 2 | |||
1152.2.k.c.865.4 | 8 | 16.3 | odd | 4 | |||
1152.2.k.f.289.4 | 8 | 8.5 | even | 2 | |||
1152.2.k.f.865.4 | 8 | 16.13 | even | 4 | |||
3072.2.a.i.1.2 | 4 | 96.11 | even | 8 | |||
3072.2.a.n.1.3 | 4 | 96.5 | odd | 8 | |||
3072.2.a.o.1.2 | 4 | 96.53 | odd | 8 | |||
3072.2.a.t.1.3 | 4 | 96.59 | even | 8 | |||
3072.2.d.f.1537.3 | 8 | 96.35 | even | 8 | |||
3072.2.d.f.1537.6 | 8 | 96.83 | even | 8 | |||
3072.2.d.i.1537.2 | 8 | 96.77 | odd | 8 | |||
3072.2.d.i.1537.7 | 8 | 96.29 | odd | 8 | |||
9216.2.a.x.1.2 | 4 | 32.5 | even | 8 | |||
9216.2.a.y.1.2 | 4 | 32.27 | odd | 8 | |||
9216.2.a.bn.1.3 | 4 | 32.21 | even | 8 | |||
9216.2.a.bo.1.3 | 4 | 32.11 | odd | 8 |