Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(257,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.b (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: | \(4.08834058349\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 512.257 |
Dual form | 512.2.b.a.257.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.41421i | − 0.816497i | −0.912871 | − | 0.408248i | \(-0.866140\pi\) | ||||
0.912871 | − | 0.408248i | \(-0.133860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.82843i | 1.26491i | 0.774597 | + | 0.632456i | \(0.217953\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00000 | −1.51186 | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421i | 0.426401i | 0.977008 | + | 0.213201i | \(0.0683888\pi\) | ||||
−0.977008 | + | 0.213201i | \(0.931611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843i | 0.784465i | 0.919866 | + | 0.392232i | \(0.128297\pi\) | ||||
−0.919866 | + | 0.392232i | \(0.871703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.07107i | 1.62221i | 0.584898 | + | 0.811107i | \(0.301135\pi\) | ||||
−0.584898 | + | 0.811107i | \(0.698865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.65685i | 1.23443i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.65685i | − 1.08866i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528i | 1.57568i | 0.615882 | + | 0.787839i | \(0.288800\pi\) | ||||
−0.615882 | + | 0.787839i | \(0.711200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 11.3137i | − 1.91237i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.82843i | − 0.464991i | −0.972598 | − | 0.232495i | \(-0.925311\pi\) | ||||
0.972598 | − | 0.232495i | \(-0.0746890\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24264i | 0.646997i | 0.946229 | + | 0.323498i | \(0.104859\pi\) | ||||
−0.946229 | + | 0.323498i | \(0.895141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843i | 0.421637i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.65685i | 0.792118i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.82843i | − 0.388514i | −0.980951 | − | 0.194257i | \(-0.937770\pi\) | ||||
0.980951 | − | 0.194257i | \(-0.0622296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.0000 | 1.32453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.24264i | 0.552345i | 0.961108 | + | 0.276172i | \(0.0890661\pi\) | ||||
−0.961108 | + | 0.276172i | \(0.910934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 8.48528i | − 1.08643i | −0.839594 | − | 0.543214i | \(-0.817207\pi\) | ||||
0.839594 | − | 0.543214i | \(-0.182793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00000 | −0.503953 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.00000 | −0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.24264i | − 0.518321i | −0.965834 | − | 0.259161i | \(-0.916554\pi\) | ||||
0.965834 | − | 0.259161i | \(-0.0834459\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685i | 0.681005i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.24264i | 0.489898i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.65685i | − 0.644658i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.89949i | 1.08661i | 0.839535 | + | 0.543305i | \(0.182827\pi\) | ||||
−0.839535 | + | 0.543305i | \(0.817173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 11.3137i | − 1.22714i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0000 | 1.28654 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 11.3137i | − 1.18600i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 11.3137i | − 1.17318i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.0000 | −2.05196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | −0.406138 | −0.203069 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203069 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.41421i | 0.142134i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 2.82843i | − 0.281439i | −0.990050 | − | 0.140720i | \(-0.955058\pi\) | ||||
0.990050 | − | 0.140720i | \(-0.0449416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0000 | −1.18240 | −0.591198 | − | 0.806527i | \(-0.701345\pi\) | ||||
−0.591198 | + | 0.806527i | \(0.701345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.0000 | −1.56144 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 9.89949i | − 0.957020i | −0.878082 | − | 0.478510i | \(-0.841177\pi\) | ||||
0.878082 | − | 0.478510i | \(-0.158823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 14.1421i | − 1.35457i | −0.735720 | − | 0.677285i | \(-0.763156\pi\) | ||||
0.735720 | − | 0.677285i | \(-0.236844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 11.3137i | − 1.05501i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.82843i | 0.261488i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.0000 | 1.46672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.82843i | 0.255031i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.07107i | 0.617802i | 0.951094 | + | 0.308901i | \(0.0999612\pi\) | ||||
−0.951094 | + | 0.308901i | \(0.900039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 28.2843i | − 2.45256i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.0000 | 1.37706 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0000 | 1.53784 | 0.768922 | − | 0.639343i | \(-0.220793\pi\) | ||||
0.768922 | + | 0.639343i | \(0.220793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.24264i | 0.359856i | 0.983680 | + | 0.179928i | \(0.0575865\pi\) | ||||
−0.983680 | + | 0.179928i | \(0.942414\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.0000 | −1.99309 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 12.7279i | − 1.04978i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.82843i | 0.231714i | 0.993266 | + | 0.115857i | \(0.0369614\pi\) | ||||
−0.993266 | + | 0.115857i | \(0.963039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | −0.325515 | −0.162758 | − | 0.986666i | \(-0.552039\pi\) | ||||
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.6274i | 1.81748i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 8.48528i | − 0.677199i | −0.940931 | − | 0.338600i | \(-0.890047\pi\) | ||||
0.940931 | − | 0.338600i | \(-0.109953\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0000 | 1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.89949i | 0.775388i | 0.921788 | + | 0.387694i | \(0.126728\pi\) | ||||
−0.921788 | + | 0.387694i | \(0.873272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.65685i | 0.440386i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.07107i | 0.540738i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1421i | 1.07521i | 0.843198 | + | 0.537603i | \(0.180670\pi\) | ||||
−0.843198 | + | 0.537603i | \(0.819330\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.0000 | 0.907115 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.41421i | − 0.105703i | −0.998602 | − | 0.0528516i | \(-0.983169\pi\) | ||||
0.998602 | − | 0.0528516i | \(-0.0168310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.48528i | − 0.630706i | −0.948974 | − | 0.315353i | \(-0.897877\pi\) | ||||
0.948974 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0000 | −0.887066 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | 0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.65685i | − 0.413670i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22.6274i | 1.64590i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.3137i | 0.810191i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1421i | 1.00759i | 0.863825 | + | 0.503793i | \(0.168062\pi\) | ||||
−0.863825 | + | 0.503793i | \(0.831938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | −0.423207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 33.9411i | − 2.38220i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 5.65685i | − 0.395092i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0000 | −0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 24.0416i | − 1.65509i | −0.561396 | − | 0.827547i | \(-0.689736\pi\) | ||||
0.561396 | − | 0.827547i | \(-0.310264\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 5.65685i | − 0.387601i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0000 | −0.818393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32.0000 | −2.17230 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 5.65685i | − 0.382255i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 11.3137i | − 0.761042i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.2132i | 1.40797i | 0.710215 | + | 0.703985i | \(0.248598\pi\) | ||||
−0.710215 | + | 0.703985i | \(0.751402\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4558i | 1.68217i | 0.540903 | + | 0.841085i | \(0.318082\pi\) | ||||
−0.540903 | + | 0.841085i | \(0.681918\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0000 | −0.786146 | −0.393073 | − | 0.919507i | \(-0.628588\pi\) | ||||
−0.393073 | + | 0.919507i | \(0.628588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3137i | 0.734904i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0000 | 0.772988 | 0.386494 | − | 0.922292i | \(-0.373686\pi\) | ||||
0.386494 | + | 0.922292i | \(0.373686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 9.89949i | − 0.635053i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.4558i | 1.62631i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0000 | −1.27257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0000 | 0.887214 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.24264i | 0.267793i | 0.990995 | + | 0.133897i | \(0.0427490\pi\) | ||||
−0.990995 | + | 0.133897i | \(0.957251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.65685i | − 0.355643i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.0000 | −1.00196 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.00000 | −0.124757 | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3137i | 0.703000i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.48528i | 0.525226i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28.0000 | −1.72655 | −0.863277 | − | 0.504730i | \(-0.831592\pi\) | ||||
−0.863277 | + | 0.504730i | \(0.831592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9706i | 1.03858i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.7990i | 1.20717i | 0.797300 | + | 0.603583i | \(0.206261\pi\) | ||||
−0.797300 | + | 0.603583i | \(0.793739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.0000 | 1.94386 | 0.971931 | − | 0.235267i | \(-0.0755965\pi\) | ||||
0.971931 | + | 0.235267i | \(0.0755965\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.0000 | −0.968364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.24264i | − 0.255841i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.48528i | 0.509831i | 0.966963 | + | 0.254916i | \(0.0820477\pi\) | ||||
−0.966963 | + | 0.254916i | \(0.917952\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000 | 1.19310 | 0.596550 | − | 0.802576i | \(-0.296538\pi\) | ||||
0.596550 | + | 0.802576i | \(0.296538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.0416i | 1.42913i | 0.699571 | + | 0.714563i | \(0.253375\pi\) | ||||
−0.699571 | + | 0.714563i | \(0.746625\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 28.2843i | 1.67542i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.00000 | 0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.65685i | 0.331611i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.48528i | − 0.495715i | −0.968796 | − | 0.247858i | \(-0.920273\pi\) | ||||
0.968796 | − | 0.247858i | \(-0.0797265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | −0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.00000 | 0.464207 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 11.3137i | − 0.654289i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 16.9706i | − 0.978167i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.00000 | −0.229794 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.0000 | 1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.07107i | 0.403567i | 0.979430 | + | 0.201784i | \(0.0646738\pi\) | ||||
−0.979430 | + | 0.201784i | \(0.935326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.9706i | 0.965422i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0000 | 1.13410 | 0.567048 | − | 0.823685i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823685i | \(0.308085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 11.3137i | − 0.637455i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.82843i | − 0.158860i | −0.996840 | − | 0.0794301i | \(-0.974690\pi\) | ||||
0.996840 | − | 0.0794301i | \(-0.0253101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0000 | −0.781404 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 28.2843i | − 1.57378i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 8.48528i | − 0.470679i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.0000 | −1.10600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7279i | 0.699590i | 0.936826 | + | 0.349795i | \(0.113749\pi\) | ||||
−0.936826 | + | 0.349795i | \(0.886251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.82843i | − 0.154997i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.0000 | 1.63420 | 0.817102 | − | 0.576493i | \(-0.195579\pi\) | ||||
0.817102 | + | 0.576493i | \(0.195579\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 19.7990i | − 1.07533i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.3137i | 0.612672i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.0000 | −0.861411 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5563i | 0.835109i | 0.908652 | + | 0.417554i | \(0.137113\pi\) | ||||
−0.908652 | + | 0.417554i | \(0.862887\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.7990i | 1.05982i | 0.848055 | + | 0.529908i | \(0.177773\pi\) | ||||
−0.848055 | + | 0.529908i | \(0.822227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0000 | 0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3137i | 0.600469i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 22.6274i | − 1.19757i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.0000 | 1.90001 | 0.950004 | − | 0.312239i | \(-0.101079\pi\) | ||||
0.950004 | + | 0.312239i | \(0.101079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.0000 | −1.63158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 12.7279i | − 0.668043i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.3137i | 0.592187i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | 0.835193 | 0.417597 | − | 0.908633i | \(-0.362873\pi\) | ||||
0.417597 | + | 0.908633i | \(0.362873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.3137i | 0.587378i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 36.7696i | − 1.90386i | −0.306323 | − | 0.951928i | \(-0.599099\pi\) | ||||
0.306323 | − | 0.951928i | \(-0.400901\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.00000 | 0.413118 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 29.6985i | − 1.52551i | −0.646688 | − | 0.762754i | \(-0.723847\pi\) | ||||
0.646688 | − | 0.762754i | \(-0.276153\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 11.3137i | − 0.579619i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0000 | 0.817562 | 0.408781 | − | 0.912633i | \(-0.365954\pi\) | ||||
0.408781 | + | 0.912633i | \(0.365954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.24264i | 0.215666i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.7990i | 1.00385i | 0.864912 | + | 0.501924i | \(0.167374\pi\) | ||||
−0.864912 | + | 0.501924i | \(0.832626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.0000 | 0.504433 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 22.6274i | − 1.13851i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.82843i | − 0.141955i | −0.997478 | − | 0.0709773i | \(-0.977388\pi\) | ||||
0.997478 | − | 0.0709773i | \(-0.0226118\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −40.0000 | −2.00250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.0000 | −1.79775 | −0.898877 | − | 0.438201i | \(-0.855616\pi\) | ||||
−0.898877 | + | 0.438201i | \(0.855616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.6274i | 1.12715i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 14.1421i | − 0.702728i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 25.4558i | − 1.25564i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 16.9706i | − 0.835067i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.0000 | −1.37447 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 26.8701i | − 1.31269i | −0.754462 | − | 0.656344i | \(-0.772102\pi\) | ||||
0.754462 | − | 0.656344i | \(-0.227898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 8.48528i | − 0.413547i | −0.978389 | − | 0.206774i | \(-0.933704\pi\) | ||||
0.978389 | − | 0.206774i | \(-0.0662964\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.9411i | 1.64253i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.65685i | 0.273115i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0000 | −0.961139 | −0.480569 | − | 0.876957i | \(-0.659570\pi\) | ||||
−0.480569 | + | 0.876957i | \(0.659570\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.9411i | 1.62735i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 28.2843i | − 1.35302i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | 0.190910 | 0.0954548 | − | 0.995434i | \(-0.469569\pi\) | ||||
0.0954548 | + | 0.995434i | \(0.469569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.3553i | 1.67978i | 0.542754 | + | 0.839891i | \(0.317381\pi\) | ||||
−0.542754 | + | 0.839891i | \(0.682619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 33.9411i | − 1.60896i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.0000 | −0.943858 | −0.471929 | − | 0.881636i | \(-0.656442\pi\) | ||||
−0.471929 | + | 0.881636i | \(0.656442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.82843i | − 0.133185i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.65685i | 0.265782i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.0000 | 1.50018 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.00000 | −0.0935561 | −0.0467780 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467780 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.6274i | 1.05616i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 14.1421i | − 0.658665i | −0.944214 | − | 0.329332i | \(-0.893176\pi\) | ||||
0.944214 | − | 0.329332i | \(-0.106824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.0000 | 1.48396 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.3848i | 0.850746i | 0.905018 | + | 0.425373i | \(0.139857\pi\) | ||||
−0.905018 | + | 0.425373i | \(0.860143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.9706i | 0.783628i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0000 | −0.552931 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | −0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 21.2132i | − 0.973329i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.82843i | − 0.129505i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 22.6274i | − 1.02958i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 11.3137i | − 0.513729i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | 0.543772 | 0.271886 | − | 0.962329i | \(-0.412353\pi\) | ||||
0.271886 | + | 0.962329i | \(0.412353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.0000 | 0.633102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5563i | 0.702048i | 0.936366 | + | 0.351024i | \(0.114166\pi\) | ||||
−0.936366 | + | 0.351024i | \(0.885834\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 33.9411i | − 1.52863i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 12.7279i | − 0.569780i | −0.958560 | − | 0.284890i | \(-0.908043\pi\) | ||||
0.958560 | − | 0.284890i | \(-0.0919571\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 16.9706i | − 0.758189i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.0000 | −0.891756 | −0.445878 | − | 0.895094i | \(-0.647108\pi\) | ||||
−0.445878 | + | 0.895094i | \(0.647108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 7.07107i | − 0.314037i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.82843i | 0.125368i | 0.998033 | + | 0.0626839i | \(0.0199660\pi\) | ||||
−0.998033 | + | 0.0626839i | \(0.980034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 40.0000 | 1.76604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 33.9411i | − 1.49562i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.0000 | 0.877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.0000 | −0.613351 | −0.306676 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306676 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 9.89949i | − 0.432875i | −0.976297 | − | 0.216437i | \(-0.930556\pi\) | ||||
0.976297 | − | 0.216437i | \(-0.0694437\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 16.9706i | − 0.740656i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.0000 | −1.39394 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.24264i | 0.184115i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5.65685i | − 0.245026i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.0000 | 1.21055 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.00000 | −0.0863064 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.7279i | 0.548230i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 8.48528i | − 0.364811i | −0.983223 | − | 0.182405i | \(-0.941612\pi\) | ||||
0.983223 | − | 0.182405i | \(-0.0583883\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.0000 | −0.514969 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.0000 | 1.71341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 26.8701i | − 1.14888i | −0.818546 | − | 0.574440i | \(-0.805220\pi\) | ||||
0.818546 | − | 0.574440i | \(-0.194780\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 8.48528i | − 0.362143i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −60.0000 | −2.55609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0000 | 1.36078 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 11.3137i | − 0.480240i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 31.1127i | − 1.31829i | −0.752017 | − | 0.659144i | \(-0.770919\pi\) | ||||
0.752017 | − | 0.659144i | \(-0.229081\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.07107i | 0.298010i | 0.988836 | + | 0.149005i | \(0.0476070\pi\) | ||||
−0.988836 | + | 0.149005i | \(0.952393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.5980i | 1.66590i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.0000 | 0.839921 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.0000 | −1.25767 | −0.628833 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628833 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 32.5269i | − 1.36121i | −0.732651 | − | 0.680604i | \(-0.761717\pi\) | ||||
0.732651 | − | 0.680604i | \(-0.238283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 11.3137i | − 0.472637i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.65685i | 0.235091i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 39.5980i | − 1.64280i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.00000 | −0.330759 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.41421i | 0.0583708i | 0.999574 | + | 0.0291854i | \(0.00929133\pi\) | ||||
−0.999574 | + | 0.0291854i | \(0.990709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.5685i | 2.33087i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.0000 | 0.822690 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.0000 | 0.739171 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 45.2548i | 1.85527i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.65685i | 0.231520i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0000 | 1.47092 | 0.735460 | − | 0.677568i | \(-0.236966\pi\) | ||||
0.735460 | + | 0.677568i | \(0.236966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.00000 | 0.163163 | 0.0815817 | − | 0.996667i | \(-0.474003\pi\) | ||||
0.0815817 | + | 0.996667i | \(0.474003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 4.24264i | − 0.172774i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.4558i | 1.03493i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.0000 | −1.94506 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 8.48528i | − 0.342717i | −0.985209 | − | 0.171359i | \(-0.945184\pi\) | ||||
0.985209 | − | 0.171359i | \(-0.0548157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.00000 | −0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.0000 | −1.12724 | −0.563619 | − | 0.826035i | \(-0.690591\pi\) | ||||
−0.563619 | + | 0.826035i | \(0.690591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.41421i | 0.0568420i | 0.999596 | + | 0.0284210i | \(0.00904791\pi\) | ||||
−0.999596 | + | 0.0284210i | \(0.990952\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.6274i | 0.908007i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 48.0000 | 1.92308 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.1421i | 0.564782i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3137i | 0.451107i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.00000 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −34.0000 | −1.35138 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.6274i | 0.897942i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.4558i | 1.00860i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.00000 | 0.158238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.00000 | −0.157991 | −0.0789953 | − | 0.996875i | \(-0.525171\pi\) | ||||
−0.0789953 | + | 0.996875i | \(0.525171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4.24264i | − 0.167313i | −0.996495 | − | 0.0836567i | \(-0.973340\pi\) | ||||
0.996495 | − | 0.0836567i | \(-0.0266599\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.9706i | 0.668215i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.2548i | 1.77368i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 48.0833i | − 1.88164i | −0.338902 | − | 0.940822i | \(-0.610055\pi\) | ||||
0.338902 | − | 0.940822i | \(-0.389945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.0000 | −0.781465 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.5269i | 1.26707i | 0.773715 | + | 0.633534i | \(0.218396\pi\) | ||||
−0.773715 | + | 0.633534i | \(0.781604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 31.1127i | − 1.21014i | −0.796171 | − | 0.605072i | \(-0.793144\pi\) | ||||
0.796171 | − | 0.605072i | \(-0.206856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.0000 | −0.621389 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 80.0000 | 3.10227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 33.9411i | − 1.31421i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 33.9411i | − 1.31224i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.0000 | −0.770943 | −0.385472 | − | 0.922720i | \(-0.625961\pi\) | ||||
−0.385472 | + | 0.922720i | \(0.625961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.9706i | 0.653197i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.4264i | 1.63058i | 0.579053 | + | 0.815290i | \(0.303422\pi\) | ||||
−0.579053 | + | 0.815290i | \(0.696578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.0000 | 0.614024 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.0000 | 1.14960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 29.6985i | − 1.13638i | −0.822897 | − | 0.568190i | \(-0.807644\pi\) | ||||
0.822897 | − | 0.568190i | \(-0.192356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.9117i | 1.94524i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.0000 | 1.37349 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.00000 | 0.304776 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 46.6690i | − 1.77537i | −0.460447 | − | 0.887687i | \(-0.652311\pi\) | ||||
0.460447 | − | 0.887687i | \(-0.347689\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 5.65685i | − 0.214886i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.0000 | −0.455186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.9706i | 0.641886i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.0833i | 1.81608i | 0.418884 | + | 0.908040i | \(0.362421\pi\) | ||||
−0.418884 | + | 0.908040i | \(0.637579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3137i | 0.425496i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.48528i | 0.318671i | 0.987224 | + | 0.159336i | \(0.0509352\pi\) | ||||
−0.987224 | + | 0.159336i | \(0.949065\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.0000 | −1.19841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 11.3137i | − 0.423109i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.3137i | 0.422518i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.0000 | 1.78761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 16.9706i | − 0.631142i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 25.4558i | − 0.945406i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.0000 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0000 | −1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 16.9706i | − 0.627679i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.7990i | 0.731292i | 0.930754 | + | 0.365646i | \(0.119152\pi\) | ||||
−0.930754 | + | 0.365646i | \(0.880848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.0000 | 1.32788 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00000 | 0.221013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 24.0416i | − 0.884386i | −0.896920 | − | 0.442193i | \(-0.854201\pi\) | ||||
0.896920 | − | 0.442193i | \(-0.145799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.2843i | 1.03905i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.00000 | −0.146746 | −0.0733729 | − | 0.997305i | \(-0.523376\pi\) | ||||
−0.0733729 | + | 0.997305i | \(0.523376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.00000 | −0.293097 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.89949i | 0.362204i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 39.5980i | 1.44688i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.00000 | 0.218652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 11.3137i | − 0.411748i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.4558i | 0.925208i | 0.886565 | + | 0.462604i | \(0.153085\pi\) | ||||
−0.886565 | + | 0.462604i | \(0.846915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | −0.652499 | −0.326250 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 56.5685i | 2.04792i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 11.3137i | − 0.409048i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0000 | 1.58668 | 0.793340 | − | 0.608778i | \(-0.208340\pi\) | ||||
0.793340 | + | 0.608778i | \(0.208340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.82843i | 0.101863i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.48528i | 0.305194i | 0.988288 | + | 0.152597i | \(0.0487637\pi\) | ||||
−0.988288 | + | 0.152597i | \(0.951236\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.0000 | −0.862105 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.0000 | 0.573997 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 14.1421i | − 0.506695i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.65685i | 0.202418i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 48.0000 | 1.71538 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.0000 | 0.856597 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 46.6690i | − 1.66357i | −0.555097 | − | 0.831786i | \(-0.687319\pi\) | ||||
0.555097 | − | 0.831786i | \(-0.312681\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 39.5980i | 1.40973i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −56.0000 | −1.99113 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | 0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 11.3137i | − 0.401256i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 19.7990i | − 0.701316i | −0.936504 | − | 0.350658i | \(-0.885958\pi\) | ||||
0.936504 | − | 0.350658i | \(-0.114042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0000 | −0.423999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.65685i | 0.199626i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.2548i | 1.59502i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.0000 | 0.985647 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.0416i | 0.844216i | 0.906546 | + | 0.422108i | \(0.138710\pi\) | ||||
−0.906546 | + | 0.422108i | \(0.861290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 45.2548i | − 1.58716i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.0000 | −0.980797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.0000 | −1.04957 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 11.3137i | − 0.395333i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.48528i | 0.296138i | 0.988977 | + | 0.148069i | \(0.0473058\pi\) | ||||
−0.988977 | + | 0.148069i | \(0.952694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | 0.139431 | 0.0697156 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697156 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 21.2132i | − 0.737655i | −0.929498 | − | 0.368828i | \(-0.879759\pi\) | ||||
0.929498 | − | 0.368828i | \(-0.120241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.4558i | 0.884118i | 0.896986 | + | 0.442059i | \(0.145752\pi\) | ||||
−0.896986 | + | 0.442059i | \(0.854248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0000 | 0.416275 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.0000 | −1.24733 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.9411i | 1.17458i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 45.2548i | − 1.56424i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0000 | −0.690477 | −0.345238 | − | 0.938515i | \(-0.612202\pi\) | ||||
−0.345238 | + | 0.938515i | \(0.612202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.0000 | −1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 28.2843i | − 0.974162i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.1421i | 0.486504i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.0000 | −1.23697 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.0000 | 1.16688 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3137i | 0.387829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.4264i | 1.45265i | 0.687350 | + | 0.726326i | \(0.258774\pi\) | ||||
−0.687350 | + | 0.726326i | \(0.741226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.0000 | −0.683986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.0000 | 1.16142 | 0.580709 | − | 0.814111i | \(-0.302775\pi\) | ||||
0.580709 | + | 0.814111i | \(0.302775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1838i | 1.30281i | 0.758729 | + | 0.651407i | \(0.225821\pi\) | ||||
−0.758729 | + | 0.651407i | \(0.774179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 11.3137i | − 0.385570i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.0000 | −1.36004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.41421i | 0.0480292i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 11.3137i | − 0.383791i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | 0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00000 | −0.135379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 22.6274i | − 0.764946i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.48528i | 0.286528i | 0.989685 | + | 0.143264i | \(0.0457597\pi\) | ||||
−0.989685 | + | 0.143264i | \(0.954240\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.0000 | −0.404750 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.0000 | −1.14549 | −0.572745 | − | 0.819734i | \(-0.694121\pi\) | ||||
−0.572745 | + | 0.819734i | \(0.694121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.0122i | 1.38017i | 0.723728 | + | 0.690085i | \(0.242427\pi\) | ||||
−0.723728 | + | 0.690085i | \(0.757573\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.9706i | 0.570459i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.0000 | −0.940148 | −0.470074 | − | 0.882627i | \(-0.655773\pi\) | ||||
−0.470074 | + | 0.882627i | \(0.655773\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0000 | −1.07325 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 7.07107i | − 0.236890i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.00000 | 0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 67.8823i | 2.26400i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3137i | 0.376914i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0000 | −0.798670 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.0000 | 0.797787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7.07107i | − 0.234791i | −0.993085 | − | 0.117395i | \(-0.962545\pi\) | ||||
0.993085 | − | 0.117395i | \(-0.0374545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2.82843i | − 0.0938130i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.0000 | −0.463332 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 33.9411i | − 1.12206i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 28.2843i | − 0.934029i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.0000 | 1.45143 | 0.725713 | − | 0.687998i | \(-0.241510\pi\) | ||||
0.725713 | + | 0.687998i | \(0.241510\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | 0.329511 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.3137i | 0.372395i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.48528i | 0.278994i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.0000 | −0.394132 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 60.0000 | 1.96854 | 0.984268 | − | 0.176682i | \(-0.0565363\pi\) | ||||
0.984268 | + | 0.176682i | \(0.0565363\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 63.6396i | 2.08570i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 28.2843i | − 0.925985i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.0000 | 0.523256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.0000 | 0.653372 | 0.326686 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326686 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 19.7990i | − 0.646116i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 36.7696i | − 1.19865i | −0.800505 | − | 0.599327i | \(-0.795435\pi\) | ||||
0.800505 | − | 0.599327i | \(-0.204565\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000 | 0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −64.0000 | −2.08192 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 60.8112i | − 1.97610i | −0.154140 | − | 0.988049i | \(-0.549261\pi\) | ||||
0.154140 | − | 0.988049i | \(-0.450739\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.3137i | 0.367259i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.00000 | −0.129709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.0000 | −0.971795 | −0.485898 | − | 0.874016i | \(-0.661507\pi\) | ||||
−0.485898 | + | 0.874016i | \(0.661507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.6274i | 0.732206i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.9706i | 0.548580i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −72.0000 | −2.32500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 9.89949i | − 0.319007i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 11.3137i | − 0.364201i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.0000 | −0.643157 | −0.321578 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321578 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.0000 | −1.28499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.5563i | 0.499227i | 0.968346 | + | 0.249614i | \(0.0803036\pi\) | ||||
−0.968346 | + | 0.249614i | \(0.919696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 16.9706i | − 0.544051i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0000 | −0.384308 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0000 | 0.383914 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 16.9706i | − 0.542382i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 14.1421i | − 0.451524i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.0000 | −1.27451 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 16.9706i | − 0.539633i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.0000 | 0.571213 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 11.3137i | − 0.358669i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 14.1421i | − 0.447886i | −0.974602 | − | 0.223943i | \(-0.928107\pi\) | ||||
0.974602 | − | 0.223943i | \(-0.0718929\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.0000 | −0.506218 |
(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 | 512.2.b.a.257.1 | 2 | ||
3.2 | odd | 2 | 4608.2.d.a.2305.1 | 2 | |||
4.3 | odd | 2 | 512.2.b.b.257.2 | 2 | |||
8.3 | odd | 2 | 512.2.b.b.257.1 | 2 | |||
8.5 | even | 2 | inner | 512.2.b.a.257.2 | 2 | ||
12.11 | even | 2 | 4608.2.d.b.2305.1 | 2 | |||
16.3 | odd | 4 | 512.2.a.c.1.1 | ✓ | 2 | ||
16.5 | even | 4 | 512.2.a.d.1.1 | yes | 2 | ||
16.11 | odd | 4 | 512.2.a.c.1.2 | yes | 2 | ||
16.13 | even | 4 | 512.2.a.d.1.2 | yes | 2 | ||
24.5 | odd | 2 | 4608.2.d.a.2305.2 | 2 | |||
24.11 | even | 2 | 4608.2.d.b.2305.2 | 2 | |||
32.3 | odd | 8 | 1024.2.e.b.769.1 | 2 | |||
32.5 | even | 8 | 1024.2.e.d.257.1 | 2 | |||
32.11 | odd | 8 | 1024.2.e.e.257.1 | 2 | |||
32.13 | even | 8 | 1024.2.e.c.769.1 | 2 | |||
32.19 | odd | 8 | 1024.2.e.e.769.1 | 2 | |||
32.21 | even | 8 | 1024.2.e.c.257.1 | 2 | |||
32.27 | odd | 8 | 1024.2.e.b.257.1 | 2 | |||
32.29 | even | 8 | 1024.2.e.d.769.1 | 2 | |||
48.5 | odd | 4 | 4608.2.a.m.1.2 | 2 | |||
48.11 | even | 4 | 4608.2.a.f.1.2 | 2 | |||
48.29 | odd | 4 | 4608.2.a.m.1.1 | 2 | |||
48.35 | even | 4 | 4608.2.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.2.a.c.1.1 | ✓ | 2 | 16.3 | odd | 4 | ||
512.2.a.c.1.2 | yes | 2 | 16.11 | odd | 4 | ||
512.2.a.d.1.1 | yes | 2 | 16.5 | even | 4 | ||
512.2.a.d.1.2 | yes | 2 | 16.13 | even | 4 | ||
512.2.b.a.257.1 | 2 | 1.1 | even | 1 | trivial | ||
512.2.b.a.257.2 | 2 | 8.5 | even | 2 | inner | ||
512.2.b.b.257.1 | 2 | 8.3 | odd | 2 | |||
512.2.b.b.257.2 | 2 | 4.3 | odd | 2 | |||
1024.2.e.b.257.1 | 2 | 32.27 | odd | 8 | |||
1024.2.e.b.769.1 | 2 | 32.3 | odd | 8 | |||
1024.2.e.c.257.1 | 2 | 32.21 | even | 8 | |||
1024.2.e.c.769.1 | 2 | 32.13 | even | 8 | |||
1024.2.e.d.257.1 | 2 | 32.5 | even | 8 | |||
1024.2.e.d.769.1 | 2 | 32.29 | even | 8 | |||
1024.2.e.e.257.1 | 2 | 32.11 | odd | 8 | |||
1024.2.e.e.769.1 | 2 | 32.19 | odd | 8 | |||
4608.2.a.f.1.1 | 2 | 48.35 | even | 4 | |||
4608.2.a.f.1.2 | 2 | 48.11 | even | 4 | |||
4608.2.a.m.1.1 | 2 | 48.29 | odd | 4 | |||
4608.2.a.m.1.2 | 2 | 48.5 | odd | 4 | |||
4608.2.d.a.2305.1 | 2 | 3.2 | odd | 2 | |||
4608.2.d.a.2305.2 | 2 | 24.5 | odd | 2 | |||
4608.2.d.b.2305.1 | 2 | 12.11 | even | 2 | |||
4608.2.d.b.2305.2 | 2 | 24.11 | even | 2 |