Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), 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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 768) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.1 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.h.1537.8 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.86370i | − 1.72790i | −0.503577 | − | 0.863950i | \(-0.667983\pi\) | ||||
0.503577 | − | 0.863950i | \(-0.332017\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | −0.925820 | −0.462910 | − | 0.886405i | \(-0.653195\pi\) | ||||
−0.462910 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.46410i | − 0.441443i | −0.975337 | − | 0.220722i | \(-0.929159\pi\) | ||||
0.975337 | − | 0.220722i | \(-0.0708412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264i | 1.17670i | 0.808608 | + | 0.588348i | \(0.200222\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.86370 | −0.997604 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.46410i | − 1.71238i | −0.516659 | − | 0.856191i | \(-0.672825\pi\) | ||||
0.516659 | − | 0.856191i | \(-0.327175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.44949i | 0.534522i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.92820 | −1.98564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.76268i | 1.62719i | 0.581432 | + | 0.813595i | \(0.302492\pi\) | ||||
−0.581432 | + | 0.813595i | \(0.697508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.34847 | 1.31982 | 0.659912 | − | 0.751343i | \(-0.270594\pi\) | ||||
0.659912 | + | 0.751343i | \(0.270594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.46410 | −0.254867 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.46410i | 1.59973i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 0.656339i | − 0.107901i | −0.998544 | − | 0.0539507i | \(-0.982819\pi\) | ||||
0.998544 | − | 0.0539507i | \(-0.0171814\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.24264 | 0.679366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.53590 | −0.708388 | −0.354194 | − | 0.935172i | \(-0.615245\pi\) | ||||
−0.354194 | + | 0.935172i | \(0.615245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.46410i | − 0.528271i | −0.964486 | − | 0.264135i | \(-0.914913\pi\) | ||||
0.964486 | − | 0.264135i | \(-0.0850865\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.86370i | 0.575967i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.46410i | 0.485071i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.62158i | 0.634823i | 0.948288 | + | 0.317411i | \(0.102814\pi\) | ||||
−0.948288 | + | 0.317411i | \(0.897186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.46410 | −0.988644 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.8564i | 1.80395i | 0.431788 | + | 0.901975i | \(0.357883\pi\) | ||||
−0.431788 | + | 0.901975i | \(0.642117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.656339i | − 0.0840356i | −0.999117 | − | 0.0420178i | \(-0.986621\pi\) | ||||
0.999117 | − | 0.0420178i | \(-0.0133786\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.44949 | 0.308607 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.3923 | 2.03322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 14.9282i | − 1.82377i | −0.410445 | − | 0.911885i | \(-0.634627\pi\) | ||||
0.410445 | − | 0.911885i | \(-0.365373\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843i | 0.340503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.41473 | −0.761288 | −0.380644 | − | 0.924722i | \(-0.624298\pi\) | ||||
−0.380644 | + | 0.924722i | \(0.624298\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.92820i | 1.14641i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.58630i | 0.408697i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.44949 | −0.275589 | −0.137795 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137795 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.46410i | − 0.599763i | −0.953976 | − | 0.299882i | \(-0.903053\pi\) | ||||
0.953976 | − | 0.299882i | \(-0.0969472\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3843i | 1.45173i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.76268 | 0.939458 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.92820 | 0.522388 | 0.261194 | − | 0.965286i | \(-0.415884\pi\) | ||||
0.261194 | + | 0.965286i | \(0.415884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 10.3923i | − 1.08941i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 7.34847i | − 0.762001i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −28.8391 | −2.95883 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.07180 | 0.108824 | 0.0544122 | − | 0.998519i | \(-0.482671\pi\) | ||||
0.0544122 | + | 0.998519i | \(0.482671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.46410i | 0.147148i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.4195i | 1.43480i | 0.696663 | + | 0.717399i | \(0.254667\pi\) | ||||
−0.696663 | + | 0.717399i | \(0.745333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.20736 | 0.316031 | 0.158016 | − | 0.987437i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987437i | \(0.449490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.46410 | 0.923602 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.00000i | − 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.41421i | 0.135457i | 0.997704 | + | 0.0677285i | \(0.0215752\pi\) | ||||
−0.997704 | + | 0.0677285i | \(0.978425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.656339 | −0.0622969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.9282i | 1.01906i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.24264i | − 0.392232i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.48528 | 0.777844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.85641 | 0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.53590i | 0.408988i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 19.0411i | 1.70309i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.5211 | 1.28854 | 0.644268 | − | 0.764799i | \(-0.277162\pi\) | ||||
0.644268 | + | 0.764799i | \(0.277162\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.46410 | −0.304997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9282i | 1.30428i | 0.758097 | + | 0.652142i | \(0.226129\pi\) | ||||
−0.758097 | + | 0.652142i | \(0.773871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.2832i | 1.58536i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.86370 | 0.332535 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.3923 | −1.22962 | −0.614809 | − | 0.788676i | \(-0.710767\pi\) | ||||
−0.614809 | + | 0.788676i | \(0.710767\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92820i | 0.587643i | 0.955860 | + | 0.293821i | \(0.0949270\pi\) | ||||
−0.955860 | + | 0.293821i | \(0.905073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843i | 0.238197i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.21166 | 0.519445 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33.8564 | 2.81162 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.37945i | 0.440702i | 0.975421 | + | 0.220351i | \(0.0707203\pi\) | ||||
−0.975421 | + | 0.220351i | \(0.929280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.59059 | −0.536335 | −0.268167 | − | 0.963372i | \(-0.586418\pi\) | ||||
−0.268167 | + | 0.963372i | \(0.586418\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.46410 | 0.280056 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 28.3923i | − 2.28052i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.17209i | 0.173352i | 0.996237 | + | 0.0866758i | \(0.0276244\pi\) | ||||
−0.996237 | + | 0.0866758i | \(0.972376\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.62158 | 0.366515 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.53590i | − 0.355279i | −0.984096 | − | 0.177639i | \(-0.943154\pi\) | ||||
0.984096 | − | 0.177639i | \(-0.0568461\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.65685i | 0.440386i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.72741 | 0.597965 | 0.298982 | − | 0.954259i | \(-0.403353\pi\) | ||||
0.298982 | + | 0.954259i | \(0.403353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.46410i | 0.570794i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 17.2480i | − 1.31134i | −0.755048 | − | 0.655669i | \(-0.772387\pi\) | ||||
0.755048 | − | 0.655669i | \(-0.227613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.3190 | 1.83835 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8564 | 1.04151 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.9282i | 1.41476i | 0.706833 | + | 0.707380i | \(0.250123\pi\) | ||||
−0.706833 | + | 0.707380i | \(0.749877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 7.07107i | − 0.525588i | −0.964852 | − | 0.262794i | \(-0.915356\pi\) | ||||
0.964852 | − | 0.262794i | \(-0.0846440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.656339 | −0.0485180 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.53590 | −0.186443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.07180i | 0.370887i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.44949i | − 0.178174i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.72741 | −0.559136 | −0.279568 | − | 0.960126i | \(-0.590191\pi\) | ||||
−0.279568 | + | 0.960126i | \(0.590191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 16.3923i | − 1.17388i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.76268i | 0.624315i | 0.950030 | + | 0.312158i | \(0.101052\pi\) | ||||
−0.950030 | + | 0.312158i | \(0.898948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.6622 | −1.32293 | −0.661463 | − | 0.749977i | \(-0.730064\pi\) | ||||
−0.661463 | + | 0.749977i | \(0.730064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.9282 | −1.05295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 21.4641i | − 1.50648i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.5254i | 1.22402i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.9282 | −0.755920 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 6.92820i | − 0.476957i | −0.971148 | − | 0.238479i | \(-0.923351\pi\) | ||||
0.971148 | − | 0.238479i | \(-0.0766487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.41473i | 0.439530i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.3843 | −0.912799 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.0000 | −1.22192 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.00000i | 0.270295i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 14.6969i | − 0.988623i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.5211 | −0.972403 | −0.486201 | − | 0.873847i | \(-0.661618\pi\) | ||||
−0.486201 | + | 0.873847i | \(0.661618\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.92820 | 0.661880 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 11.3205i | − 0.751369i | −0.926748 | − | 0.375684i | \(-0.877408\pi\) | ||||
0.926748 | − | 0.375684i | \(-0.122592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8690i | 1.11474i | 0.830265 | + | 0.557368i | \(0.188189\pi\) | ||||
−0.830265 | + | 0.557368i | \(0.811811\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.58630 | 0.235961 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9282 | −0.846955 | −0.423477 | − | 0.905907i | \(-0.639191\pi\) | ||||
−0.423477 | + | 0.905907i | \(0.639191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.9282i | 0.712877i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.44949i | 0.159111i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.72741 | 0.499844 | 0.249922 | − | 0.968266i | \(-0.419595\pi\) | ||||
0.249922 | + | 0.968266i | \(0.419595\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.7846 | −1.72535 | −0.862674 | − | 0.505760i | \(-0.831212\pi\) | ||||
−0.862674 | + | 0.505760i | \(0.831212\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.86370i | 0.246843i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.6675 | 2.01495 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.46410 | −0.346273 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 6.53590i | − 0.412542i | −0.978495 | − | 0.206271i | \(-0.933867\pi\) | ||||
0.978495 | − | 0.206271i | \(-0.0661329\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.14110i | 0.260349i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.3843 | 0.838155 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.7846 | −1.42126 | −0.710632 | − | 0.703563i | \(-0.751591\pi\) | ||||
−0.710632 | + | 0.703563i | \(0.751591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.60770i | 0.0998973i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 8.76268i | − 0.542396i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.6274 | −1.39527 | −0.697633 | − | 0.716455i | \(-0.745763\pi\) | ||||
−0.697633 | + | 0.716455i | \(0.745763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.8564 | 1.09691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 4.92820i | − 0.301601i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.2784i | 0.626687i | 0.949640 | + | 0.313344i | \(0.101449\pi\) | ||||
−0.949640 | + | 0.313344i | \(0.898551\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.20736 | −0.194834 | −0.0974168 | − | 0.995244i | \(-0.531058\pi\) | ||||
−0.0974168 | + | 0.995244i | \(0.531058\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.3923 | −0.628971 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.5359i | 0.876548i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 12.5249i | − 0.752545i | −0.926509 | − | 0.376273i | \(-0.877206\pi\) | ||||
0.926509 | − | 0.376273i | \(-0.122794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.34847 | −0.439941 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.928203 | −0.0553720 | −0.0276860 | − | 0.999617i | \(-0.508814\pi\) | ||||
−0.0276860 | + | 0.999617i | \(0.508814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.85641i | 0.585903i | 0.956127 | + | 0.292951i | \(0.0946374\pi\) | ||||
−0.956127 | + | 0.292951i | \(0.905363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 28.8391i | 1.70828i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.1106 | 0.655840 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.07180i | − 0.0628298i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 10.8332i | − 0.632884i | −0.948612 | − | 0.316442i | \(-0.897512\pi\) | ||||
0.948612 | − | 0.316442i | \(-0.102488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 53.5370 | 3.11705 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.46410 | 0.0849558 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 12.0000i | − 0.693978i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.48528i | 0.489083i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.4195 | 0.828381 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.53590 | −0.145205 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 22.9282i | − 1.30858i | −0.756243 | − | 0.654291i | \(-0.772967\pi\) | ||||
0.756243 | − | 0.654291i | \(-0.227033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 3.20736i | − 0.182461i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.4254 | −1.83867 | −0.919337 | − | 0.393471i | \(-0.871274\pi\) | ||||
−0.919337 | + | 0.393471i | \(0.871274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.85641 | −0.217977 | −0.108988 | − | 0.994043i | \(-0.534761\pi\) | ||||
−0.108988 | + | 0.994043i | \(0.534761\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 9.46410i | − 0.533242i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.69213i | 0.375867i | 0.982182 | + | 0.187934i | \(0.0601790\pi\) | ||||
−0.982182 | + | 0.187934i | \(0.939821\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8295 | 0.718312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.8564i | 1.43869i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 42.1218i | − 2.33650i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.41421 | 0.0782062 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.92820 | 0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.07180i | 0.0589113i | 0.999566 | + | 0.0294556i | \(0.00937738\pi\) | ||||
−0.999566 | + | 0.0294556i | \(0.990623\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.656339i | 0.0359671i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −57.6781 | −3.15129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.85641 | 0.536913 | 0.268456 | − | 0.963292i | \(-0.413486\pi\) | ||||
0.268456 | + | 0.963292i | \(0.413486\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 18.0000i | − 0.977626i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 10.7589i | − 0.582627i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959 | 1.05808 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.9282 | 0.588355 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.53590i | 0.136134i | 0.997681 | + | 0.0680671i | \(0.0216832\pi\) | ||||
−0.997681 | + | 0.0680671i | \(0.978317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.4249i | 1.46802i | 0.679139 | + | 0.734010i | \(0.262353\pi\) | ||||
−0.679139 | + | 0.734010i | \(0.737647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.24264 | −0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.928203 | −0.0494033 | −0.0247016 | − | 0.999695i | \(-0.507864\pi\) | ||||
−0.0247016 | + | 0.999695i | \(0.507864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.7846i | 1.31543i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 8.48528i | − 0.449089i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.8380 | −0.994234 | −0.497117 | − | 0.867684i | \(-0.665608\pi\) | ||||
−0.497117 | + | 0.867684i | \(0.665608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −36.7128 | −1.93225 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 8.85641i | − 0.464841i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.4548i | 0.808942i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3886 | −0.855476 | −0.427738 | − | 0.903903i | \(-0.640689\pi\) | ||||
−0.427738 | + | 0.903903i | \(0.640689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.53590 | 0.236129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 11.3205i | − 0.587731i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.2827i | 0.687753i | 0.939015 | + | 0.343877i | \(0.111740\pi\) | ||||
−0.939015 | + | 0.343877i | \(0.888260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.0411 | 0.983279 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.1769 | −1.91471 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.3205i | 0.684229i | 0.939658 | + | 0.342114i | \(0.111143\pi\) | ||||
−0.939658 | + | 0.342114i | \(0.888857\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 14.5211i | − 0.743937i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.8391 | 1.47361 | 0.736804 | − | 0.676106i | \(-0.236334\pi\) | ||||
0.736804 | + | 0.676106i | \(0.236334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.8564 | 0.706188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.46410i | 0.176090i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 9.52056i | − 0.482711i | −0.970437 | − | 0.241356i | \(-0.922408\pi\) | ||||
0.970437 | − | 0.241356i | \(-0.0775921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.79796 | 0.495504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.9282 | 0.753028 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.46410i | 0.476191i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 23.0807i | − 1.15839i | −0.815190 | − | 0.579193i | \(-0.803368\pi\) | ||||
0.815190 | − | 0.579193i | \(-0.196632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.2832 | 0.915307 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.3923 | −0.918468 | −0.459234 | − | 0.888315i | \(-0.651876\pi\) | ||||
−0.459234 | + | 0.888315i | \(0.651876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.1769i | 1.55303i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.86370i | − 0.191989i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.960947 | −0.0476324 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.07180 | 0.448571 | 0.224286 | − | 0.974523i | \(-0.427995\pi\) | ||||
0.224286 | + | 0.974523i | \(0.427995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.3923i | 0.709920i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 33.9411i | − 1.67013i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.1117 | −1.03633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.92820 | 0.339276 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 0.392305i | − 0.0191653i | −0.999954 | − | 0.00958267i | \(-0.996950\pi\) | ||||
0.999954 | − | 0.00958267i | \(-0.00305031\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 19.6975i | − 0.959995i | −0.877270 | − | 0.479998i | \(-0.840638\pi\) | ||||
0.877270 | − | 0.479998i | \(-0.159362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843 | 0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.3923 | 1.66827 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.60770i | 0.0778018i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 6.21166i | − 0.299902i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.34418 | 0.209252 | 0.104626 | − | 0.994512i | \(-0.466636\pi\) | ||||
0.104626 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.8564 | −1.43481 | −0.717404 | − | 0.696658i | \(-0.754670\pi\) | ||||
−0.717404 | + | 0.696658i | \(0.754670\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 33.8564i | − 1.62329i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.1117i | 1.00991i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.83272 | −0.278381 | −0.139190 | − | 0.990266i | \(-0.544450\pi\) | ||||
−0.139190 | + | 0.990266i | \(0.544450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 35.3205i | − 1.67813i | −0.544033 | − | 0.839064i | \(-0.683103\pi\) | ||||
0.544033 | − | 0.839064i | \(-0.316897\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 19.0411i | − 0.902635i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.37945 | 0.254439 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.39230 | −0.301672 | −0.150836 | − | 0.988559i | \(-0.548196\pi\) | ||||
−0.150836 | + | 0.988559i | \(0.548196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.64102i | 0.312713i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.59059i | 0.309653i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −40.1528 | −1.88239 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7846 | 0.972263 | 0.486132 | − | 0.873886i | \(-0.338408\pi\) | ||||
0.486132 | + | 0.873886i | \(0.338408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3.46410i | − 0.161690i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.1870i | 1.45252i | 0.687418 | + | 0.726262i | \(0.258744\pi\) | ||||
−0.687418 | + | 0.726262i | \(0.741256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.2180 | −1.35788 | −0.678938 | − | 0.734196i | \(-0.737560\pi\) | ||||
−0.678938 | + | 0.734196i | \(0.737560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −28.3923 | −1.31666 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.2487i | 1.39974i | 0.714269 | + | 0.699872i | \(0.246760\pi\) | ||||
−0.714269 | + | 0.699872i | \(0.753240\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.5665i | 1.68848i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.17209 | 0.100085 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.07180 | −0.233201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 74.1051i | 3.40018i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4.62158i | − 0.211608i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.0421 | −1.32697 | −0.663485 | − | 0.748190i | \(-0.730923\pi\) | ||||
−0.663485 | + | 0.748190i | \(0.730923\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.78461 | 0.126967 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6.92820i | − 0.315244i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.14110i | − 0.188038i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.4896 | −0.520642 | −0.260321 | − | 0.965522i | \(-0.583828\pi\) | ||||
−0.260321 | + | 0.965522i | \(0.583828\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.53590 | −0.205120 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.85641i | 0.264296i | 0.991230 | + | 0.132148i | \(0.0421874\pi\) | ||||
−0.991230 | + | 0.132148i | \(0.957813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 30.3548i | − 1.36711i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.7128 | 0.704816 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.00000i | − 0.179065i | −0.995984 | − | 0.0895323i | \(-0.971463\pi\) | ||||
0.995984 | − | 0.0895323i | \(-0.0285372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 7.72741i | − 0.345235i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.3853 | −1.04270 | −0.521349 | − | 0.853343i | \(-0.674571\pi\) | ||||
−0.521349 | + | 0.853343i | \(0.674571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 55.7128 | 2.47919 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000i | 0.222058i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 7.24693i | − 0.321215i | −0.987018 | − | 0.160607i | \(-0.948655\pi\) | ||||
0.987018 | − | 0.160607i | \(-0.0513453\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796 | 0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.46410 | 0.329548 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 12.3923i | − 0.546070i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.14110i | 0.182126i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.2480 | −0.757102 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.3205 | 0.934068 | 0.467034 | − | 0.884239i | \(-0.345322\pi\) | ||||
0.467034 | + | 0.884239i | \(0.345322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.4641i | 1.37583i | 0.725792 | + | 0.687915i | \(0.241474\pi\) | ||||
−0.725792 | + | 0.687915i | \(0.758526\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 24.3190i | − 1.06137i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.4558 | −1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 13.8564i | − 0.601317i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 19.2442i | − 0.833558i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.4548 | −0.668170 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.9282 | 0.816812 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.46410i | 0.0630633i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 28.1827i | − 1.21167i | −0.795590 | − | 0.605835i | \(-0.792839\pi\) | ||||
0.795590 | − | 0.605835i | \(-0.207161\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.07107 | −0.303449 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.46410 | 0.234056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 23.1769i | − 0.990973i | −0.868616 | − | 0.495487i | \(-0.834990\pi\) | ||||
0.868616 | − | 0.495487i | \(-0.165010\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.656339i | 0.0280119i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.4056 | 2.78637 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | 0.255146 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.53590i | 0.107643i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 28.0069i | − 1.18669i | −0.804949 | − | 0.593345i | \(-0.797807\pi\) | ||||
0.804949 | − | 0.593345i | \(-0.202193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6969 | 0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.07180 | 0.214131 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.46410i | − 0.0617045i | −0.999524 | − | 0.0308523i | \(-0.990178\pi\) | ||||
0.999524 | − | 0.0308523i | \(-0.00982214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 69.5467i | − 2.92585i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.44949 | −0.102869 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.46410 | 0.145223 | 0.0726113 | − | 0.997360i | \(-0.476867\pi\) | ||||
0.0726113 | + | 0.997360i | \(0.476867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 31.7128i | − 1.32714i | −0.748114 | − | 0.663570i | \(-0.769041\pi\) | ||||
0.748114 | − | 0.663570i | \(-0.230959\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.72741i | 0.322817i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0812 | 1.17107 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.8564 | −0.909894 | −0.454947 | − | 0.890518i | \(-0.650342\pi\) | ||||
−0.454947 | + | 0.890518i | \(0.650342\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 6.00000i | − 0.249351i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.3843i | 0.555273i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.76646 | 0.280238 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.3923 | −0.677738 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 42.9282i | − 1.77184i | −0.463841 | − | 0.885918i | \(-0.653529\pi\) | ||||
0.463841 | − | 0.885918i | \(-0.346471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 54.8497i | − 2.26004i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.76268 | 0.360449 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.7128 | 1.54868 | 0.774340 | − | 0.632770i | \(-0.218082\pi\) | ||||
0.774340 | + | 0.632770i | \(0.218082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 32.7846i | − 1.34404i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.6622i | 0.763792i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.96953 | −0.284767 | −0.142384 | − | 0.989812i | \(-0.545477\pi\) | ||||
−0.142384 | + | 0.989812i | \(0.545477\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.7128 | −0.804102 | −0.402051 | − | 0.915617i | \(-0.631703\pi\) | ||||
−0.402051 | + | 0.915617i | \(0.631703\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.9282i | 0.607923i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 34.2185i | − 1.39118i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8434 | −1.29248 | −0.646241 | − | 0.763133i | \(-0.723660\pi\) | ||||
−0.646241 | + | 0.763133i | \(0.723660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.4641 | −0.869769 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 12.0000i | − 0.485468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.11012i | 0.246785i | 0.992358 | + | 0.123393i | \(0.0393775\pi\) | ||||
−0.992358 | + | 0.123393i | \(0.960623\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.5254 | 0.706691 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.8564 | 1.60456 | 0.802279 | − | 0.596949i | \(-0.203621\pi\) | ||||
0.802279 | + | 0.596949i | \(0.203621\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 12.0000i | − 0.482321i | −0.970485 | − | 0.241160i | \(-0.922472\pi\) | ||||
0.970485 | − | 0.241160i | \(-0.0775280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.82843i | − 0.113501i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0716 | −0.483638 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.9282i | 0.436430i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.27362i | 0.0906553i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5612 | 0.937955 | 0.468977 | − | 0.883210i | \(-0.344623\pi\) | ||||
0.468977 | + | 0.883210i | \(0.344623\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.92820 | −0.275371 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 56.1051i | − 2.22646i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.24264i | − 0.168100i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.41473 | 0.253763 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.6077 | −1.01144 | −0.505722 | − | 0.862697i | \(-0.668774\pi\) | ||||
−0.505722 | + | 0.862697i | \(0.668774\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.5359i | 1.12535i | 0.826680 | + | 0.562673i | \(0.190227\pi\) | ||||
−0.826680 | + | 0.562673i | \(0.809773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.3843i | 0.527005i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.9107 | −1.60836 | −0.804182 | − | 0.594383i | \(-0.797396\pi\) | ||||
−0.804182 | + | 0.594383i | \(0.797396\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.2872 | 0.796342 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.0000i | 0.705476i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 24.9754i | − 0.977362i | −0.872463 | − | 0.488681i | \(-0.837478\pi\) | ||||
0.872463 | − | 0.488681i | \(-0.162522\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.6781 | 2.25367 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000i | 0.934907i | 0.884018 | + | 0.467454i | \(0.154829\pi\) | ||||
−0.884018 | + | 0.467454i | \(0.845171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.51626i | − 0.253453i | −0.991938 | − | 0.126727i | \(-0.959553\pi\) | ||||
0.991938 | − | 0.126727i | \(-0.0404471\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.6969 | −0.570782 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 70.6410 | 2.73934 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 24.7846i | − 0.959664i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.5211i | 0.561417i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.960947 | −0.0370969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | 0.308377 | 0.154189 | − | 0.988041i | \(-0.450724\pi\) | ||||
0.154189 | + | 0.988041i | \(0.450724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 9.92820i | − 0.382137i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3.30890i | − 0.127171i | −0.997976 | − | 0.0635857i | \(-0.979746\pi\) | ||||
0.997976 | − | 0.0635857i | \(-0.0202536\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.62536 | −0.100752 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3205 | −0.433803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.1769i | 0.963368i | 0.876345 | + | 0.481684i | \(0.159975\pi\) | ||||
−0.876345 | + | 0.481684i | \(0.840025\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.6076i | 2.12466i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.8690 | 0.643594 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.6077 | −0.746994 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 26.3923i | − 1.00401i | −0.864865 | − | 0.502005i | \(-0.832596\pi\) | ||||
0.864865 | − | 0.502005i | \(-0.167404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3.58630i | − 0.136232i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.7685 | 1.01539 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7128 | 0.595165 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.9282i | 0.488990i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 14.9743i | − 0.565573i | −0.959183 | − | 0.282787i | \(-0.908741\pi\) | ||||
0.959183 | − | 0.282787i | \(-0.0912588\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.89898 | −0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.9282 | 0.411580 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 35.3205i | − 1.32836i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.0913i | 1.84366i | 0.387590 | + | 0.921832i | \(0.373308\pi\) | ||||
−0.387590 | + | 0.921832i | \(0.626692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.44949 | 0.0918630 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.7846 | −0.778390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 24.0000i | − 0.897549i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 7.72741i | − 0.288585i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.27362 | −0.0847919 | −0.0423959 | − | 0.999101i | \(-0.513499\pi\) | ||||
−0.0423959 | + | 0.999101i | \(0.513499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.85641 | −0.292588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.7846i | 0.996130i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 86.9977i | − 3.23101i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.10634 | 0.300648 | 0.150324 | − | 0.988637i | \(-0.451968\pi\) | ||||
0.150324 | + | 0.988637i | \(0.451968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000i | 0.443836i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.07107i | 0.261176i | 0.991437 | + | 0.130588i | \(0.0416865\pi\) | ||||
−0.991437 | + | 0.130588i | \(0.958314\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.86370 | 0.142515 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.8564 | −0.805091 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 36.0000i | − 1.32428i | −0.749380 | − | 0.662141i | \(-0.769648\pi\) | ||||
0.749380 | − | 0.662141i | \(-0.230352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 31.6675i | − 1.16333i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.3233 | −1.00240 | −0.501198 | − | 0.865333i | \(-0.667107\pi\) | ||||
−0.501198 | + | 0.865333i | \(0.667107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7846 | 0.761489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.46410i | 0.199921i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.79796i | 0.358010i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.1886 | 1.68545 | 0.842723 | − | 0.538348i | \(-0.180951\pi\) | ||||
0.842723 | + | 0.538348i | \(0.180951\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.53590 | −0.238181 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.4641i | 0.926734i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.6365i | 1.22254i | 0.791422 | + | 0.611270i | \(0.209341\pi\) | ||||
−0.791422 | + | 0.611270i | \(0.790659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.14110 | 0.150313 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.2487 | 1.89401 | 0.947007 | − | 0.321212i | \(-0.104090\pi\) | ||||
0.947007 | + | 0.321212i | \(0.104090\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.46410i | − 0.125409i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 13.3843i | − 0.483909i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58.7878 | −2.12270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.7846i | 0.820568i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 48.9155i | − 1.75937i | −0.475560 | − | 0.879684i | \(-0.657754\pi\) | ||||
0.475560 | − | 0.879684i | \(-0.342246\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −72.9571 | −2.62070 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.60770 | 0.0576757 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.8564i | 1.21303i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.39182i | 0.336066i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.76268 | −0.313153 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.39230 | 0.299534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.4641i | 0.836405i | 0.908354 | + | 0.418202i | \(0.137340\pi\) | ||||
−0.908354 | + | 0.418202i | \(0.862660\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.6274i | 0.805557i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −44.0908 | −1.56769 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.78461 | 0.0988844 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 17.8564i | − 0.633301i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.9439i | 0.777292i | 0.921387 | + | 0.388646i | \(0.127057\pi\) | ||||
−0.921387 | + | 0.388646i | \(0.872943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.79796 | 0.346627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.92820 | −0.174129 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.85641i | 0.206668i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 26.7685i | − 0.943466i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.2784 | 0.361818 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.67949 | 0.234838 | 0.117419 | − | 0.993082i | \(-0.462538\pi\) | ||||
0.117419 | + | 0.993082i | \(0.462538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.3923i | 1.90997i | 0.296651 | + | 0.954986i | \(0.404130\pi\) | ||||
−0.296651 | + | 0.954986i | \(0.595870\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.20736i | 0.112487i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.5254 | −0.613887 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.8564 | −0.904601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3923i | 0.363137i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.1784i | 0.878734i | 0.898308 | + | 0.439367i | \(0.144797\pi\) | ||||
−0.898308 | + | 0.439367i | \(0.855203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.97382 | −0.347666 | −0.173833 | − | 0.984775i | \(-0.555615\pi\) | ||||
−0.173833 | + | 0.984775i | \(0.555615\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.5359 | 0.506075 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.7846i | 1.55731i | 0.627450 | + | 0.778657i | \(0.284099\pi\) | ||||
−0.627450 | + | 0.778657i | \(0.715901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.61729i | − 0.0561706i | −0.999606 | − | 0.0280853i | \(-0.991059\pi\) | ||||
0.999606 | − | 0.0280853i | \(-0.00894101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.5249 | −0.434482 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 29.8564i | − 1.03322i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.34847i | 0.254000i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.0106 | 0.897987 | 0.448994 | − | 0.893535i | \(-0.351783\pi\) | ||||
0.448994 | + | 0.893535i | \(0.351783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −47.7846 | −1.64775 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.928203i | 0.0319690i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.3185i | 0.664577i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.6937 | −0.745404 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.85641 | 0.338271 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.85641i | 0.0636368i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 47.0208i | − 1.60996i | −0.593301 | − | 0.804980i | \(-0.702176\pi\) | ||||
0.593301 | − | 0.804980i | \(-0.297824\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.8391 | 0.986276 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.1769 | −1.47490 | −0.737448 | − | 0.675404i | \(-0.763969\pi\) | ||||
−0.737448 | + | 0.675404i | \(0.763969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 32.2487i | − 1.10031i | −0.835062 | − | 0.550156i | \(-0.814568\pi\) | ||||
0.835062 | − | 0.550156i | \(-0.185432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 11.1106i | − 0.378649i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.1213 | −1.26362 | −0.631812 | − | 0.775122i | \(-0.717688\pi\) | ||||
−0.631812 | + | 0.775122i | \(0.717688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −66.6410 | −2.26586 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.00000i | 0.169809i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.58630i | 0.121657i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.3350 | 2.14602 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.07180 | −0.0362748 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 46.6410i | − 1.57675i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 35.7071i | − 1.20574i | −0.797839 | − | 0.602871i | \(-0.794023\pi\) | ||||
0.797839 | − | 0.602871i | \(-0.205977\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.8332 | −0.365396 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.6410 | −1.23447 | −0.617234 | − | 0.786780i | \(-0.711747\pi\) | ||||
−0.617234 | + | 0.786780i | \(0.711747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.60770i | 0.188714i | 0.995538 | + | 0.0943570i | \(0.0300795\pi\) | ||||
−0.995538 | + | 0.0943570i | \(0.969920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 53.5370i | − 1.79963i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.5665 | 1.22778 | 0.613891 | − | 0.789391i | \(-0.289603\pi\) | ||||
0.613891 | + | 0.789391i | \(0.289603\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.5692 | −1.19295 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.46410i | − 0.0490492i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.1117i | 0.706475i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 73.1330 | 2.44457 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 64.3923i | 2.14760i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 16.0096i | − 0.533358i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.48528 | 0.282372 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.3205 | −0.908164 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 42.3923i | − 1.40761i | −0.710392 | − | 0.703807i | \(-0.751482\pi\) | ||||
0.710392 | − | 0.703807i | \(-0.248518\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 14.4195i | − 0.478266i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0726 | 0.731298 | 0.365649 | − | 0.930753i | \(-0.380847\pi\) | ||||
0.365649 | + | 0.930753i | \(0.380847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | −0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.53590i | 0.0838342i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 36.5665i | − 1.20753i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.582009 | −0.0191987 | −0.00959936 | − | 0.999954i | \(-0.503056\pi\) | ||||
−0.00959936 | + | 0.999954i | \(0.503056\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.9282 | −0.755510 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 27.2154i | − 0.895805i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.51626i | 0.214253i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.20736 | −0.105344 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.3205 | −1.48692 | −0.743459 | − | 0.668782i | \(-0.766816\pi\) | ||||
−0.743459 | + | 0.668782i | \(0.766816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.46410i | 0.244626i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.4254i | 1.06156i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5959 | 0.640855 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.85641i | 0.125849i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 36.2891i | − 1.18299i | −0.806309 | − | 0.591495i | \(-0.798538\pi\) | ||||
0.806309 | − | 0.591495i | \(-0.201462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8295 | 0.417785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.46410 | −0.307867 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 29.0718i | − 0.944706i | −0.881409 | − | 0.472353i | \(-0.843405\pi\) | ||||
0.881409 | − | 0.472353i | \(-0.156595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 16.9706i | − 0.550888i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.69213 | 0.217007 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.3923 | −1.50279 | −0.751397 | − | 0.659850i | \(-0.770620\pi\) | ||||
−0.751397 | + | 0.659850i | \(0.770620\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.8564i | 0.966131i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 12.8295i | − 0.414717i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.2538 | 1.13840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 23.1822i | − 0.746262i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3800 | 0.333797 | 0.166899 | − | 0.985974i | \(-0.446625\pi\) | ||||
0.166899 | + | 0.985974i | \(0.446625\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.8564 | 0.830627 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.2487i | 0.713995i | 0.934105 | + | 0.356998i | \(0.116200\pi\) | ||||
−0.934105 | + | 0.356998i | \(0.883800\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 16.9706i | − 0.544051i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −42.1218 | −1.34898 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.1769 | −1.12541 | −0.562705 | − | 0.826658i | \(-0.690239\pi\) | ||||
−0.562705 | + | 0.826658i | \(0.690239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 7.21539i | − 0.230605i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.41421i | − 0.0451524i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.7370 | 0.757093 | 0.378547 | − | 0.925582i | \(-0.376424\pi\) | ||||
0.378547 | + | 0.925582i | \(0.376424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.8564 | 1.07875 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 6.92820i | − 0.220527i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.79796i | 0.311557i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.2474 | 0.389053 | 0.194527 | − | 0.980897i | \(-0.437683\pi\) | ||||
0.194527 | + | 0.980897i | \(0.437683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.07180 | 0.0340124 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 72.1051i | 2.28589i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 17.6269i | − 0.558250i | −0.960255 | − | 0.279125i | \(-0.909956\pi\) | ||||
0.960255 | − | 0.279125i | \(-0.0900443\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.656339 | 0.0207656 |
(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 | 3072.2.d.h.1537.1 | 8 | ||
4.3 | odd | 2 | inner | 3072.2.d.h.1537.5 | 8 | ||
8.3 | odd | 2 | inner | 3072.2.d.h.1537.4 | 8 | ||
8.5 | even | 2 | inner | 3072.2.d.h.1537.8 | 8 | ||
16.3 | odd | 4 | 3072.2.a.l.1.1 | 4 | |||
16.5 | even | 4 | 3072.2.a.l.1.4 | 4 | |||
16.11 | odd | 4 | 3072.2.a.r.1.4 | 4 | |||
16.13 | even | 4 | 3072.2.a.r.1.1 | 4 | |||
32.3 | odd | 8 | 768.2.j.f.193.2 | yes | 8 | ||
32.5 | even | 8 | 768.2.j.f.577.4 | yes | 8 | ||
32.11 | odd | 8 | 768.2.j.e.577.3 | yes | 8 | ||
32.13 | even | 8 | 768.2.j.e.193.1 | ✓ | 8 | ||
32.19 | odd | 8 | 768.2.j.e.193.3 | yes | 8 | ||
32.21 | even | 8 | 768.2.j.e.577.1 | yes | 8 | ||
32.27 | odd | 8 | 768.2.j.f.577.2 | yes | 8 | ||
32.29 | even | 8 | 768.2.j.f.193.4 | yes | 8 | ||
48.5 | odd | 4 | 9216.2.a.bi.1.1 | 4 | |||
48.11 | even | 4 | 9216.2.a.bc.1.1 | 4 | |||
48.29 | odd | 4 | 9216.2.a.bc.1.4 | 4 | |||
48.35 | even | 4 | 9216.2.a.bi.1.4 | 4 | |||
96.5 | odd | 8 | 2304.2.k.e.577.1 | 8 | |||
96.11 | even | 8 | 2304.2.k.l.577.4 | 8 | |||
96.29 | odd | 8 | 2304.2.k.e.1729.2 | 8 | |||
96.35 | even | 8 | 2304.2.k.e.1729.1 | 8 | |||
96.53 | odd | 8 | 2304.2.k.l.577.3 | 8 | |||
96.59 | even | 8 | 2304.2.k.e.577.2 | 8 | |||
96.77 | odd | 8 | 2304.2.k.l.1729.4 | 8 | |||
96.83 | even | 8 | 2304.2.k.l.1729.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.e.193.1 | ✓ | 8 | 32.13 | even | 8 | ||
768.2.j.e.193.3 | yes | 8 | 32.19 | odd | 8 | ||
768.2.j.e.577.1 | yes | 8 | 32.21 | even | 8 | ||
768.2.j.e.577.3 | yes | 8 | 32.11 | odd | 8 | ||
768.2.j.f.193.2 | yes | 8 | 32.3 | odd | 8 | ||
768.2.j.f.193.4 | yes | 8 | 32.29 | even | 8 | ||
768.2.j.f.577.2 | yes | 8 | 32.27 | odd | 8 | ||
768.2.j.f.577.4 | yes | 8 | 32.5 | even | 8 | ||
2304.2.k.e.577.1 | 8 | 96.5 | odd | 8 | |||
2304.2.k.e.577.2 | 8 | 96.59 | even | 8 | |||
2304.2.k.e.1729.1 | 8 | 96.35 | even | 8 | |||
2304.2.k.e.1729.2 | 8 | 96.29 | odd | 8 | |||
2304.2.k.l.577.3 | 8 | 96.53 | odd | 8 | |||
2304.2.k.l.577.4 | 8 | 96.11 | even | 8 | |||
2304.2.k.l.1729.3 | 8 | 96.83 | even | 8 | |||
2304.2.k.l.1729.4 | 8 | 96.77 | odd | 8 | |||
3072.2.a.l.1.1 | 4 | 16.3 | odd | 4 | |||
3072.2.a.l.1.4 | 4 | 16.5 | even | 4 | |||
3072.2.a.r.1.1 | 4 | 16.13 | even | 4 | |||
3072.2.a.r.1.4 | 4 | 16.11 | odd | 4 | |||
3072.2.d.h.1537.1 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.d.h.1537.4 | 8 | 8.3 | odd | 2 | inner | ||
3072.2.d.h.1537.5 | 8 | 4.3 | odd | 2 | inner | ||
3072.2.d.h.1537.8 | 8 | 8.5 | even | 2 | inner | ||
9216.2.a.bc.1.1 | 4 | 48.11 | even | 4 | |||
9216.2.a.bc.1.4 | 4 | 48.29 | odd | 4 | |||
9216.2.a.bi.1.1 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bi.1.4 | 4 | 48.35 | even | 4 |