Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6336,2,Mod(3169,6336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6336, 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("6336.3169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6336 = 2^{6} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6336.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: | \(50.5932147207\) |
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: | no (minimal twist has level 2112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3169.8 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6336.3169 |
Dual form | 6336.2.f.l.3169.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6336\mathbb{Z}\right)^\times\).
\(n\) | \(1729\) | \(3521\) | \(4159\) | \(4357\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.82843i | 1.26491i | 0.774597 | + | 0.632456i | \(0.217953\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.89898 | 1.67325 | 0.836624 | − | 0.547777i | \(-0.184526\pi\) | ||||
0.836624 | + | 0.547777i | \(0.184526\pi\) | |||||||
\(18\) | 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 | \(-0.272230\pi\) | ||||
0.656041 | + | 0.754725i | \(0.272230\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.635674i | − 0.118042i | −0.998257 | − | 0.0590209i | \(-0.981202\pi\) | ||||
0.998257 | − | 0.0590209i | \(-0.0187979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.12096 | 1.63817 | 0.819086 | − | 0.573671i | \(-0.194481\pi\) | ||||
0.819086 | + | 0.573671i | \(0.194481\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8990 | 1.70213 | 0.851067 | − | 0.525057i | \(-0.175956\pi\) | ||||
0.851067 | + | 0.525057i | \(0.175956\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.89898i | − 1.35708i | −0.734563 | − | 0.678541i | \(-0.762613\pi\) | ||||
0.734563 | − | 0.678541i | \(-0.237387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.635674 | 0.0927227 | 0.0463613 | − | 0.998925i | \(-0.485237\pi\) | ||||
0.0463613 | + | 0.998925i | \(0.485237\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.75663i | − 1.34018i | −0.742282 | − | 0.670088i | \(-0.766256\pi\) | ||||
0.742282 | − | 0.670088i | \(-0.233744\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82843 | −0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5.79796i | − 0.754830i | −0.926044 | − | 0.377415i | \(-0.876813\pi\) | ||||
0.926044 | − | 0.377415i | \(-0.123187\pi\) | |||||||
\(60\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9494 | 1.41813 | 0.709065 | − | 0.705143i | \(-0.249117\pi\) | ||||
0.709065 | + | 0.705143i | \(0.249117\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.79796 | 0.912682 | 0.456341 | − | 0.889805i | \(-0.349160\pi\) | ||||
0.456341 | + | 0.889805i | \(0.349160\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 9.79796i | − 1.07547i | −0.843115 | − | 0.537733i | \(-0.819281\pi\) | ||||
0.843115 | − | 0.537733i | \(-0.180719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.5133i | 2.11651i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7980 | 1.67458 | 0.837290 | − | 0.546759i | \(-0.184139\pi\) | ||||
0.837290 | + | 0.546759i | \(0.184139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 5.02118i | − 0.499626i | −0.968294 | − | 0.249813i | \(-0.919631\pi\) | ||||
0.968294 | − | 0.249813i | \(-0.0803692\pi\) | |||||||
\(102\) | 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 | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9494i | 1.14454i | 0.820064 | + | 0.572272i | \(0.193938\pi\) | ||||
−0.820064 | + | 0.572272i | \(0.806062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.7980i | 1.65967i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7980i | 1.20553i | 0.797918 | + | 0.602767i | \(0.205935\pi\) | ||||
−0.797918 | + | 0.602767i | \(0.794065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 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 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.29253 | −0.526208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.79796 | 0.149312 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.635674i | 0.0520765i | 0.999661 | + | 0.0260382i | \(0.00828917\pi\) | ||||
−0.999661 | + | 0.0260382i | \(0.991711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.92820 | 0.563809 | 0.281905 | − | 0.959442i | \(-0.409034\pi\) | ||||
0.281905 | + | 0.959442i | \(0.409034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.0424 | −0.777101 | −0.388551 | − | 0.921427i | \(-0.627024\pi\) | ||||
−0.388551 | + | 0.921427i | \(0.627024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26.5959 | −2.04584 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.90702i | − 0.144988i | −0.997369 | − | 0.0724942i | \(-0.976904\pi\) | ||||
0.997369 | − | 0.0724942i | \(-0.0230959\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4.00000i | − 0.298974i | −0.988764 | − | 0.149487i | \(-0.952238\pi\) | ||||
0.988764 | − | 0.149487i | \(-0.0477622\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 10.0424i | − 0.746443i | −0.927742 | − | 0.373221i | \(-0.878253\pi\) | ||||
0.927742 | − | 0.373221i | \(-0.121747\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | \(-0.260689\pi\) | ||||
0.682967 | + | 0.730449i | \(0.260689\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5959 | −1.55451 | −0.777254 | − | 0.629187i | \(-0.783388\pi\) | ||||
−0.777254 | + | 0.629187i | \(0.783388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.1489i | 1.43555i | 0.696274 | + | 0.717776i | \(0.254840\pi\) | ||||
−0.696274 | + | 0.717776i | \(0.745160\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.46410 | −0.245564 | −0.122782 | − | 0.992434i | \(-0.539182\pi\) | ||||
−0.122782 | + | 0.992434i | \(0.539182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.8270i | 2.15305i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.1701 | 1.71659 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.79796i | 0.384824i | 0.981314 | + | 0.192412i | \(0.0616310\pi\) | ||||
−0.981314 | + | 0.192412i | \(0.938369\pi\) | |||||||
\(228\) | 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 | \(-0.616203\pi\) | ||||
−0.357008 | + | 0.934101i | \(0.616203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.79796i | 0.117286i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.27135 | 0.0822367 | 0.0411184 | − | 0.999154i | \(-0.486908\pi\) | ||||
0.0411184 | + | 0.999154i | \(0.486908\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7980 | −0.759973 | −0.379987 | − | 0.924992i | \(-0.624071\pi\) | ||||
−0.379987 | + | 0.924992i | \(0.624071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 19.7990i | − 1.26491i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.8270 | 1.96147 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.20204i | − 0.138992i | −0.997582 | − | 0.0694958i | \(-0.977861\pi\) | ||||
0.997582 | − | 0.0694958i | \(-0.0221390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.29253i | 0.395608i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.20204 | −0.262116 | −0.131058 | − | 0.991375i | \(-0.541837\pi\) | ||||
−0.131058 | + | 0.991375i | \(0.541837\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.3137 | −0.697633 | −0.348817 | − | 0.937191i | \(-0.613416\pi\) | ||||
−0.348817 | + | 0.937191i | \(0.613416\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.5959 | 1.69520 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 26.7272i | − 1.62959i | −0.579752 | − | 0.814793i | \(-0.696851\pi\) | ||||
0.579752 | − | 0.814793i | \(-0.303149\pi\) | |||||||
\(270\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8990 | −0.650179 | −0.325089 | − | 0.945683i | \(-0.605394\pi\) | ||||
−0.325089 | + | 0.945683i | \(0.605394\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.8990i | 1.24232i | 0.783686 | + | 0.621158i | \(0.213337\pi\) | ||||
−0.783686 | + | 0.621158i | \(0.786663\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.5959 | 1.79976 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 17.6062i | − 1.02857i | −0.857620 | − | 0.514284i | \(-0.828058\pi\) | ||||
0.857620 | − | 0.514284i | \(-0.171942\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.3991 | 0.954793 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 39.5959i | 2.28989i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.635674 | −0.0360458 | −0.0180229 | − | 0.999838i | \(-0.505737\pi\) | ||||
−0.0180229 | + | 0.999838i | \(0.505737\pi\) | |||||||
\(312\) | 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 | \(0.0253101\pi\) | ||||
−0.996840 | + | 0.0794301i | \(0.974690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.635674 | 0.0355909 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 33.7980i | − 1.88057i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 18.8776i | − 1.04714i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.12096i | 0.493927i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.20204i | 0.332943i | 0.986046 | + | 0.166472i | \(0.0532374\pi\) | ||||
−0.986046 | + | 0.166472i | \(0.946763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 9.40669i | − 0.503528i | −0.967789 | − | 0.251764i | \(-0.918989\pi\) | ||||
0.967789 | − | 0.251764i | \(-0.0810107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 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 | \(-0.596505\pi\) | ||||
−0.298557 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | \(-0.631941\pi\) | ||||
−0.402737 | + | 0.915316i | \(0.631941\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.82843i | 0.143407i | 0.997426 | + | 0.0717035i | \(0.0228435\pi\) | ||||
−0.997426 | + | 0.0717035i | \(0.977156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.4120 | 2.19544 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | \(-0.702534\pi\) | ||||
−0.594207 | + | 0.804312i | \(0.702534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 57.3939i | 2.85899i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.7128 | 1.36037 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 2.20204i | − 0.107577i | −0.998552 | − | 0.0537884i | \(-0.982870\pi\) | ||||
0.998552 | − | 0.0537884i | \(-0.0171296\pi\) | |||||||
\(420\) | 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 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.6969 | −1.00395 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.27135 | −0.0612387 | −0.0306194 | − | 0.999531i | \(-0.509748\pi\) | ||||
−0.0306194 | + | 0.999531i | \(0.509748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4.00000i | − 0.190046i | −0.995475 | − | 0.0950229i | \(-0.969708\pi\) | ||||
0.995475 | − | 0.0950229i | \(-0.0302924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.6834i | 2.11820i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.79796 | 0.368008 | 0.184004 | − | 0.982925i | \(-0.441094\pi\) | ||||
0.184004 | + | 0.982925i | \(0.441094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8990i | 0.513213i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.2767i | 1.64300i | 0.570209 | + | 0.821500i | \(0.306862\pi\) | ||||
−0.570209 | + | 0.821500i | \(0.693138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8202 | −1.15349 | −0.576746 | − | 0.816924i | \(-0.695678\pi\) | ||||
−0.576746 | + | 0.816924i | \(0.695678\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 12.0000i | − 0.555294i | −0.960683 | − | 0.277647i | \(-0.910445\pi\) | ||||
0.960683 | − | 0.277647i | \(-0.0895545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.89898 | 0.409176 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.6969i | 0.674342i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.4415 | 1.20814 | 0.604071 | − | 0.796931i | \(-0.293544\pi\) | ||||
0.604071 | + | 0.796931i | \(0.293544\pi\) | |||||||
\(480\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.0000i | 1.08310i | 0.840667 | + | 0.541552i | \(0.182163\pi\) | ||||
−0.840667 | + | 0.541552i | \(0.817837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.38551i | − 0.197513i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.7128 | −1.23565 | −0.617827 | − | 0.786314i | \(-0.711987\pi\) | ||||
−0.617827 | + | 0.786314i | \(0.711987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.2020 | 0.631983 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.3840i | 1.43540i | 0.696354 | + | 0.717699i | \(0.254805\pi\) | ||||
−0.696354 | + | 0.717699i | \(0.745195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 25.7980i | − 1.13679i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.635674i | 0.0279569i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.7980 | −0.867364 | −0.433682 | − | 0.901066i | \(-0.642786\pi\) | ||||
−0.433682 | + | 0.901066i | \(0.642786\pi\) | |||||||
\(522\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 68.5821i | 2.97062i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.6274 | −0.978269 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.11416 | −0.132668 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.47848i | 0.105017i | 0.998620 | + | 0.0525083i | \(0.0167216\pi\) | ||||
−0.998620 | + | 0.0525083i | \(0.983278\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.9971 | 2.36842 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 12.0000i | − 0.505740i | −0.967500 | − | 0.252870i | \(-0.918626\pi\) | ||||
0.967500 | − | 0.252870i | \(-0.0813744\pi\) | |||||||
\(564\) | 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 | \(-0.357162\pi\) | ||||
0.433830 | + | 0.900995i | \(0.357162\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 18.6969i | − 0.782443i | −0.920297 | − | 0.391221i | \(-0.872053\pi\) | ||||
0.920297 | − | 0.391221i | \(-0.127947\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.75663 | 0.404078 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.7980i | 0.899698i | 0.893105 | + | 0.449849i | \(0.148522\pi\) | ||||
−0.893105 | + | 0.449849i | \(0.851478\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 44.6834i | − 1.84115i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.1010 | −0.537994 | −0.268997 | − | 0.963141i | \(-0.586692\pi\) | ||||
−0.268997 | + | 0.963141i | \(0.586692\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.74983 | 0.153214 | 0.0766070 | − | 0.997061i | \(-0.475591\pi\) | ||||
0.0766070 | + | 0.997061i | \(0.475591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.1918 | 1.49729 | 0.748643 | − | 0.662973i | \(-0.230706\pi\) | ||||
0.748643 | + | 0.662973i | \(0.230706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 20.0000i | − 0.803868i | −0.915669 | − | 0.401934i | \(-0.868338\pi\) | ||||
0.915669 | − | 0.401934i | \(-0.131662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 44.0477i | − 1.74523i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.59592 | 0.221025 | 0.110513 | − | 0.993875i | \(-0.464751\pi\) | ||||
0.110513 | + | 0.993875i | \(0.464751\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 23.5959i | − 0.930532i | −0.885171 | − | 0.465266i | \(-0.845959\pi\) | ||||
0.885171 | − | 0.465266i | \(-0.154041\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.5904 | −1.83166 | −0.915829 | − | 0.401569i | \(-0.868465\pi\) | ||||
−0.915829 | + | 0.401569i | \(0.868465\pi\) | |||||||
\(648\) | 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 | \(0.0414881\pi\) | ||||
−0.991518 | + | 0.129970i | \(0.958512\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.0265 | −1.52489 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 21.3939i | − 0.833387i | −0.909047 | − | 0.416694i | \(-0.863189\pi\) | ||||
0.909047 | − | 0.416694i | \(-0.136811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 10.7423i | − 0.417825i | −0.977934 | − | 0.208913i | \(-0.933008\pi\) | ||||
0.977934 | − | 0.208913i | \(-0.0669924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.00000i | − 0.154881i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3.74983i | − 0.144118i | −0.997400 | − | 0.0720589i | \(-0.977043\pi\) | ||||
0.997400 | − | 0.0720589i | \(-0.0229569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.7980i | 1.44630i | 0.690692 | + | 0.723149i | \(0.257306\pi\) | ||||
−0.690692 | + | 0.723149i | \(0.742694\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.65685i | 0.216137i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 35.2767i | − 1.33238i | −0.745781 | − | 0.666191i | \(-0.767924\pi\) | ||||
0.745781 | − | 0.666191i | \(-0.232076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.9411 | 1.28011 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 57.3939 | 2.14942 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 17.7980i | − 0.665606i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.2631 | −0.867567 | −0.433783 | − | 0.901017i | \(-0.642822\pi\) | ||||
−0.433783 | + | 0.901017i | \(0.642822\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.1278 | 0.554984 | 0.277492 | − | 0.960728i | \(-0.410497\pi\) | ||||
0.277492 | + | 0.960728i | \(0.410497\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.79796 | −0.0658721 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.3031 | −0.699735 | −0.349868 | − | 0.936799i | \(-0.613773\pi\) | ||||
−0.349868 | + | 0.936799i | \(0.613773\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.3281i | 0.371476i | 0.982599 | + | 0.185738i | \(0.0594675\pi\) | ||||
−0.982599 | + | 0.185738i | \(0.940533\pi\) | |||||||
\(774\) | 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 | 0 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.5959 | 1.12200 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 22.9131i | − 0.811625i | −0.913956 | − | 0.405813i | \(-0.866989\pi\) | ||||
0.913956 | − | 0.405813i | \(-0.133011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.38551 | 0.155148 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.79796i | 0.275184i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.50510 | 0.193549 | 0.0967745 | − | 0.995306i | \(-0.469147\pi\) | ||||
0.0967745 | + | 0.995306i | \(0.469147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.69694i | − 0.0947023i | −0.998878 | − | 0.0473512i | \(-0.984922\pi\) | ||||
0.998878 | − | 0.0473512i | \(-0.0150780\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | \(0.0208435\pi\) | ||||
−0.997857 | + | 0.0654350i | \(0.979157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.921404 | −0.0321181 | −0.0160591 | − | 0.999871i | \(-0.505112\pi\) | ||||
−0.0160591 | + | 0.999871i | \(0.505112\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 51.1918i | − 1.78011i | −0.455849 | − | 0.890057i | \(-0.650664\pi\) | ||||
0.455849 | − | 0.890057i | \(-0.349336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.7975i | 1.66008i | 0.557706 | + | 0.830038i | \(0.311682\pi\) | ||||
−0.557706 | + | 0.830038i | \(0.688318\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −48.2929 | −1.67325 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 28.4041i | − 0.982964i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.0477 | 1.52070 | 0.760348 | − | 0.649516i | \(-0.225029\pi\) | ||||
0.760348 | + | 0.649516i | \(0.225029\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5959 | 0.986066 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 75.2246i | − 2.58781i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.89898 | −0.235665 | −0.117832 | − | 0.993034i | \(-0.537595\pi\) | ||||
−0.117832 | + | 0.993034i | \(0.537595\pi\) | |||||||
\(858\) | 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 | \(-0.755096\pi\) | ||||
−0.718336 | + | 0.695697i | \(0.755096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.39388 | 0.183397 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6.92820i | − 0.235023i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −86.8241 | −2.94192 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.20204 | 0.141570 | 0.0707852 | − | 0.997492i | \(-0.477450\pi\) | ||||
0.0707852 | + | 0.997492i | \(0.477450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.7980i | 1.00278i | 0.865221 | + | 0.501391i | \(0.167178\pi\) | ||||
−0.865221 | + | 0.501391i | \(0.832822\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.2979 | 1.35307 | 0.676535 | − | 0.736410i | \(-0.263481\pi\) | ||||
0.676535 | + | 0.736410i | \(0.263481\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.11416i | − 0.104211i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3137 | 0.378176 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.0477 | −1.45937 | −0.729683 | − | 0.683786i | \(-0.760332\pi\) | ||||
−0.729683 | + | 0.683786i | \(0.760332\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.79796 | 0.324265 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 75.1918i | 2.47497i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 20.7846i | − 0.683394i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.2929i | 1.12390i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6062i | 0.573947i | 0.957939 | + | 0.286973i | \(0.0926492\pi\) | ||||
−0.957939 | + | 0.286973i | \(0.907351\pi\) | |||||||
\(942\) | 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 | \(-0.828399\pi\) | ||||
0.858171 | − | 0.513365i | \(-0.171601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.0689i | 1.59284i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.2929 | 1.04607 | 0.523034 | − | 0.852312i | \(-0.324800\pi\) | ||||
0.523034 | + | 0.852312i | \(0.324800\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53.3939i | 1.72779i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.1918 | 1.68361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.5959i | 1.01396i | 0.861957 | + | 0.506981i | \(0.169238\pi\) | ||||
−0.861957 | + | 0.506981i | \(0.830762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.79796 | −0.249479 | −0.124739 | − | 0.992190i | \(-0.539809\pi\) | ||||
−0.124739 | + | 0.992190i | \(0.539809\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7980i | 0.504905i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.3485 | −0.904176 | −0.452088 | − | 0.891973i | \(-0.649321\pi\) | ||||
−0.452088 | + | 0.891973i | \(0.649321\pi\) | |||||||
\(984\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6336.2.f.l.3169.8 | 8 | ||
3.2 | odd | 2 | 2112.2.f.g.1057.6 | yes | 8 | ||
4.3 | odd | 2 | inner | 6336.2.f.l.3169.6 | 8 | ||
8.3 | odd | 2 | inner | 6336.2.f.l.3169.3 | 8 | ||
8.5 | even | 2 | inner | 6336.2.f.l.3169.1 | 8 | ||
12.11 | even | 2 | 2112.2.f.g.1057.2 | ✓ | 8 | ||
24.5 | odd | 2 | 2112.2.f.g.1057.3 | yes | 8 | ||
24.11 | even | 2 | 2112.2.f.g.1057.7 | yes | 8 | ||
48.5 | odd | 4 | 8448.2.a.ct.1.4 | 4 | |||
48.11 | even | 4 | 8448.2.a.cm.1.4 | 4 | |||
48.29 | odd | 4 | 8448.2.a.cm.1.1 | 4 | |||
48.35 | even | 4 | 8448.2.a.ct.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2112.2.f.g.1057.2 | ✓ | 8 | 12.11 | even | 2 | ||
2112.2.f.g.1057.3 | yes | 8 | 24.5 | odd | 2 | ||
2112.2.f.g.1057.6 | yes | 8 | 3.2 | odd | 2 | ||
2112.2.f.g.1057.7 | yes | 8 | 24.11 | even | 2 | ||
6336.2.f.l.3169.1 | 8 | 8.5 | even | 2 | inner | ||
6336.2.f.l.3169.3 | 8 | 8.3 | odd | 2 | inner | ||
6336.2.f.l.3169.6 | 8 | 4.3 | odd | 2 | inner | ||
6336.2.f.l.3169.8 | 8 | 1.1 | even | 1 | trivial | ||
8448.2.a.cm.1.1 | 4 | 48.29 | odd | 4 | |||
8448.2.a.cm.1.4 | 4 | 48.11 | even | 4 | |||
8448.2.a.ct.1.1 | 4 | 48.35 | even | 4 | |||
8448.2.a.ct.1.4 | 4 | 48.5 | odd | 4 |