Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.10 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.c.5615.9 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.17792 | −0.526780 | −0.263390 | − | 0.964689i | \(-0.584841\pi\) | ||||
−0.263390 | + | 0.964689i | \(0.584841\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.90595i | 0.876176i | 0.898932 | + | 0.438088i | \(0.144344\pi\) | ||||
−0.898932 | + | 0.438088i | \(0.855656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.05317i | − 0.292096i | −0.989278 | − | 0.146048i | \(-0.953345\pi\) | ||||
0.989278 | − | 0.146048i | \(-0.0466554\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.48837i | − 1.57366i | −0.617169 | − | 0.786830i | \(-0.711721\pi\) | ||||
0.617169 | − | 0.786830i | \(-0.288279\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.11597 | 0.714853 | 0.357426 | − | 0.933941i | \(-0.383654\pi\) | ||||
0.357426 | + | 0.933941i | \(0.383654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.812516 | −0.169421 | −0.0847107 | − | 0.996406i | \(-0.526997\pi\) | ||||
−0.0847107 | + | 0.996406i | \(0.526997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.61251 | −0.722503 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.03607 | 0.749480 | 0.374740 | − | 0.927130i | \(-0.377732\pi\) | ||||
0.374740 | + | 0.927130i | \(0.377732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.108779i | 0.0195372i | 0.999952 | + | 0.00976861i | \(0.00310949\pi\) | ||||
−0.999952 | + | 0.00976861i | \(0.996891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.17792i | − 0.199104i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.97034i | 1.63911i | 0.572998 | + | 0.819557i | \(0.305780\pi\) | ||||
−0.572998 | + | 0.819557i | \(0.694220\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 9.44298i | − 1.47475i | −0.675486 | − | 0.737373i | \(-0.736066\pi\) | ||||
0.675486 | − | 0.737373i | \(-0.263934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3446 | −1.57754 | −0.788770 | − | 0.614688i | \(-0.789282\pi\) | ||||
−0.788770 | + | 0.614688i | \(0.789282\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.03126 | −0.588019 | −0.294010 | − | 0.955802i | \(-0.594990\pi\) | ||||
−0.294010 | + | 0.955802i | \(0.594990\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.97772 | 0.409022 | 0.204511 | − | 0.978864i | \(-0.434440\pi\) | ||||
0.204511 | + | 0.978864i | \(0.434440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.42296i | − 0.461552i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.868874i | 0.113118i | 0.998399 | + | 0.0565589i | \(0.0180129\pi\) | ||||
−0.998399 | + | 0.0565589i | \(0.981987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.33629i | − 0.683242i | −0.939838 | − | 0.341621i | \(-0.889024\pi\) | ||||
0.939838 | − | 0.341621i | \(-0.110976\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.24054i | 0.153870i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.97987 | 0.486218 | 0.243109 | − | 0.969999i | \(-0.421833\pi\) | ||||
0.243109 | + | 0.969999i | \(0.421833\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.844302 | 0.100200 | 0.0501001 | − | 0.998744i | \(-0.484046\pi\) | ||||
0.0501001 | + | 0.998744i | \(0.484046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.59513 | 0.420778 | 0.210389 | − | 0.977618i | \(-0.432527\pi\) | ||||
0.210389 | + | 0.977618i | \(0.432527\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.90595 | −0.331164 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.48320i | 1.06694i | 0.845818 | + | 0.533472i | \(0.179113\pi\) | ||||
−0.845818 | + | 0.533472i | \(0.820887\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.71280i | − 0.297769i | −0.988855 | − | 0.148884i | \(-0.952432\pi\) | ||||
0.988855 | − | 0.148884i | \(-0.0475682\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.64276i | 0.828973i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.22575i | 0.235930i | 0.993018 | + | 0.117965i | \(0.0376370\pi\) | ||||
−0.993018 | + | 0.117965i | \(0.962363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.05317 | 0.110402 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.67035 | −0.376570 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.93019 | −0.399050 | −0.199525 | − | 0.979893i | \(-0.563940\pi\) | ||||
−0.199525 | + | 0.979893i | \(0.563940\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.0700 | −1.79803 | −0.899016 | − | 0.437915i | \(-0.855717\pi\) | ||||
−0.899016 | + | 0.437915i | \(0.855717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 17.8616i | − 1.75995i | −0.475017 | − | 0.879977i | \(-0.657558\pi\) | ||||
0.475017 | − | 0.879977i | \(-0.342442\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7.67720i | − 0.742183i | −0.928596 | − | 0.371091i | \(-0.878984\pi\) | ||||
0.928596 | − | 0.371091i | \(-0.121016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.6991i | 1.21635i | 0.793801 | + | 0.608177i | \(0.208099\pi\) | ||||
−0.793801 | + | 0.608177i | \(0.791901\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 15.4017i | − 1.44887i | −0.689342 | − | 0.724437i | \(-0.742100\pi\) | ||||
0.689342 | − | 0.724437i | \(-0.257900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.957076 | 0.0892478 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.48837 | 0.594788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.55546 | 0.232315 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1448 | 0.907380 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 17.1514i | − 1.52194i | −0.648787 | − | 0.760970i | \(-0.724724\pi\) | ||||
0.648787 | − | 0.760970i | \(-0.275276\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 10.5118i | − 0.918421i | −0.888328 | − | 0.459210i | \(-0.848132\pi\) | ||||
0.888328 | − | 0.459210i | \(-0.151868\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.11597i | 0.270189i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 13.6268i | − 1.16422i | −0.813110 | − | 0.582110i | \(-0.802227\pi\) | ||||
0.813110 | − | 0.582110i | \(-0.197773\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.37620 | 0.456003 | 0.228002 | − | 0.973661i | \(-0.426781\pi\) | ||||
0.228002 | + | 0.973661i | \(0.426781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.06045 | 0.255928 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.75416 | −0.394811 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.3187 | 1.41880 | 0.709401 | − | 0.704805i | \(-0.248965\pi\) | ||||
0.709401 | + | 0.704805i | \(0.248965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 4.50773i | − 0.366834i | −0.983035 | − | 0.183417i | \(-0.941284\pi\) | ||||
0.983035 | − | 0.183417i | \(-0.0587158\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.128132i | − 0.0102918i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.84696i | 0.706064i | 0.935611 | + | 0.353032i | \(0.114849\pi\) | ||||
−0.935611 | + | 0.353032i | \(0.885151\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 0.812516i | − 0.0640352i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.38238 | 0.656558 | 0.328279 | − | 0.944581i | \(-0.393531\pi\) | ||||
0.328279 | + | 0.944581i | \(0.393531\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.93563 | 0.691460 | 0.345730 | − | 0.938334i | \(-0.387631\pi\) | ||||
0.345730 | + | 0.938334i | \(0.387631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8908 | 0.914680 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1612 | 1.07666 | 0.538328 | − | 0.842736i | \(-0.319056\pi\) | ||||
0.538328 | + | 0.842736i | \(0.319056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.61251i | − 0.273080i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 20.3695i | − 1.52249i | −0.648467 | − | 0.761243i | \(-0.724589\pi\) | ||||
0.648467 | − | 0.761243i | \(-0.275411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2659i | 1.35770i | 0.734279 | + | 0.678848i | \(0.237520\pi\) | ||||
−0.734279 | + | 0.678848i | \(0.762480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 11.7442i | − 0.863453i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8549 | 1.37880 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.83849 | −0.567173 | −0.283587 | − | 0.958947i | \(-0.591524\pi\) | ||||
−0.283587 | + | 0.958947i | \(0.591524\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0241 | −0.937498 | −0.468749 | − | 0.883331i | \(-0.655295\pi\) | ||||
−0.468749 | + | 0.883331i | \(0.655295\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.9576 | −1.06568 | −0.532842 | − | 0.846215i | \(-0.678876\pi\) | ||||
−0.532842 | + | 0.846215i | \(0.678876\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 16.9147i | − 1.19905i | −0.800356 | − | 0.599525i | \(-0.795356\pi\) | ||||
0.800356 | − | 0.599525i | \(-0.204644\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.03607i | 0.283277i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1230i | 0.776867i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.05485i | 0.626337i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.68386 | −0.391293 | −0.195647 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195647 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.1851 | 0.831017 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.108779 | −0.00738437 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.83333 | −0.459660 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.43963i | 0.230335i | 0.993346 | + | 0.115167i | \(0.0367404\pi\) | ||||
−0.993346 | + | 0.115167i | \(0.963260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.86522i | − 0.588406i | −0.955743 | − | 0.294203i | \(-0.904946\pi\) | ||||
0.955743 | − | 0.294203i | \(-0.0950541\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 17.3653i | − 1.14753i | −0.819019 | − | 0.573767i | \(-0.805482\pi\) | ||||
0.819019 | − | 0.573767i | \(-0.194518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 9.99149i | − 0.654564i | −0.944927 | − | 0.327282i | \(-0.893867\pi\) | ||||
0.944927 | − | 0.327282i | \(-0.106133\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.74848 | 0.309757 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.5708 | −1.58935 | −0.794677 | − | 0.607032i | \(-0.792360\pi\) | ||||
−0.794677 | + | 0.607032i | \(0.792360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.1786 | 1.49306 | 0.746532 | − | 0.665349i | \(-0.231717\pi\) | ||||
0.746532 | + | 0.665349i | \(0.231717\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.17792 | 0.0752543 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.28164i | − 0.208806i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 21.3670i | − 1.34868i | −0.738423 | − | 0.674338i | \(-0.764429\pi\) | ||||
0.738423 | − | 0.674338i | \(-0.235571\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.36113i | − 0.148443i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 29.5594i | − 1.84386i | −0.387352 | − | 0.921932i | \(-0.626610\pi\) | ||||
0.387352 | − | 0.921932i | \(-0.373390\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.97034 | −0.619527 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8001 | 0.974277 | 0.487139 | − | 0.873325i | \(-0.338041\pi\) | ||||
0.487139 | + | 0.873325i | \(0.338041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.50751 | −0.215464 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.41502 | −0.391131 | −0.195565 | − | 0.980691i | \(-0.562654\pi\) | ||||
−0.195565 | + | 0.980691i | \(0.562654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0927686i | 0.00563529i | 0.999996 | + | 0.00281765i | \(0.000896886\pi\) | ||||
−0.999996 | + | 0.00281765i | \(0.999103\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 10.4978i | − 0.633040i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 19.7900i | − 1.18907i | −0.804071 | − | 0.594534i | \(-0.797337\pi\) | ||||
0.804071 | − | 0.594534i | \(-0.202663\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4404i | 0.861443i | 0.902485 | + | 0.430721i | \(0.141741\pi\) | ||||
−0.902485 | + | 0.430721i | \(0.858259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.3759 | −1.21122 | −0.605612 | − | 0.795760i | \(-0.707071\pi\) | ||||
−0.605612 | + | 0.795760i | \(0.707071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.44298 | 0.557402 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25.0989 | −1.47641 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2919 | 0.601262 | 0.300631 | − | 0.953741i | \(-0.402803\pi\) | ||||
0.300631 | + | 0.953741i | \(0.402803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 1.02346i | − 0.0595882i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.855715i | 0.0494873i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 10.3446i | − 0.596254i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.28571i | 0.359919i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.8799 | −1.13461 | −0.567304 | − | 0.823508i | \(-0.692014\pi\) | ||||
−0.567304 | + | 0.823508i | \(0.692014\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.94464 | 0.450499 | 0.225250 | − | 0.974301i | \(-0.427680\pi\) | ||||
0.225250 | + | 0.974301i | \(0.427680\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.2451 | −1.59651 | −0.798254 | − | 0.602321i | \(-0.794243\pi\) | ||||
−0.798254 | + | 0.602321i | \(0.794243\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.8609 | 0.778506 | 0.389253 | − | 0.921131i | \(-0.372733\pi\) | ||||
0.389253 | + | 0.921131i | \(0.372733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7286i | 0.656677i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 20.2176i | − 1.12494i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.80458i | 0.211040i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 4.03126i | − 0.222250i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5450 | 0.799468 | 0.399734 | − | 0.916631i | \(-0.369103\pi\) | ||||
0.399734 | + | 0.916631i | \(0.369103\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.68795 | −0.256130 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.26170 | 0.286623 | 0.143312 | − | 0.989678i | \(-0.454225\pi\) | ||||
0.143312 | + | 0.989678i | \(0.454225\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.316105 | −0.0171181 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 15.5549i | − 0.835029i | −0.908670 | − | 0.417514i | \(-0.862901\pi\) | ||||
0.908670 | − | 0.417514i | \(-0.137099\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 17.1607i | − 0.918594i | −0.888283 | − | 0.459297i | \(-0.848101\pi\) | ||||
0.888283 | − | 0.459297i | \(-0.151899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5438i | 0.827314i | 0.910433 | + | 0.413657i | \(0.135749\pi\) | ||||
−0.910433 | + | 0.413657i | \(0.864251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.994517 | −0.0527835 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.9471 | −0.788876 | −0.394438 | − | 0.918923i | \(-0.629061\pi\) | ||||
−0.394438 | + | 0.918923i | \(0.629061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.29073 | −0.488986 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.23476 | −0.221657 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.86184i | − 0.149387i | −0.997207 | − | 0.0746934i | \(-0.976202\pi\) | ||||
0.997207 | − | 0.0746934i | \(-0.0237978\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.97772i | 0.154596i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 20.7327i | − 1.07350i | −0.843743 | − | 0.536748i | \(-0.819653\pi\) | ||||
0.843743 | − | 0.536748i | \(-0.180347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 4.25066i | − 0.218920i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.1561 | −1.44628 | −0.723141 | − | 0.690700i | \(-0.757302\pi\) | ||||
−0.723141 | + | 0.690700i | \(0.757302\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.9733 | 1.53156 | 0.765781 | − | 0.643101i | \(-0.222352\pi\) | ||||
0.765781 | + | 0.643101i | \(0.222352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.42296 | 0.174450 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.4931 | −1.49536 | −0.747679 | − | 0.664060i | \(-0.768832\pi\) | ||||
−0.747679 | + | 0.664060i | \(0.768832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.27190i | 0.266612i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 11.1704i | − 0.562045i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0845i | 1.10839i | 0.832386 | + | 0.554196i | \(0.186974\pi\) | ||||
−0.832386 | + | 0.554196i | \(0.813026\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 7.42054i | − 0.370564i | −0.982685 | − | 0.185282i | \(-0.940680\pi\) | ||||
0.982685 | − | 0.185282i | \(-0.0593198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.114562 | 0.00570674 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.9733 | −1.43615 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.3983 | 1.84923 | 0.924615 | − | 0.380904i | \(-0.124387\pi\) | ||||
0.924615 | + | 0.380904i | \(0.124387\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.868874 | −0.0427545 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.19546i | 0.156859i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 8.55960i | − 0.418164i | −0.977898 | − | 0.209082i | \(-0.932952\pi\) | ||||
0.977898 | − | 0.209082i | \(-0.0670475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.56688i | 0.320050i | 0.987113 | + | 0.160025i | \(0.0511575\pi\) | ||||
−0.987113 | + | 0.160025i | \(0.948842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.4393i | 1.13697i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.33629 | 0.258241 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.61014 | 0.270231 | 0.135116 | − | 0.990830i | \(-0.456859\pi\) | ||||
0.135116 | + | 0.990830i | \(0.456859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.96675 | 0.382857 | 0.191429 | − | 0.981507i | \(-0.438688\pi\) | ||||
0.191429 | + | 0.981507i | \(0.438688\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.53178 | −0.121111 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.9176i | 1.61880i | 0.587258 | + | 0.809400i | \(0.300208\pi\) | ||||
−0.587258 | + | 0.809400i | \(0.699792\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.31862i | − 0.300207i | −0.988670 | − | 0.150103i | \(-0.952039\pi\) | ||||
0.988670 | − | 0.150103i | \(-0.0479606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.62175i | − 0.124283i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 11.9562i | − 0.564246i | −0.959378 | − | 0.282123i | \(-0.908961\pi\) | ||||
0.959378 | − | 0.282123i | \(-0.0910387\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.4408 | 1.29214 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.24054 | −0.0581575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.7774 | 0.504144 | 0.252072 | − | 0.967708i | \(-0.418888\pi\) | ||||
0.252072 | + | 0.967708i | \(0.418888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.36887 | 0.110329 | 0.0551647 | − | 0.998477i | \(-0.482432\pi\) | ||||
0.0551647 | + | 0.998477i | \(0.482432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.4537i | 1.78709i | 0.448969 | + | 0.893547i | \(0.351791\pi\) | ||||
−0.448969 | + | 0.893547i | \(0.648209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 5.09381i | − 0.235713i | −0.993031 | − | 0.117857i | \(-0.962398\pi\) | ||||
0.993031 | − | 0.117857i | \(-0.0376023\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.97987i | 0.183773i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 30.0609i | − 1.38220i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.2565 | −0.516483 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.8166 | 0.951137 | 0.475568 | − | 0.879679i | \(-0.342242\pi\) | ||||
0.475568 | + | 0.879679i | \(0.342242\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5004 | 0.478778 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.62943 | 0.210212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 26.1716i | − 1.18595i | −0.805222 | − | 0.592973i | \(-0.797954\pi\) | ||||
0.805222 | − | 0.592973i | \(-0.202046\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 27.7686i | − 1.25318i | −0.779349 | − | 0.626590i | \(-0.784450\pi\) | ||||
0.779349 | − | 0.626590i | \(-0.215550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 26.1875i | − 1.17943i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.844302i | 0.0378721i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7781 | 0.616791 | 0.308395 | − | 0.951258i | \(-0.400208\pi\) | ||||
0.308395 | + | 0.951258i | \(0.400208\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.5875 | −1.45300 | −0.726502 | − | 0.687165i | \(-0.758855\pi\) | ||||
−0.726502 | + | 0.687165i | \(0.758855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.2850 | 0.947168 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.1161 | −0.758657 | −0.379328 | − | 0.925262i | \(-0.623845\pi\) | ||||
−0.379328 | + | 0.925262i | \(0.623845\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.59513i | 0.159039i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.0394i | 0.927109i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 11.7146i | − 0.515209i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 22.6308i | − 0.991471i | −0.868473 | − | 0.495736i | \(-0.834898\pi\) | ||||
0.868473 | − | 0.495736i | \(-0.165102\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0252 | 0.831914 | 0.415957 | − | 0.909384i | \(-0.363447\pi\) | ||||
0.415957 | + | 0.909384i | \(0.363447\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.705796 | 0.0307450 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3398 | −0.971296 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.94503 | −0.430767 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.04310i | 0.390967i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.90595i | − 0.125168i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 17.3996i | − 0.748066i | −0.927415 | − | 0.374033i | \(-0.877975\pi\) | ||||
0.927415 | − | 0.374033i | \(-0.122025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 14.9585i | − 0.640751i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.96571 | −0.212318 | −0.106159 | − | 0.994349i | \(-0.533855\pi\) | ||||
−0.106159 | + | 0.994349i | \(0.533855\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.5763 | 0.535768 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.48320 | −0.403267 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.67400 | −0.240415 | −0.120208 | − | 0.992749i | \(-0.538356\pi\) | ||||
−0.120208 | + | 0.992749i | \(0.538356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.8946i | 0.460793i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 25.4752i | − 1.07365i | −0.843693 | − | 0.536826i | \(-0.819623\pi\) | ||||
0.843693 | − | 0.536826i | \(-0.180377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.1420i | 0.763238i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.5120i | 0.817986i | 0.912537 | + | 0.408993i | \(0.134120\pi\) | ||||
−0.912537 | + | 0.408993i | \(0.865880\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.0268 | 1.59137 | 0.795686 | − | 0.605709i | \(-0.207111\pi\) | ||||
0.795686 | + | 0.605709i | \(0.207111\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.93522 | 0.122407 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.32632 | 0.221738 | 0.110869 | − | 0.993835i | \(-0.464637\pi\) | ||||
0.110869 | + | 0.993835i | \(0.464637\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.71280 | 0.112546 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.65311i | 0.358375i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.6946i | 1.06053i | 0.847832 | + | 0.530265i | \(0.177908\pi\) | ||||
−0.847832 | + | 0.530265i | \(0.822092\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.338951i | 0.0139662i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 35.9249i | − 1.47526i | −0.675205 | − | 0.737630i | \(-0.735945\pi\) | ||||
0.675205 | − | 0.737630i | \(-0.264055\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.64276 | −0.313322 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.08090 | −0.330177 | −0.165088 | − | 0.986279i | \(-0.552791\pi\) | ||||
−0.165088 | + | 0.986279i | \(0.552791\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.0492 | 1.59285 | 0.796425 | − | 0.604738i | \(-0.206722\pi\) | ||||
0.796425 | + | 0.604738i | \(0.206722\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.01012 | −0.122379 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.0636i | 1.58554i | 0.609519 | + | 0.792772i | \(0.291363\pi\) | ||||
−0.609519 | + | 0.792772i | \(0.708637\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.24559i | 0.171758i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 27.0877i | − 1.09406i | −0.837112 | − | 0.547031i | \(-0.815758\pi\) | ||||
0.837112 | − | 0.547031i | \(-0.184242\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.2143i | 0.411213i | 0.978635 | + | 0.205607i | \(0.0659167\pi\) | ||||
−0.978635 | + | 0.205607i | \(0.934083\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.5400 | −1.14712 | −0.573560 | − | 0.819164i | \(-0.694438\pi\) | ||||
−0.573560 | + | 0.819164i | \(0.694438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.22575 | −0.0891730 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.11281 | 0.244512 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 64.6912 | 2.57941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 17.9037i | − 0.712734i | −0.934346 | − | 0.356367i | \(-0.884015\pi\) | ||||
0.934346 | − | 0.356367i | \(-0.115985\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.2029i | 0.801728i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.05317i | 0.0417280i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.5576i | 1.44394i | 0.691925 | + | 0.721969i | \(0.256763\pi\) | ||||
−0.691925 | + | 0.721969i | \(0.743237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.5306 | −1.12514 | −0.562568 | − | 0.826751i | \(-0.690187\pi\) | ||||
−0.562568 | + | 0.826751i | \(0.690187\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.0326 | −0.984134 | −0.492067 | − | 0.870557i | \(-0.663758\pi\) | ||||
−0.492067 | + | 0.870557i | \(0.663758\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.52490 | −0.0991112 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.1196 | 1.68740 | 0.843699 | − | 0.536816i | \(-0.180373\pi\) | ||||
0.843699 | + | 0.536816i | \(0.180373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.3820i | 0.483806i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.36352i | 0.325796i | 0.986643 | + | 0.162898i | \(0.0520842\pi\) | ||||
−0.986643 | + | 0.162898i | \(0.947916\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.48754i | 0.330127i | 0.986283 | + | 0.165064i | \(0.0527829\pi\) | ||||
−0.986283 | + | 0.165064i | \(0.947217\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 3.67035i | − 0.142330i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.27937 | −0.126978 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.5070 | 0.598641 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.4287 | −0.980206 | −0.490103 | − | 0.871664i | \(-0.663041\pi\) | ||||
−0.490103 | + | 0.871664i | \(0.663041\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.0820 | 0.656515 | 0.328258 | − | 0.944588i | \(-0.393539\pi\) | ||||
0.328258 | + | 0.944588i | \(0.393539\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 3.93019i | − 0.150827i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.0552i | 1.68573i | 0.538128 | + | 0.842863i | \(0.319132\pi\) | ||||
−0.538128 | + | 0.842863i | \(0.680868\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0513i | 0.613288i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 3.13604i | − 0.119474i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3483 | 0.698002 | 0.349001 | − | 0.937122i | \(-0.386521\pi\) | ||||
0.349001 | + | 0.937122i | \(0.386521\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.33271 | −0.240213 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −61.2695 | −2.32075 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.6724 | −1.27179 | −0.635894 | − | 0.771777i | \(-0.719368\pi\) | ||||
−0.635894 | + | 0.771777i | \(0.719368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.0673i | 1.17172i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 18.0700i | − 0.679592i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 15.9147i | − 0.597689i | −0.954302 | − | 0.298845i | \(-0.903399\pi\) | ||||
0.954302 | − | 0.298845i | \(-0.0966013\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 0.0883844i | − 0.00331002i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.60495 | −0.134818 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.6441 | 1.29201 | 0.646004 | − | 0.763334i | \(-0.276439\pi\) | ||||
0.646004 | + | 0.763334i | \(0.276439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.8616 | 0.665200 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.5804 | −0.541501 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 38.6477i | − 1.43336i | −0.697400 | − | 0.716682i | \(-0.745660\pi\) | ||||
0.697400 | − | 0.716682i | \(-0.254340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 67.1197i | 2.48251i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.45768i | 0.164648i | 0.996606 | + | 0.0823240i | \(0.0262342\pi\) | ||||
−0.996606 | + | 0.0823240i | \(0.973766\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.5653i | 0.426013i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0619 | 1.17942 | 0.589709 | − | 0.807616i | \(-0.299243\pi\) | ||||
0.589709 | + | 0.807616i | \(0.299243\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.9201 | −1.64796 | −0.823979 | − | 0.566620i | \(-0.808251\pi\) | ||||
−0.823979 | + | 0.566620i | \(0.808251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.4000 | −0.747397 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.67720 | 0.280519 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 20.4697i | − 0.746951i | −0.927640 | − | 0.373475i | \(-0.878166\pi\) | ||||
0.927640 | − | 0.373475i | \(-0.121834\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.30973i | 0.193241i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.4003i | 0.414352i | 0.978304 | + | 0.207176i | \(0.0664273\pi\) | ||||
−0.978304 | + | 0.207176i | \(0.933573\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.5142i | 1.17864i | 0.807901 | + | 0.589319i | \(0.200604\pi\) | ||||
−0.807901 | + | 0.589319i | \(0.799396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.6991 | −0.459739 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.915070 | 0.0330413 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.1134 | 0.905614 | 0.452807 | − | 0.891609i | \(-0.350423\pi\) | ||||
0.452807 | + | 0.891609i | \(0.350423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.4890 | −1.52822 | −0.764112 | − | 0.645083i | \(-0.776823\pi\) | ||||
−0.764112 | + | 0.645083i | \(0.776823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 0.392964i | − 0.0141157i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 29.4240i | − 1.05423i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.45350i | 0.0877930i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 10.4210i | − 0.371941i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.1415 | −0.682322 | −0.341161 | − | 0.940005i | \(-0.610820\pi\) | ||||
−0.341161 | + | 0.940005i | \(0.610820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4017 | 0.547623 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.62001 | −0.199572 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.9802 | −0.530625 | −0.265312 | − | 0.964162i | \(-0.585475\pi\) | ||||
−0.265312 | + | 0.964162i | \(0.585475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.1563i | 0.925343i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.4473i | 0.368675i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.957076i | 0.0337325i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 20.4899i | − 0.720388i | −0.932877 | − | 0.360194i | \(-0.882711\pi\) | ||||
0.932877 | − | 0.360194i | \(-0.117289\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0258 | −0.668087 | −0.334043 | − | 0.942558i | \(-0.608413\pi\) | ||||
−0.334043 | + | 0.942558i | \(0.608413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.87374 | −0.345862 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.2335 | −1.12771 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.0750 | 1.36373 | 0.681863 | − | 0.731480i | \(-0.261170\pi\) | ||||
0.681863 | + | 0.731480i | \(0.261170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.1369i | 1.32937i | 0.747124 | + | 0.664684i | \(0.231434\pi\) | ||||
−0.747124 | + | 0.664684i | \(0.768566\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.8842i | 0.482802i | 0.970425 | + | 0.241401i | \(0.0776070\pi\) | ||||
−0.970425 | + | 0.241401i | \(0.922393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 0.705296i | − 0.0244960i | −0.999925 | − | 0.0122480i | \(-0.996101\pi\) | ||||
0.999925 | − | 0.0122480i | \(-0.00389875\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.48837i | 0.224809i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5254 | −0.364248 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.4627 | 1.74217 | 0.871083 | − | 0.491136i | \(-0.163418\pi\) | ||||
0.871083 | + | 0.491136i | \(0.163418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.7101 | −0.438280 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.0064 | −0.481835 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.55546i | 0.0878068i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8.10106i | − 0.277701i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 10.7370i | − 0.367628i | −0.982961 | − | 0.183814i | \(-0.941156\pi\) | ||||
0.982961 | − | 0.183814i | \(-0.0588444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 9.75153i | − 0.333106i | −0.986033 | − | 0.166553i | \(-0.946736\pi\) | ||||
0.986033 | − | 0.166553i | \(-0.0532637\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.9169 | −0.986630 | −0.493315 | − | 0.869851i | \(-0.664215\pi\) | ||||
−0.493315 | + | 0.869851i | \(0.664215\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.0259 | 0.545528 | 0.272764 | − | 0.962081i | \(-0.412062\pi\) | ||||
0.272764 | + | 0.962081i | \(0.412062\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.6807 | −0.567161 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.5577 | −0.934831 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 4.19146i | − 0.142022i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.1448i | 0.342958i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.24225i | − 0.0757154i | −0.999283 | − | 0.0378577i | \(-0.987947\pi\) | ||||
0.999283 | − | 0.0378577i | \(-0.0120534\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.97799i | 0.336167i | 0.985773 | + | 0.168083i | \(0.0537578\pi\) | ||||
−0.985773 | + | 0.168083i | \(0.946242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.8382 | −0.667609 | −0.333805 | − | 0.942642i | \(-0.608333\pi\) | ||||
−0.333805 | + | 0.942642i | \(0.608333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.8500 | 1.17015 | 0.585074 | − | 0.810980i | \(-0.301065\pi\) | ||||
0.585074 | + | 0.810980i | \(0.301065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.1514 | 0.575239 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.5613 | −0.420347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.9935i | 0.802016i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.439039i | 0.0146428i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 19.3206i | − 0.643661i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 21.5157i | − 0.715207i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.69626 | 0.122732 | 0.0613662 | − | 0.998115i | \(-0.480454\pi\) | ||||
0.0613662 | + | 0.998115i | \(0.480454\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.1975 | −1.69625 | −0.848125 | − | 0.529796i | \(-0.822268\pi\) | ||||
−0.848125 | + | 0.529796i | \(0.822268\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.88327 | 0.260898 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.5118 | 0.347130 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 50.4632i | − 1.66463i | −0.554306 | − | 0.832313i | \(-0.687016\pi\) | ||||
0.554306 | − | 0.832313i | \(-0.312984\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 0.889190i | − 0.0292681i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 36.0180i | − 1.18426i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 8.22557i | − 0.269872i | −0.990854 | − | 0.134936i | \(-0.956917\pi\) | ||||
0.990854 | − | 0.134936i | \(-0.0430829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.11597 | −0.102122 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.2095 | −0.726327 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.968784 | 0.0316488 | 0.0158244 | − | 0.999875i | \(-0.494963\pi\) | ||||
0.0158244 | + | 0.999875i | \(0.494963\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.2805 | 0.367734 | 0.183867 | − | 0.982951i | \(-0.441138\pi\) | ||||
0.183867 | + | 0.982951i | \(0.441138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.67257i | 0.249853i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.8442i | 1.87968i | 0.341609 | + | 0.939842i | \(0.389028\pi\) | ||||
−0.341609 | + | 0.939842i | \(0.610972\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 3.78627i | − 0.122907i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 23.4368i | − 0.759193i | −0.925152 | − | 0.379596i | \(-0.876063\pi\) | ||||
0.925152 | − | 0.379596i | \(-0.123937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.23309 | 0.298776 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.6268 | 0.440034 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9882 | 0.999618 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.3413 | 0.493855 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 44.8294i | − 1.44162i | −0.693135 | − | 0.720808i | \(-0.743771\pi\) | ||||
0.693135 | − | 0.720808i | \(-0.256229\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.3436i | 0.428216i | 0.976810 | + | 0.214108i | \(0.0686844\pi\) | ||||
−0.976810 | + | 0.214108i | \(0.931316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.37620i | 0.172353i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 11.0654i | − 0.354015i | −0.984210 | − | 0.177007i | \(-0.943358\pi\) | ||||
0.984210 | − | 0.177007i | \(-0.0566416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.46793 | −0.206716 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.7128 | −1.55370 | −0.776849 | − | 0.629687i | \(-0.783183\pi\) | ||||
−0.776849 | + | 0.629687i | \(0.783183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.6188 | 0.561381 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.40517 | 0.267269 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.6581i | 1.41861i | 0.704901 | + | 0.709306i | \(0.250991\pi\) | ||||
−0.704901 | + | 0.709306i | \(0.749009\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.9241i | 0.631636i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5408i | 0.650534i | 0.945622 | + | 0.325267i | \(0.105454\pi\) | ||||
−0.945622 | + | 0.325267i | \(0.894546\pi\) | |||||||
\(998\) | 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 | 6048.2.j.c.5615.10 | 32 | ||
3.2 | odd | 2 | inner | 6048.2.j.c.5615.23 | 32 | ||
4.3 | odd | 2 | 1512.2.j.c.323.31 | yes | 32 | ||
8.3 | odd | 2 | inner | 6048.2.j.c.5615.24 | 32 | ||
8.5 | even | 2 | 1512.2.j.c.323.1 | ✓ | 32 | ||
12.11 | even | 2 | 1512.2.j.c.323.2 | yes | 32 | ||
24.5 | odd | 2 | 1512.2.j.c.323.32 | yes | 32 | ||
24.11 | even | 2 | inner | 6048.2.j.c.5615.9 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.1 | ✓ | 32 | 8.5 | even | 2 | ||
1512.2.j.c.323.2 | yes | 32 | 12.11 | even | 2 | ||
1512.2.j.c.323.31 | yes | 32 | 4.3 | odd | 2 | ||
1512.2.j.c.323.32 | yes | 32 | 24.5 | odd | 2 | ||
6048.2.j.c.5615.9 | 32 | 24.11 | even | 2 | inner | ||
6048.2.j.c.5615.10 | 32 | 1.1 | even | 1 | trivial | ||
6048.2.j.c.5615.23 | 32 | 3.2 | odd | 2 | inner | ||
6048.2.j.c.5615.24 | 32 | 8.3 | odd | 2 | inner |