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 | 289.4 | ||
Root | \(0.500000 - 0.0297061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.289 |
Dual form | 1152.2.k.f.865.4 |
$q$-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 | ||||||||
\(5\) | 1.74912 | − | 1.74912i | 0.782229 | − | 0.782229i | −0.197977 | − | 0.980207i | \(-0.563437\pi\) |
0.980207 | + | 0.197977i | \(0.0634373\pi\) | |||||||
\(6\) | 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 | −0.774894 | − | 0.632091i | \(-0.782197\pi\) |
0.632091 | + | 0.774894i | \(0.282197\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.88784 | − | 2.88784i | −0.800943 | − | 0.800943i | 0.182300 | − | 0.983243i | \(-0.441646\pi\) |
−0.983243 | + | 0.182300i | \(0.941646\pi\) | |||||||
\(14\) | 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 | \(-0.985134\pi\) |
−0.0466864 | − | 0.998910i | \(-0.514866\pi\) | |||||||
\(20\) | 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 | 0.360821 | − | 0.932635i | \(-0.382496\pi\) |
−0.932635 | + | 0.360821i | \(0.882496\pi\) | |||||||
\(30\) | 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 | −0.446235 | − | 0.894916i | \(-0.647235\pi\) |
0.894916 | + | 0.446235i | \(0.147235\pi\) | |||||||
\(38\) | 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 | −0.736190 | − | 0.676775i | \(-0.763377\pi\) |
0.676775 | + | 0.736190i | \(0.263377\pi\) | |||||||
\(44\) | 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 | −0.861615 | − | 0.507562i | \(-0.830547\pi\) |
0.507562 | + | 0.861615i | \(0.330547\pi\) | |||||||
\(54\) | 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 | ||||||||
\(61\) | 4.38607 | + | 4.38607i | 0.561579 | + | 0.561579i | 0.929756 | − | 0.368177i | \(-0.120018\pi\) |
−0.368177 | + | 0.929756i | \(0.620018\pi\) | |||||||
\(62\) | 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 | 0.565733 | − | 0.824589i | \(-0.308593\pi\) |
−0.824589 | + | 0.565733i | \(0.808593\pi\) | |||||||
\(68\) | 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 | 0.671013 | − | 0.741445i | \(-0.265859\pi\) |
−0.741445 | + | 0.671013i | \(0.765859\pi\) | |||||||
\(84\) | 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 | −0.225498 | − | 0.974244i | \(-0.572401\pi\) |
0.974244 | + | 0.225498i | \(0.0724010\pi\) | |||||||
\(102\) | 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 | \(-0.338849\pi\) |
0.874560 | − | 0.484918i | \(-0.161151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.76901 | − | 2.76901i | −0.265224 | − | 0.265224i | 0.561949 | − | 0.827172i | \(-0.310052\pi\) |
−0.827172 | + | 0.561949i | \(0.810052\pi\) | |||||||
\(110\) | 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 | 0.852542 | − | 0.522659i | \(-0.175060\pi\) |
−0.522659 | + | 0.852542i | \(0.675060\pi\) | |||||||
\(132\) | 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 | −0.00119925 | − | 0.999999i | \(-0.500382\pi\) |
0.999999 | + | 0.00119925i | \(0.000381735\pi\) | |||||||
\(140\) | 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 | −0.952467 | − | 0.304640i | \(-0.901464\pi\) |
0.304640 | + | 0.952467i | \(0.401464\pi\) | |||||||
\(150\) | 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 | 0.821607 | − | 0.570054i | \(-0.193078\pi\) |
−0.570054 | + | 0.821607i | \(0.693078\pi\) | |||||||
\(158\) | 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 | 0.889029 | − | 0.457852i | \(-0.151381\pi\) |
−0.457852 | + | 0.889029i | \(0.651381\pi\) | |||||||
\(164\) | 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 | 0.852955 | − | 0.521985i | \(-0.174808\pi\) |
−0.521985 | + | 0.852955i | \(0.674808\pi\) | |||||||
\(174\) | 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 | 0.999975 | − | 0.00713130i | \(-0.00226998\pi\) |
−0.00713130 | + | 0.999975i | \(0.502270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.34628 | + | 6.34628i | −0.471715 | + | 0.471715i | −0.902469 | − | 0.430754i | \(-0.858248\pi\) |
0.430754 | + | 0.902469i | \(0.358248\pi\) | |||||||
\(182\) | 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 | −0.661631 | − | 0.749830i | \(-0.730135\pi\) |
0.749830 | + | 0.661631i | \(0.230135\pi\) | |||||||
\(198\) | 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 | 0.837402 | − | 0.546588i | \(-0.184073\pi\) |
−0.546588 | + | 0.837402i | \(0.684073\pi\) | |||||||
\(212\) | 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 | 0.728081 | − | 0.685492i | \(-0.240413\pi\) |
−0.685492 | + | 0.728081i | \(0.740413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.34275 | + | 5.34275i | −0.353059 | + | 0.353059i | −0.861246 | − | 0.508188i | \(-0.830316\pi\) |
0.508188 | + | 0.861246i | \(0.330316\pi\) | |||||||
\(230\) | 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 | −0.328611 | − | 0.944465i | \(-0.606581\pi\) |
0.944465 | + | 0.328611i | \(0.106581\pi\) | |||||||
\(252\) | 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 | \(0.0980037\pi\) |
0.303046 | + | 0.952976i | \(0.401996\pi\) | |||||||
\(270\) | 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 | −0.970289 | − | 0.241951i | \(-0.922213\pi\) |
0.241951 | + | 0.970289i | \(0.422213\pi\) | |||||||
\(278\) | 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 | −0.561115 | − | 0.827738i | \(-0.689628\pi\) |
0.827738 | + | 0.561115i | \(0.189628\pi\) | |||||||
\(284\) | 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 | −0.904976 | − | 0.425463i | \(-0.860111\pi\) |
0.425463 | + | 0.904976i | \(0.360111\pi\) | |||||||
\(294\) | 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 | 0.939431 | − | 0.342738i | \(-0.111354\pi\) |
−0.342738 | + | 0.939431i | \(0.611354\pi\) | |||||||
\(308\) | 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 | 0.491346 | − | 0.870964i | \(-0.336505\pi\) |
−0.870964 | + | 0.491346i | \(0.836505\pi\) | |||||||
\(318\) | 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 | \(0.526880\pi\) |
−0.996436 | + | 0.0843464i | \(0.973120\pi\) | |||||||
\(332\) | 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 | −0.855188 | − | 0.518317i | \(-0.826559\pi\) |
0.518317 | + | 0.855188i | \(0.326559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.74255 | + | 4.74255i | 0.253863 | + | 0.253863i | 0.822552 | − | 0.568690i | \(-0.192549\pi\) |
−0.568690 | + | 0.822552i | \(0.692549\pi\) | |||||||
\(350\) | 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 | −0.131004 | − | 0.991382i | \(-0.541820\pi\) |
0.991382 | + | 0.131004i | \(0.0418200\pi\) | |||||||
\(374\) | 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 | −0.478523 | − | 0.878075i | \(-0.658828\pi\) |
0.878075 | + | 0.478523i | \(0.158828\pi\) | |||||||
\(380\) | 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 | \(0.576514\pi\) |
−0.971248 | + | 0.238069i | \(0.923486\pi\) | |||||||
\(390\) | 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 | 0.916145 | − | 0.400847i | \(-0.131284\pi\) |
−0.400847 | + | 0.916145i | \(0.631284\pi\) | |||||||
\(398\) | 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 | 0.522822 | − | 0.852442i | \(-0.324879\pi\) |
−0.852442 | + | 0.522822i | \(0.824879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.2239 | − | 17.2239i | 0.839443 | − | 0.839443i | −0.149343 | − | 0.988785i | \(-0.547716\pi\) |
0.988785 | + | 0.149343i | \(0.0477158\pi\) | |||||||
\(422\) | 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 | −0.973662 | − | 0.227997i | \(-0.926782\pi\) |
0.227997 | + | 0.973662i | \(0.426782\pi\) | |||||||
\(444\) | 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 | 0.666585 | − | 0.745429i | \(-0.267755\pi\) |
−0.745429 | + | 0.666585i | \(0.767755\pi\) | |||||||
\(462\) | 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 | 0.981807 | − | 0.189883i | \(-0.0608108\pi\) |
−0.189883 | + | 0.981807i | \(0.560811\pi\) | |||||||
\(468\) | 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 | −0.851243 | − | 0.524772i | \(-0.824151\pi\) |
0.524772 | + | 0.851243i | \(0.324151\pi\) | |||||||
\(492\) | 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 | 0.762715 | − | 0.646735i | \(-0.223866\pi\) |
−0.646735 | + | 0.762715i | \(0.723866\pi\) | |||||||
\(500\) | 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 | 0.995368 | − | 0.0961393i | \(-0.0306494\pi\) |
−0.0961393 | + | 0.995368i | \(0.530649\pi\) | |||||||
\(510\) | 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 | −0.822192 | − | 0.569210i | \(-0.807249\pi\) |
0.569210 | + | 0.822192i | \(0.307249\pi\) | |||||||
\(524\) | 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 | 0.602457 | − | 0.798152i | \(-0.294189\pi\) |
−0.798152 | + | 0.602457i | \(0.794189\pi\) | |||||||
\(542\) | 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 | \(-0.933406\pi\) |
−0.207689 | − | 0.978195i | \(-0.566594\pi\) | |||||||
\(548\) | 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 | 0.681767 | − | 0.731569i | \(-0.261212\pi\) |
−0.731569 | + | 0.681767i | \(0.761212\pi\) | |||||||
\(558\) | 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 | \(0.0772544\pi\) |
0.240326 | + | 0.970692i | \(0.422746\pi\) | |||||||
\(564\) | 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 | −0.945672 | − | 0.325122i | \(-0.894595\pi\) |
0.325122 | + | 0.945672i | \(0.394595\pi\) | |||||||
\(572\) | 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 | \(-0.384335\pi\) |
0.934703 | − | 0.355429i | \(-0.115665\pi\) | |||||||
\(588\) | 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 | −0.462389 | − | 0.886677i | \(-0.653007\pi\) |
0.886677 | + | 0.462389i | \(0.153007\pi\) | |||||||
\(614\) | 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 | −0.433372 | − | 0.901215i | \(-0.642676\pi\) |
0.901215 | + | 0.433372i | \(0.142676\pi\) | |||||||
\(620\) | 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 | 0.546625 | − | 0.837378i | \(-0.315912\pi\) |
−0.837378 | + | 0.546625i | \(0.815912\pi\) | |||||||
\(644\) | 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 | 0.668324 | − | 0.743870i | \(-0.267012\pi\) |
−0.743870 | + | 0.668324i | \(0.767012\pi\) | |||||||
\(654\) | 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 | 0.123290 | − | 0.992371i | \(-0.460656\pi\) |
−0.992371 | + | 0.123290i | \(0.960656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7033 | + | 10.7033i | −0.416311 | + | 0.416311i | −0.883930 | − | 0.467619i | \(-0.845112\pi\) |
0.467619 | + | 0.883930i | \(0.345112\pi\) | |||||||
\(662\) | 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 | \(-0.489988\pi\) |
0.999505 | − | 0.0314484i | \(-0.0100120\pi\) | |||||||
\(678\) | 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 | −0.909472 | − | 0.415766i | \(-0.863513\pi\) |
0.415766 | + | 0.909472i | \(0.363513\pi\) | |||||||
\(684\) | 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 | 0.171399 | − | 0.985202i | \(-0.445171\pi\) |
−0.985202 | + | 0.171399i | \(0.945171\pi\) | |||||||
\(692\) | 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 | 0.922493 | − | 0.386014i | \(-0.126148\pi\) |
−0.386014 | + | 0.922493i | \(0.626148\pi\) | |||||||
\(702\) | 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 | \(-0.462837\pi\) |
0.993192 | − | 0.116485i | \(-0.0371626\pi\) | |||||||
\(710\) | 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 | \(-0.902167\pi\) |
−0.302536 | − | 0.953138i | \(-0.597833\pi\) | |||||||
\(734\) | 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 | 0.928691 | − | 0.370855i | \(-0.120935\pi\) |
−0.370855 | + | 0.928691i | \(0.620935\pi\) | |||||||
\(740\) | 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 | −0.371340 | − | 0.928497i | \(-0.621101\pi\) |
0.928497 | + | 0.371340i | \(0.121101\pi\) | |||||||
\(758\) | 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 | \(0.599810\pi\) |
−0.951240 | + | 0.308450i | \(0.900190\pi\) | |||||||
\(774\) | 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 | 0.991267 | − | 0.131873i | \(-0.0420992\pi\) |
−0.131873 | + | 0.991267i | \(0.542099\pi\) | |||||||
\(788\) | 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 | \(-0.993840\pi\) |
−0.0193524 | − | 0.999813i | \(-0.506160\pi\) | |||||||
\(798\) | 0 | 0 |