Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2112,2,Mod(1057,2112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2112.1057");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2112 = 2^{6} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2112.f (of order \(2\), degree \(1\), 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: | \(16.8644049069\) |
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: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1057.6 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2112.1057 |
Dual form | 2112.2.f.g.1057.3 |
$q$-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 \(\left(\mathbb{Z}/2112\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(1409\) | \(1729\) | \(2047\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | − 2.82843i | − 1.26491i | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
0.774597 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.00000i | − 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.29253i | 1.74523i | 0.488406 | + | 0.872617i | \(0.337579\pi\) | ||||
−0.488406 | + | 0.872617i | \(0.662421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843 | 0.730297 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.89898 | −1.67325 | −0.836624 | − | 0.547777i | \(-0.815474\pi\) | ||||
−0.836624 | + | 0.547777i | \(0.815474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.89898i | − 1.12390i | −0.827170 | − | 0.561951i | \(-0.810051\pi\) | ||||
0.827170 | − | 0.561951i | \(-0.189949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.29253 | −1.31208 | −0.656041 | − | 0.754725i | \(-0.727770\pi\) | ||||
−0.656041 | + | 0.754725i | \(0.727770\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.635674i | 0.118042i | 0.998257 | + | 0.0590209i | \(0.0187979\pi\) | ||||
−0.998257 | + | 0.0590209i | \(0.981202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.12096 | 1.63817 | 0.819086 | − | 0.573671i | \(-0.194481\pi\) | ||||
0.819086 | + | 0.573671i | \(0.194481\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.92820i | 1.13899i | 0.821995 | + | 0.569495i | \(0.192861\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.29253 | −1.00761 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8990 | −1.70213 | −0.851067 | − | 0.525057i | \(-0.824044\pi\) | ||||
−0.851067 | + | 0.525057i | \(0.824044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.89898i | − 1.35708i | −0.734563 | − | 0.678541i | \(-0.762613\pi\) | ||||
0.734563 | − | 0.678541i | \(-0.237387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843i | 0.421637i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.635674 | −0.0927227 | −0.0463613 | − | 0.998925i | \(-0.514763\pi\) | ||||
−0.0463613 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 6.89898i | − 0.966050i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.75663i | 1.34018i | 0.742282 | + | 0.670088i | \(0.233744\pi\) | ||||
−0.742282 | + | 0.670088i | \(0.766256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82843 | −0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.89898 | 0.648886 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.79796i | 0.754830i | 0.926044 | + | 0.377415i | \(0.123187\pi\) | ||||
−0.926044 | + | 0.377415i | \(0.876813\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.02118i | − 0.642896i | −0.946927 | − | 0.321448i | \(-0.895830\pi\) | ||||
0.946927 | − | 0.321448i | \(-0.104170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.7980 | 2.20757 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.7980i | 1.68569i | 0.538157 | + | 0.842844i | \(0.319121\pi\) | ||||
−0.538157 | + | 0.842844i | \(0.680879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.29253i | − 0.757531i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9494 | −1.41813 | −0.709065 | − | 0.705143i | \(-0.750883\pi\) | ||||
−0.709065 | + | 0.705143i | \(0.750883\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.79796 | 0.912682 | 0.456341 | − | 0.889805i | \(-0.349160\pi\) | ||||
0.456341 | + | 0.889805i | \(0.349160\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3.00000i | − 0.346410i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.92820 | −0.779484 | −0.389742 | − | 0.920924i | \(-0.627436\pi\) | ||||
−0.389742 | + | 0.920924i | \(0.627436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.79796i | 1.07547i | 0.843115 | + | 0.537733i | \(0.180719\pi\) | ||||
−0.843115 | + | 0.537733i | \(0.819281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.5133i | 2.11651i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.635674 | −0.0681515 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.7980 | −1.67458 | −0.837290 | − | 0.546759i | \(-0.815861\pi\) | ||||
−0.837290 | + | 0.546759i | \(0.815861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.12096i | 0.945799i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.8564 | −1.42164 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000i | 0.100504i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.02118i | 0.499626i | 0.968294 | + | 0.249813i | \(0.0803692\pi\) | ||||
−0.968294 | + | 0.249813i | \(0.919631\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.12096 | −0.898714 | −0.449357 | − | 0.893352i | \(-0.648347\pi\) | ||||
−0.449357 | + | 0.893352i | \(0.648347\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.00000i | − 0.773389i | −0.922208 | − | 0.386695i | \(-0.873617\pi\) | ||||
0.922208 | − | 0.386695i | \(-0.126383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9494i | 1.14454i | 0.820064 | + | 0.572272i | \(0.193938\pi\) | ||||
−0.820064 | + | 0.572272i | \(0.806062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.92820 | −0.657596 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.7980i | 1.65967i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 6.29253i | − 0.581744i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 10.8990i | − 0.982728i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 5.65685i | − 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.89898 | 0.783511 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 13.7980i | − 1.20553i | −0.797918 | − | 0.602767i | \(-0.794065\pi\) | ||||
0.797918 | − | 0.602767i | \(-0.205935\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.82843 | −0.243432 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 16.8990i | − 1.43335i | −0.697406 | − | 0.716676i | \(-0.745662\pi\) | ||||
0.697406 | − | 0.716676i | \(-0.254338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 0.635674i | − 0.0535334i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.29253 | 0.526208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.79796 | 0.149312 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 7.00000i | − 0.577350i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 0.635674i | − 0.0520765i | −0.999661 | − | 0.0260382i | \(-0.991711\pi\) | ||||
0.999661 | − | 0.0260382i | \(-0.00828917\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.92820 | 0.563809 | 0.281905 | − | 0.959442i | \(-0.409034\pi\) | ||||
0.281905 | + | 0.959442i | \(0.409034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.89898 | 0.557749 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 25.7980i | − 2.07214i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.65685i | − 0.451466i | −0.974189 | − | 0.225733i | \(-0.927522\pi\) | ||||
0.974189 | − | 0.225733i | \(-0.0724777\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.75663 | −0.773751 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.20204i | 0.172477i | 0.996275 | + | 0.0862386i | \(0.0274847\pi\) | ||||
−0.996275 | + | 0.0862386i | \(0.972515\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 2.82843i | − 0.220193i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.0424 | 0.777101 | 0.388551 | − | 0.921427i | \(-0.372976\pi\) | ||||
0.388551 | + | 0.921427i | \(0.372976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26.5959 | −2.04584 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.89898i | 0.374634i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.90702i | 0.144988i | 0.997369 | + | 0.0724942i | \(0.0230959\pi\) | ||||
−0.997369 | + | 0.0724942i | \(0.976904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.79796 | −0.435801 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000i | 0.298974i | 0.988764 | + | 0.149487i | \(0.0477622\pi\) | ||||
−0.988764 | + | 0.149487i | \(0.952238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 10.0424i | − 0.746443i | −0.927742 | − | 0.373221i | \(-0.878253\pi\) | ||||
0.927742 | − | 0.373221i | \(-0.121747\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.02118 | 0.371176 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.5959 | 1.44072 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.89898i | 0.504503i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8776 | −1.36593 | −0.682967 | − | 0.730449i | \(-0.739311\pi\) | ||||
−0.682967 | + | 0.730449i | \(0.739311\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5959 | −1.55451 | −0.777254 | − | 0.629187i | \(-0.783388\pi\) | ||||
−0.777254 | + | 0.629187i | \(0.783388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.7980i | 1.27454i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 20.1489i | − 1.43555i | −0.696274 | − | 0.717776i | \(-0.745160\pi\) | ||||
0.696274 | − | 0.717776i | \(-0.254840\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.46410 | −0.245564 | −0.122782 | − | 0.992434i | \(-0.539182\pi\) | ||||
−0.122782 | + | 0.992434i | \(0.539182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.7980 | −0.973233 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.8270i | 2.15305i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.29253 | 0.437361 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.89898 | −0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 14.6969i | − 1.01178i | −0.862598 | − | 0.505889i | \(-0.831164\pi\) | ||||
0.862598 | − | 0.505889i | \(-0.168836\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 11.9494i | − 0.818758i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.1701 | −1.71659 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.79796i | 0.526937i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 43.4120i | − 2.92021i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.2487 | 1.62381 | 0.811907 | − | 0.583787i | \(-0.198430\pi\) | ||||
0.811907 | + | 0.583787i | \(0.198430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.79796i | − 0.384824i | −0.981314 | − | 0.192412i | \(-0.938369\pi\) | ||||
0.981314 | − | 0.192412i | \(-0.0616310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.4415i | 1.74730i | 0.486554 | + | 0.873651i | \(0.338254\pi\) | ||||
−0.486554 | + | 0.873651i | \(0.661746\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8990 | 0.714016 | 0.357008 | − | 0.934101i | \(-0.383797\pi\) | ||||
0.357008 | + | 0.934101i | \(0.383797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.79796i | 0.117286i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 6.92820i | − 0.450035i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.27135 | −0.0822367 | −0.0411184 | − | 0.999154i | \(-0.513092\pi\) | ||||
−0.0411184 | + | 0.999154i | \(0.513092\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7980 | −0.759973 | −0.379987 | − | 0.924992i | \(-0.624071\pi\) | ||||
−0.379987 | + | 0.924992i | \(0.624071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.7990i | 1.26491i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.8270 | 1.96147 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.79796 | −0.620920 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.20204i | 0.138992i | 0.997582 | + | 0.0694958i | \(0.0221390\pi\) | ||||
−0.997582 | + | 0.0694958i | \(0.977861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.29253i | 0.395608i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.5133 | −1.22197 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.20204 | 0.262116 | 0.131058 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131058 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 0.635674i | − 0.0393473i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.3137 | 0.697633 | 0.348817 | − | 0.937191i | \(-0.386584\pi\) | ||||
0.348817 | + | 0.937191i | \(0.386584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.5959 | 1.69520 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 15.7980i | − 0.966819i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.7272i | 1.62959i | 0.579752 | + | 0.814793i | \(0.303149\pi\) | ||||
−0.579752 | + | 0.814793i | \(0.696851\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.92820 | 0.420858 | 0.210429 | − | 0.977609i | \(-0.432514\pi\) | ||||
0.210429 | + | 0.977609i | \(0.432514\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000i | 0.180907i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 10.6780i | − 0.641581i | −0.947150 | − | 0.320790i | \(-0.896051\pi\) | ||||
0.947150 | − | 0.320790i | \(-0.103949\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.12096 | −0.546057 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.8990 | 0.650179 | 0.325089 | − | 0.945683i | \(-0.394606\pi\) | ||||
0.325089 | + | 0.945683i | \(0.394606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.8990i | 1.24232i | 0.783686 | + | 0.621158i | \(0.213337\pi\) | ||||
−0.783686 | + | 0.621158i | \(0.786663\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 13.8564i | − 0.820783i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.5959 | 1.79976 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 6.00000i | − 0.351726i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.6062i | 1.02857i | 0.857620 | + | 0.514284i | \(0.171942\pi\) | ||||
−0.857620 | + | 0.514284i | \(0.828058\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.3991 | 0.954793 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 39.5959i | − 2.28989i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.02118 | −0.288459 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.2020 | −0.813207 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.69694i | − 0.153922i | −0.997034 | − | 0.0769612i | \(-0.975478\pi\) | ||||
0.997034 | − | 0.0769612i | \(-0.0245218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 9.12096i | − 0.518873i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.635674 | 0.0360458 | 0.0180229 | − | 0.999838i | \(-0.494263\pi\) | ||||
0.0180229 | + | 0.999838i | \(0.494263\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.5959 | −1.22067 | −0.610337 | − | 0.792142i | \(-0.708966\pi\) | ||||
−0.610337 | + | 0.792142i | \(0.708966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.82843i | − 0.158860i | −0.996840 | − | 0.0794301i | \(-0.974690\pi\) | ||||
0.996840 | − | 0.0794301i | \(-0.0253101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.635674 | 0.0355909 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.00000 | 0.446516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.7980i | 1.88057i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 18.8776i | − 1.04714i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.9494 | −0.660802 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.3939i | 1.39577i | 0.716208 | + | 0.697887i | \(0.245876\pi\) | ||||
−0.716208 | + | 0.697887i | \(0.754124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.92820i | − 0.379663i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 39.0265 | 2.13225 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.2020 | −0.664688 | −0.332344 | − | 0.943158i | \(-0.607839\pi\) | ||||
−0.332344 | + | 0.943158i | \(0.607839\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000i | 0.325875i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 9.12096i | − 0.493927i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.7980 | −0.958210 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6.20204i | − 0.332943i | −0.986046 | − | 0.166472i | \(-0.946763\pi\) | ||||
0.986046 | − | 0.166472i | \(-0.0532374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 9.40669i | − 0.503528i | −0.967789 | − | 0.251764i | \(-0.918989\pi\) | ||||
0.967789 | − | 0.251764i | \(-0.0810107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.29253 | 0.335870 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.7980i | 1.79381i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.00000i | − 0.0524864i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 22.0560i | − 1.15446i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.1633 | −1.00032 | −0.500158 | − | 0.865934i | \(-0.666725\pi\) | ||||
−0.500158 | + | 0.865934i | \(0.666725\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.8990 | 0.567378 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 27.0771i | − 1.40200i | −0.713161 | − | 0.701001i | \(-0.752737\pi\) | ||||
0.713161 | − | 0.701001i | \(-0.247263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 33.3939i | − 1.71533i | −0.514210 | − | 0.857664i | \(-0.671915\pi\) | ||||
0.514210 | − | 0.857664i | \(-0.328085\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.7634 | 0.805474 | 0.402737 | − | 0.915316i | \(-0.368059\pi\) | ||||
0.402737 | + | 0.915316i | \(0.368059\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.89898i | 0.452361i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.82843i | − 0.143407i | −0.997426 | − | 0.0717035i | \(-0.977156\pi\) | ||||
0.997426 | − | 0.0717035i | \(-0.0228435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.4120 | 2.19544 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.7980 | 0.696015 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.5959i | 0.985978i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.9706i | 0.851728i | 0.904787 | + | 0.425864i | \(0.140030\pi\) | ||||
−0.904787 | + | 0.425864i | \(0.859970\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7980 | 1.18841 | 0.594207 | − | 0.804312i | \(-0.297466\pi\) | ||||
0.594207 | + | 0.804312i | \(0.297466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 57.3939i | 2.85899i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2.82843i | − 0.140546i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.92820 | 0.343418 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.7980 | 1.37452 | 0.687260 | − | 0.726411i | \(-0.258813\pi\) | ||||
0.687260 | + | 0.726411i | \(0.258813\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.00000i | − 0.0986527i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.7128 | 1.36037 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.8990 | 0.827547 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.20204i | 0.107577i | 0.998552 | + | 0.0537884i | \(0.0171296\pi\) | ||||
−0.998552 | + | 0.0537884i | \(0.982870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 2.54270i | − 0.123924i | −0.998079 | − | 0.0619618i | \(-0.980264\pi\) | ||||
0.998079 | − | 0.0619618i | \(-0.0197357\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.635674 | 0.0309076 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.6969 | 1.00395 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.29253i | 0.303806i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.27135 | 0.0612387 | 0.0306194 | − | 0.999531i | \(-0.490252\pi\) | ||||
0.0306194 | + | 0.999531i | \(0.490252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.79796i | 0.0862055i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.8270i | 1.47465i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8564 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.00000 | 0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.00000i | 0.190046i | 0.995475 | + | 0.0950229i | \(0.0302924\pi\) | ||||
−0.995475 | + | 0.0950229i | \(0.969708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.6834i | 2.11820i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.635674 | 0.0300664 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.79796 | −0.368008 | −0.184004 | − | 0.982925i | \(-0.558906\pi\) | ||||
−0.184004 | + | 0.982925i | \(0.558906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8990i | 0.513213i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.92820i | 0.325515i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.20204 | 0.383675 | 0.191838 | − | 0.981427i | \(-0.438555\pi\) | ||||
0.191838 | + | 0.981427i | \(0.438555\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.89898i | 0.322017i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 35.2767i | − 1.64300i | −0.570209 | − | 0.821500i | \(-0.693138\pi\) | ||||
0.570209 | − | 0.821500i | \(-0.306862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8202 | −1.15349 | −0.576746 | − | 0.816924i | \(-0.695678\pi\) | ||||
−0.576746 | + | 0.816924i | \(0.695678\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.7980 | 1.19635 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000i | 0.555294i | 0.960683 | + | 0.277647i | \(0.0895545\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.65685 | 0.260654 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.89898 | −0.409176 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.6969i | 0.674342i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 9.75663i | − 0.446725i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.4415 | −1.20814 | −0.604071 | − | 0.796931i | \(-0.706456\pi\) | ||||
−0.604071 | + | 0.796931i | \(0.706456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.5959 | −1.98780 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.9706i | 0.770594i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3205 | 0.784867 | 0.392434 | − | 0.919780i | \(-0.371633\pi\) | ||||
0.392434 | + | 0.919780i | \(0.371633\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.20204 | −0.0995797 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 24.0000i | − 1.08310i | −0.840667 | − | 0.541552i | \(-0.817837\pi\) | ||||
0.840667 | − | 0.541552i | \(-0.182163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.38551i | − 0.197513i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.82843 | 0.127128 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000i | 0.179065i | 0.995984 | + | 0.0895323i | \(0.0285372\pi\) | ||||
−0.995984 | + | 0.0895323i | \(0.971463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.0424i | 0.448660i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.7128 | 1.23565 | 0.617827 | − | 0.786314i | \(-0.288013\pi\) | ||||
0.617827 | + | 0.786314i | \(0.288013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.2020 | 0.631983 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 26.5959i | − 1.18117i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 32.3840i | − 1.43540i | −0.696354 | − | 0.717699i | \(-0.745195\pi\) | ||||
0.696354 | − | 0.717699i | \(-0.254805\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.89898 | −0.216295 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.7980i | 1.13679i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.635674i | 0.0279569i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.90702 | −0.0837090 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.7980 | 0.867364 | 0.433682 | − | 0.901066i | \(-0.357214\pi\) | ||||
0.433682 | + | 0.901066i | \(0.357214\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 20.4949i | − 0.896179i | −0.893989 | − | 0.448090i | \(-0.852105\pi\) | ||||
0.893989 | − | 0.448090i | \(-0.147895\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −62.9253 | −2.74107 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.5959 | 0.721562 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.79796i | − 0.251610i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 68.5821i | − 2.97062i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.6274 | −0.978269 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.00000 | −0.172613 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.00000i | 0.301511i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.7204i | 0.890839i | 0.895322 | + | 0.445420i | \(0.146946\pi\) | ||||
−0.895322 | + | 0.445420i | \(0.853054\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0424 | 0.430959 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.7980 | 1.44775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.30306i | 0.0557149i | 0.999612 | + | 0.0278574i | \(0.00886845\pi\) | ||||
−0.999612 | + | 0.0278574i | \(0.991132\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.02118i | 0.214299i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.11416 | 0.132668 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.5959i | 0.831800i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 2.47848i | − 0.105017i | −0.998620 | − | 0.0525083i | \(-0.983278\pi\) | ||||
0.998620 | − | 0.0525083i | \(-0.0167216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.9971 | 2.36842 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.89898 | −0.291275 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000i | 0.505740i | 0.967500 | + | 0.252870i | \(0.0813744\pi\) | ||||
−0.967500 | + | 0.252870i | \(0.918626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 16.9706i | − 0.713957i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.6969 | −0.867661 | −0.433830 | − | 0.900995i | \(-0.642838\pi\) | ||||
−0.433830 | + | 0.900995i | \(0.642838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 18.6969i | − 0.782443i | −0.920297 | − | 0.391221i | \(-0.872053\pi\) | ||||
0.920297 | − | 0.391221i | \(-0.127947\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 18.8776i | − 0.788622i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.8776 | 0.787250 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 21.5959i | − 0.897496i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.75663 | 0.404078 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.7980 | −0.735855 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 21.7980i | − 0.899698i | −0.893105 | − | 0.449849i | \(-0.851478\pi\) | ||||
0.893105 | − | 0.449849i | \(-0.148522\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 44.6834i | − 1.84115i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.1489 | 0.828816 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.1010 | 0.537994 | 0.268997 | − | 0.963141i | \(-0.413308\pi\) | ||||
0.268997 | + | 0.963141i | \(0.413308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.46410i | − 0.141776i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.74983 | −0.153214 | −0.0766070 | − | 0.997061i | \(-0.524409\pi\) | ||||
−0.0766070 | + | 0.997061i | \(0.524409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 13.7980i | − 0.561896i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.82843i | 0.114992i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.77101 | 0.356004 | 0.178002 | − | 0.984030i | \(-0.443037\pi\) | ||||
0.178002 | + | 0.984030i | \(0.443037\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 4.00000i | − 0.161823i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.1913i | 1.21941i | 0.792627 | + | 0.609707i | \(0.208713\pi\) | ||||
−0.792627 | + | 0.609707i | \(0.791287\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −30.8270 | −1.24306 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.1918 | −1.49729 | −0.748643 | − | 0.662973i | \(-0.769294\pi\) | ||||
−0.748643 | + | 0.662973i | \(0.769294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 20.0000i | − 0.803868i | −0.915669 | − | 0.401934i | \(-0.868338\pi\) | ||||
0.915669 | − | 0.401934i | \(-0.131662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.29253i | 0.252510i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.89898i | − 0.195646i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 47.7975i | − 1.90581i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.1339 | 1.43847 | 0.719233 | − | 0.694768i | \(-0.244493\pi\) | ||||
0.719233 | + | 0.694768i | \(0.244493\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.6969 | 0.584151 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 44.0477i | − 1.74523i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.9494 | 0.472710 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.59592 | −0.221025 | −0.110513 | − | 0.993875i | \(-0.535249\pi\) | ||||
−0.110513 | + | 0.993875i | \(0.535249\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 23.5959i | − 0.930532i | −0.885171 | − | 0.465266i | \(-0.845959\pi\) | ||||
0.885171 | − | 0.465266i | \(-0.154041\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 25.1701i | − 0.991072i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.5904 | 1.83166 | 0.915829 | − | 0.401569i | \(-0.131535\pi\) | ||||
0.915829 | + | 0.401569i | \(0.131535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.79796 | 0.227590 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 6.64247i | − 0.259940i | −0.991518 | − | 0.129970i | \(-0.958512\pi\) | ||||
0.991518 | − | 0.129970i | \(-0.0414881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.0265 | −1.52489 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.79796 | −0.304227 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.3939i | 0.833387i | 0.909047 | + | 0.416694i | \(0.136811\pi\) | ||||
−0.909047 | + | 0.416694i | \(0.863189\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 10.7423i | − 0.417825i | −0.977934 | − | 0.208913i | \(-0.933008\pi\) | ||||
0.977934 | − | 0.208913i | \(-0.0669924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 43.4120 | 1.68598 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.00000i | − 0.154881i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.2487i | 0.937509i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.02118 | −0.193840 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.5959 | −1.14084 | −0.570419 | − | 0.821354i | \(-0.693219\pi\) | ||||
−0.570419 | + | 0.821354i | \(0.693219\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.00000i | 0.115470i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.74983i | 0.144118i | 0.997400 | + | 0.0720589i | \(0.0229569\pi\) | ||||
−0.997400 | + | 0.0720589i | \(0.977043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.79796 | 0.222178 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 37.7980i | − 1.44630i | −0.690692 | − | 0.723149i | \(-0.742694\pi\) | ||||
0.690692 | − | 0.723149i | \(-0.257306\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.65685i | 0.216137i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.4415 | −1.00880 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −61.3939 | −2.33892 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000i | 0.760836i | 0.924815 | + | 0.380418i | \(0.124220\pi\) | ||||
−0.924815 | + | 0.380418i | \(0.875780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −47.7975 | −1.81306 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 75.1918 | 2.84809 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8990i | 0.412237i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.2767i | 1.33238i | 0.745781 | + | 0.666191i | \(0.232076\pi\) | ||||
−0.745781 | + | 0.666191i | \(0.767924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.9411 | 1.28011 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.79796 | −0.0677151 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.81405i | 0.143240i | 0.997432 | + | 0.0716198i | \(0.0228168\pi\) | ||||
−0.997432 | + | 0.0716198i | \(0.977183\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.92820 | 0.259828 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −57.3939 | −2.14942 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 17.7980i | − 0.665606i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.27135i | − 0.0474794i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.2631 | 0.867567 | 0.433783 | − | 0.901017i | \(-0.357178\pi\) | ||||
0.433783 | + | 0.901017i | \(0.357178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 11.7980i | − 0.438771i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.90702i | − 0.0708251i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.84961 | −0.291126 | −0.145563 | − | 0.989349i | \(-0.546499\pi\) | ||||
−0.145563 | + | 0.989349i | \(0.546499\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 61.3939i | 2.27073i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 35.8481i | − 1.32408i | −0.749468 | − | 0.662041i | \(-0.769691\pi\) | ||||
0.749468 | − | 0.662041i | \(-0.230309\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.7990 | −0.730297 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.7980 | 0.508254 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 17.3031i | − 0.636503i | −0.948006 | − | 0.318252i | \(-0.896904\pi\) | ||||
0.948006 | − | 0.318252i | \(-0.103096\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.8270i | 1.13246i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.1278 | −0.554984 | −0.277492 | − | 0.960728i | \(-0.589503\pi\) | ||||
−0.277492 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.79796 | −0.0658721 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 9.79796i | − 0.358489i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.3629 | −0.998485 | −0.499243 | − | 0.866462i | \(-0.666388\pi\) | ||||
−0.499243 | + | 0.866462i | \(0.666388\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.20204 | −0.0802468 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 19.5959i | − 0.713168i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.0265i | 1.41844i | 0.704986 | + | 0.709222i | \(0.250953\pi\) | ||||
−0.704986 | + | 0.709222i | \(0.749047\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.29253 | −0.228404 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3031 | 0.699735 | 0.349868 | − | 0.936799i | \(-0.386227\pi\) | ||||
0.349868 | + | 0.936799i | \(0.386227\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 19.5133i | − 0.705503i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.4838 | −1.31735 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318079\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.20204i | 0.151333i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 10.3281i | − 0.371476i | −0.982599 | − | 0.185738i | \(-0.940533\pi\) | ||||
0.982599 | − | 0.185738i | \(-0.0594675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.3629 | −0.982903 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 53.3939i | 1.91303i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.9494i | 0.427583i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.635674 | 0.0227172 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0000 | −0.571064 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 46.2929i | − 1.65016i | −0.565014 | − | 0.825081i | \(-0.691129\pi\) | ||||
0.565014 | − | 0.825081i | \(-0.308871\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3137i | 0.402779i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.5959 | 1.12200 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.5959i | 0.978726i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.9131i | 0.811625i | 0.913956 | + | 0.405813i | \(0.133011\pi\) | ||||
−0.913956 | + | 0.405813i | \(0.866989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.38551 | 0.155148 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.7980 | 0.558193 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.79796i | − 0.275184i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.7272 | −0.940842 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.50510 | −0.193549 | −0.0967745 | − | 0.995306i | \(-0.530853\pi\) | ||||
−0.0967745 | + | 0.995306i | \(0.530853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.69694i | − 0.0947023i | −0.998878 | − | 0.0473512i | \(-0.984922\pi\) | ||||
0.998878 | − | 0.0473512i | \(-0.0150780\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.92820i | 0.242983i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.22831 | 0.218168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.5959 | −1.52523 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.74983i | − 0.130870i | −0.997857 | − | 0.0654350i | \(-0.979157\pi\) | ||||
0.997857 | − | 0.0654350i | \(-0.0208435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.921404 | −0.0321181 | −0.0160591 | − | 0.999871i | \(-0.505112\pi\) | ||||
−0.0160591 | + | 0.999871i | \(0.505112\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.00000 | −0.104447 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.1918i | 1.78011i | 0.455849 | + | 0.890057i | \(0.349336\pi\) | ||||
−0.455849 | + | 0.890057i | \(0.650664\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.7975i | 1.66008i | 0.557706 | + | 0.830038i | \(0.311682\pi\) | ||||
−0.557706 | + | 0.830038i | \(0.688318\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.6780 | 0.370417 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 48.2929 | 1.67325 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 28.4041i | − 0.982964i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 9.12096i | − 0.315266i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.0477 | −1.52070 | −0.760348 | − | 0.649516i | \(-0.774971\pi\) | ||||
−0.760348 | + | 0.649516i | \(0.774971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5959 | 0.986066 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.8990i | 0.375381i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 75.2246i | 2.58781i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.8990 | −0.717251 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 43.5959i | − 1.49445i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.9917i | 0.752983i | 0.926420 | + | 0.376491i | \(0.122870\pi\) | ||||
−0.926420 | + | 0.376491i | \(0.877130\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.8564 | 0.473879 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.89898 | 0.235665 | 0.117832 | − | 0.993034i | \(-0.462405\pi\) | ||||
0.117832 | + | 0.993034i | \(0.462405\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.20204i | − 0.0751327i | −0.999294 | − | 0.0375663i | \(-0.988039\pi\) | ||||
0.999294 | − | 0.0375663i | \(-0.0119606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.2049 | 1.43667 | 0.718336 | − | 0.695697i | \(-0.244904\pi\) | ||||
0.718336 | + | 0.695697i | \(0.244904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.39388 | 0.183397 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.5959i | 1.03909i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.92820i | 0.235023i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −86.8241 | −2.94192 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.00000 | 0.203069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 40.2337i | − 1.35859i | −0.733863 | − | 0.679297i | \(-0.762285\pi\) | ||||
0.733863 | − | 0.679297i | \(-0.237715\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.6062 | −0.593844 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.20204 | −0.141570 | −0.0707852 | − | 0.997492i | \(-0.522550\pi\) | ||||
−0.0707852 | + | 0.997492i | \(0.522550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.7980i | 1.00278i | 0.865221 | + | 0.501391i | \(0.167178\pi\) | ||||
−0.865221 | + | 0.501391i | \(0.832822\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.3991i | 0.551250i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.2979 | −1.35307 | −0.676535 | − | 0.736410i | \(-0.736519\pi\) | ||||
−0.676535 | + | 0.736410i | \(0.736519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.00000i | − 0.0335013i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.11416i | 0.104211i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3137 | 0.378176 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 39.5959 | 1.32207 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.79796i | 0.193373i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 67.3108i | − 2.24245i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.4041 | −0.944184 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.00000i | − 0.132818i | −0.997792 | − | 0.0664089i | \(-0.978846\pi\) | ||||
0.997792 | − | 0.0664089i | \(-0.0211542\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 5.02118i | − 0.166542i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.0477 | 1.45937 | 0.729683 | − | 0.683786i | \(-0.239668\pi\) | ||||
0.729683 | + | 0.683786i | \(0.239668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.79796 | 0.324265 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 14.2020i | − 0.469505i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.2555 | −0.998037 | −0.499019 | − | 0.866591i | \(-0.666306\pi\) | ||||
−0.499019 | + | 0.866591i | \(0.666306\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.69694 | 0.0888671 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 75.1918i | − 2.47497i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 20.7846i | − 0.683394i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.12096 | 0.299571 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.2929i | 1.12390i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.635674i | 0.0208110i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5133 | 0.638152 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.59592 | −0.182811 | −0.0914053 | − | 0.995814i | \(-0.529136\pi\) | ||||
−0.0914053 | + | 0.995814i | \(0.529136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 21.5959i | − 0.704756i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 17.6062i | − 0.573947i | −0.957939 | − | 0.286973i | \(-0.907351\pi\) | ||||
0.957939 | − | 0.286973i | \(-0.0926492\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 68.5821 | 2.23334 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.5959i | 1.02673i | 0.858171 | + | 0.513365i | \(0.171601\pi\) | ||||
−0.858171 | + | 0.513365i | \(0.828399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.0689i | 1.59284i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.82843 | 0.0917180 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.2929 | −1.04607 | −0.523034 | − | 0.852312i | \(-0.675200\pi\) | ||||
−0.523034 | + | 0.852312i | \(0.675200\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53.3939i | 1.72779i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.635674i | 0.0205484i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.1918 | 1.68361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.00000i | 0.257796i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 61.0825i | 1.96631i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.0265 | −1.25501 | −0.627504 | − | 0.778613i | \(-0.715923\pi\) | ||||
−0.627504 | + | 0.778613i | \(0.715923\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.7980 | −1.08575 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 31.5959i | − 1.01396i | −0.861957 | − | 0.506981i | \(-0.830762\pi\) | ||||
0.861957 | − | 0.506981i | \(-0.169238\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.8776 | 0.604567 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.79796 | 0.249479 | 0.124739 | − | 0.992190i | \(-0.460191\pi\) | ||||
0.124739 | + | 0.992190i | \(0.460191\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7980i | 0.504905i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 11.9494i | − 0.381514i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.3485 | 0.904176 | 0.452088 | − | 0.891973i | \(-0.350679\pi\) | ||||
0.452088 | + | 0.891973i | \(0.350679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −56.9898 | −1.81585 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.9971i | 1.78060i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.6184 | −1.83031 | −0.915154 | − | 0.403104i | \(-0.867931\pi\) | ||||
−0.915154 | + | 0.403104i | \(0.867931\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.3939 | −0.805850 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.79796i | 0.310616i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.0341i | 1.01453i | 0.861790 | + | 0.507265i | \(0.169344\pi\) | ||||
−0.861790 | + | 0.507265i | \(0.830656\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.92820 | 0.219199 |
(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 | 2112.2.f.g.1057.6 | yes | 8 | |
3.2 | odd | 2 | 6336.2.f.l.3169.8 | 8 | |||
4.3 | odd | 2 | inner | 2112.2.f.g.1057.2 | ✓ | 8 | |
8.3 | odd | 2 | inner | 2112.2.f.g.1057.7 | yes | 8 | |
8.5 | even | 2 | inner | 2112.2.f.g.1057.3 | yes | 8 | |
12.11 | even | 2 | 6336.2.f.l.3169.6 | 8 | |||
16.3 | odd | 4 | 8448.2.a.ct.1.1 | 4 | |||
16.5 | even | 4 | 8448.2.a.ct.1.4 | 4 | |||
16.11 | odd | 4 | 8448.2.a.cm.1.4 | 4 | |||
16.13 | even | 4 | 8448.2.a.cm.1.1 | 4 | |||
24.5 | odd | 2 | 6336.2.f.l.3169.1 | 8 | |||
24.11 | even | 2 | 6336.2.f.l.3169.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2112.2.f.g.1057.2 | ✓ | 8 | 4.3 | odd | 2 | inner | |
2112.2.f.g.1057.3 | yes | 8 | 8.5 | even | 2 | inner | |
2112.2.f.g.1057.6 | yes | 8 | 1.1 | even | 1 | trivial | |
2112.2.f.g.1057.7 | yes | 8 | 8.3 | odd | 2 | inner | |
6336.2.f.l.3169.1 | 8 | 24.5 | odd | 2 | |||
6336.2.f.l.3169.3 | 8 | 24.11 | even | 2 | |||
6336.2.f.l.3169.6 | 8 | 12.11 | even | 2 | |||
6336.2.f.l.3169.8 | 8 | 3.2 | odd | 2 | |||
8448.2.a.cm.1.1 | 4 | 16.13 | even | 4 | |||
8448.2.a.cm.1.4 | 4 | 16.11 | odd | 4 | |||
8448.2.a.ct.1.1 | 4 | 16.3 | odd | 4 | |||
8448.2.a.ct.1.4 | 4 | 16.5 | even | 4 |