Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
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([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("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (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: | \(16\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.4 | ||
Root | \(0.891007 - 0.453990i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.d.3025.13 |
$q$-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 | ||||||||
\(5\) | − 2.63506i | − 1.17844i | −0.807974 | − | 0.589218i | \(-0.799436\pi\) | ||||
0.807974 | − | 0.589218i | \(-0.200564\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.29757i | 1.29577i | 0.761740 | + | 0.647883i | \(0.224346\pi\) | ||||
−0.761740 | + | 0.647883i | \(0.775654\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0480111i | 0.0133159i | 0.999978 | + | 0.00665794i | \(0.00211930\pi\) | ||||
−0.999978 | + | 0.00665794i | \(0.997881\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.726543i | − 0.166680i | −0.996521 | − | 0.0833401i | \(-0.973441\pi\) | ||||
0.996521 | − | 0.0833401i | \(-0.0265588\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.28146 | −1.10126 | −0.550631 | − | 0.834749i | \(-0.685613\pi\) | ||||
−0.550631 | + | 0.834749i | \(0.685613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.94356 | −0.388712 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.00208i | − 1.48595i | −0.669319 | − | 0.742975i | \(-0.733414\pi\) | ||||
0.669319 | − | 0.742975i | \(-0.266586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.90868 | −0.881625 | −0.440812 | − | 0.897599i | \(-0.645310\pi\) | ||||
−0.440812 | + | 0.897599i | \(0.645310\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.63506i | − 0.445407i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.10736i | − 1.49724i | −0.662999 | − | 0.748620i | \(-0.730717\pi\) | ||||
0.662999 | − | 0.748620i | \(-0.269283\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.45412 | −0.227096 | −0.113548 | − | 0.993533i | \(-0.536222\pi\) | ||||
−0.113548 | + | 0.993533i | \(0.536222\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.85816i | 1.35086i | 0.737426 | + | 0.675428i | \(0.236041\pi\) | ||||
−0.737426 | + | 0.675428i | \(0.763959\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.23016 | −1.34636 | −0.673179 | − | 0.739480i | \(-0.735072\pi\) | ||||
−0.673179 | + | 0.739480i | \(0.735072\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.14726i | − 0.432309i | −0.976359 | − | 0.216154i | \(-0.930649\pi\) | ||||
0.976359 | − | 0.216154i | \(-0.0693515\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3244 | 1.52698 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5.90515i | − 0.768785i | −0.923170 | − | 0.384392i | \(-0.874411\pi\) | ||||
0.923170 | − | 0.384392i | \(-0.125589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.19577i | 0.281140i | 0.990071 | + | 0.140570i | \(0.0448935\pi\) | ||||
−0.990071 | + | 0.140570i | \(0.955106\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.126512 | 0.0156919 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.55452i | − 1.04510i | −0.852608 | − | 0.522550i | \(-0.824981\pi\) | ||||
0.852608 | − | 0.522550i | \(-0.175019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.86725 | −0.458958 | −0.229479 | − | 0.973314i | \(-0.573702\pi\) | ||||
−0.229479 | + | 0.973314i | \(0.573702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.56044 | −0.884883 | −0.442441 | − | 0.896797i | \(-0.645888\pi\) | ||||
−0.442441 | + | 0.896797i | \(0.645888\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.29757i | 0.489754i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6139 | 1.64419 | 0.822094 | − | 0.569352i | \(-0.192806\pi\) | ||||
0.822094 | + | 0.569352i | \(0.192806\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 9.05240i | − 0.993631i | −0.867856 | − | 0.496815i | \(-0.834503\pi\) | ||||
0.867856 | − | 0.496815i | \(-0.165497\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 8.33280i | − 0.903819i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.15394 | −0.546317 | −0.273159 | − | 0.961969i | \(-0.588068\pi\) | ||||
−0.273159 | + | 0.961969i | \(0.588068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0480111i | 0.00503293i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.91449 | −0.196422 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1803 | 1.23673 | 0.618363 | − | 0.785893i | \(-0.287796\pi\) | ||||
0.618363 | + | 0.785893i | \(0.287796\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.35250i | 0.433090i | 0.976273 | + | 0.216545i | \(0.0694788\pi\) | ||||
−0.976273 | + | 0.216545i | \(0.930521\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3214 | 1.21406 | 0.607030 | − | 0.794679i | \(-0.292361\pi\) | ||||
0.607030 | + | 0.794679i | \(0.292361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 9.69053i | − 0.936819i | −0.883512 | − | 0.468409i | \(-0.844827\pi\) | ||||
0.883512 | − | 0.468409i | \(-0.155173\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 9.08902i | − 0.870570i | −0.900293 | − | 0.435285i | \(-0.856648\pi\) | ||||
0.900293 | − | 0.435285i | \(-0.143352\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.5205 | 1.27190 | 0.635951 | − | 0.771729i | \(-0.280608\pi\) | ||||
0.635951 | + | 0.771729i | \(0.280608\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.9170i | 1.29777i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.16228 | 0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.46912 | −0.679011 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 8.05391i | − 0.720364i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9792 | 0.974242 | 0.487121 | − | 0.873334i | \(-0.338047\pi\) | ||||
0.487121 | + | 0.873334i | \(0.338047\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.770817i | 0.0673466i | 0.999433 | + | 0.0336733i | \(0.0107206\pi\) | ||||
−0.999433 | + | 0.0336733i | \(0.989279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.726543i | − 0.0629992i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.9782 | −0.937933 | −0.468967 | − | 0.883216i | \(-0.655374\pi\) | ||||
−0.468967 | + | 0.883216i | \(0.655374\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 22.0189i | − 1.86762i | −0.357767 | − | 0.933811i | \(-0.616462\pi\) | ||||
0.357767 | − | 0.933811i | \(-0.383538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.206331 | −0.0172543 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.0860 | −1.75110 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.06643i | − 0.415058i | −0.978229 | − | 0.207529i | \(-0.933458\pi\) | ||||
0.978229 | − | 0.207529i | \(-0.0665422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.94054 | 0.564813 | 0.282407 | − | 0.959295i | \(-0.408867\pi\) | ||||
0.282407 | + | 0.959295i | \(0.408867\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.9347i | 1.03894i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4181i | 1.46992i | 0.678109 | + | 0.734962i | \(0.262800\pi\) | ||||
−0.678109 | + | 0.734962i | \(0.737200\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.28146 | −0.416238 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 10.5949i | − 0.829859i | −0.909854 | − | 0.414929i | \(-0.863806\pi\) | ||||
0.909854 | − | 0.414929i | \(-0.136194\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3800 | −1.34490 | −0.672451 | − | 0.740142i | \(-0.734758\pi\) | ||||
−0.672451 | + | 0.740142i | \(0.734758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9977 | 0.999823 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.9078i | − 1.74165i | −0.491595 | − | 0.870824i | \(-0.663586\pi\) | ||||
0.491595 | − | 0.870824i | \(-0.336414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.94356 | −0.146919 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 21.6267i | − 1.61646i | −0.588869 | − | 0.808228i | \(-0.700427\pi\) | ||||
0.588869 | − | 0.808228i | \(-0.299573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6144i | 0.937619i | 0.883299 | + | 0.468810i | \(0.155317\pi\) | ||||
−0.883299 | + | 0.468810i | \(0.844683\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.9985 | −1.76440 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.5901i | 0.993808i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5578 | −0.981006 | −0.490503 | − | 0.871439i | \(-0.663187\pi\) | ||||
−0.490503 | + | 0.871439i | \(0.663187\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.0614 | −1.87594 | −0.937971 | − | 0.346713i | \(-0.887298\pi\) | ||||
−0.937971 | + | 0.346713i | \(0.887298\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.18922i | 0.227222i | 0.993525 | + | 0.113611i | \(0.0362418\pi\) | ||||
−0.993525 | + | 0.113611i | \(0.963758\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.2129 | −1.78730 | −0.893648 | − | 0.448768i | \(-0.851863\pi\) | ||||
−0.893648 | + | 0.448768i | \(0.851863\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.00208i | − 0.561636i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.83171i | 0.267618i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.12237 | 0.215979 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 5.25731i | − 0.361928i | −0.983490 | − | 0.180964i | \(-0.942078\pi\) | ||||
0.983490 | − | 0.180964i | \(-0.0579218\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.3418 | 1.59190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.90868 | −0.333223 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.151824i | 0.0102128i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.27095 | −0.152074 | −0.0760370 | − | 0.997105i | \(-0.524227\pi\) | ||||
−0.0760370 | + | 0.997105i | \(0.524227\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.44780i | 0.0960940i | 0.998845 | + | 0.0480470i | \(0.0152997\pi\) | ||||
−0.998845 | + | 0.0480470i | \(0.984700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.1128i | 0.866516i | 0.901270 | + | 0.433258i | \(0.142636\pi\) | ||||
−0.901270 | + | 0.433258i | \(0.857364\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.6984 | 0.831903 | 0.415951 | − | 0.909387i | \(-0.363449\pi\) | ||||
0.415951 | + | 0.909387i | \(0.363449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.3221i | 1.58660i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.1437 | −0.979564 | −0.489782 | − | 0.871845i | \(-0.662924\pi\) | ||||
−0.489782 | + | 0.871845i | \(0.662924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0920 | −1.10099 | −0.550497 | − | 0.834837i | \(-0.685562\pi\) | ||||
−0.550497 | + | 0.834837i | \(0.685562\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.63506i | − 0.168348i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0348821 | 0.00221949 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 11.7844i | − 0.743822i | −0.928268 | − | 0.371911i | \(-0.878703\pi\) | ||||
0.928268 | − | 0.371911i | \(-0.121297\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 22.6975i | − 1.42698i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.8905 | −0.928847 | −0.464423 | − | 0.885613i | \(-0.653738\pi\) | ||||
−0.464423 | + | 0.885613i | \(0.653738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.10736i | − 0.565904i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.1032 | 1.05463 | 0.527315 | − | 0.849670i | \(-0.323199\pi\) | ||||
0.527315 | + | 0.849670i | \(0.323199\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.29322 | −0.509448 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.32461i | 0.141734i | 0.997486 | + | 0.0708670i | \(0.0225766\pi\) | ||||
−0.997486 | + | 0.0708670i | \(0.977423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.4721 | −0.757628 | −0.378814 | − | 0.925473i | \(-0.623668\pi\) | ||||
−0.378814 | + | 0.925473i | \(0.623668\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 8.35259i | − 0.503680i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 15.6257i | − 0.938858i | −0.882970 | − | 0.469429i | \(-0.844460\pi\) | ||||
0.882970 | − | 0.469429i | \(-0.155540\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0872 | −1.55623 | −0.778115 | − | 0.628122i | \(-0.783824\pi\) | ||||
−0.778115 | + | 0.628122i | \(0.783824\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.4083i | 1.03482i | 0.855739 | + | 0.517408i | \(0.173103\pi\) | ||||
−0.855739 | + | 0.517408i | \(0.826897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.45412 | −0.0858342 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 13.6647i | − 0.798299i | −0.916886 | − | 0.399149i | \(-0.869305\pi\) | ||||
0.916886 | − | 0.399149i | \(-0.130695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.5604 | −0.905964 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 0.253569i | − 0.0146643i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.85816i | 0.510576i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.78600 | 0.331306 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.43102i | 0.481184i | 0.970626 | + | 0.240592i | \(0.0773415\pi\) | ||||
−0.970626 | + | 0.240592i | \(0.922659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.4195 | 1.44141 | 0.720703 | − | 0.693244i | \(-0.243819\pi\) | ||||
0.720703 | + | 0.693244i | \(0.243819\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.3183 | −1.37455 | −0.687277 | − | 0.726396i | \(-0.741194\pi\) | ||||
−0.687277 | + | 0.726396i | \(0.741194\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 15.2593i | − 0.857047i | −0.903531 | − | 0.428523i | \(-0.859034\pi\) | ||||
0.903531 | − | 0.428523i | \(-0.140966\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.3895 | 1.92544 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.29753i | − 0.127838i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 0.0933124i | − 0.00517604i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.23016 | −0.508875 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9170i | 1.25963i | 0.776744 | + | 0.629816i | \(0.216870\pi\) | ||||
−0.776744 | + | 0.629816i | \(0.783130\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.5417 | −1.23158 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.0474 | 1.85468 | 0.927340 | − | 0.374221i | \(-0.122090\pi\) | ||||
0.927340 | + | 0.374221i | \(0.122090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 21.0954i | − 1.14238i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.72245i | 0.0924662i | 0.998931 | + | 0.0462331i | \(0.0147217\pi\) | ||||
−0.998931 | + | 0.0462331i | \(0.985278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 7.95586i | − 0.425868i | −0.977067 | − | 0.212934i | \(-0.931698\pi\) | ||||
0.977067 | − | 0.212934i | \(-0.0683019\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.1711 | −1.23327 | −0.616637 | − | 0.787247i | \(-0.711505\pi\) | ||||
−0.616637 | + | 0.787247i | \(0.711505\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.1905i | 0.540853i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.7889 | −0.991640 | −0.495820 | − | 0.868425i | \(-0.665133\pi\) | ||||
−0.495820 | + | 0.868425i | \(0.665133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4721 | 0.972218 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.9222i | 1.04278i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.1394 | −1.31227 | −0.656134 | − | 0.754645i | \(-0.727809\pi\) | ||||
−0.656134 | + | 0.754645i | \(0.727809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.14726i | − 0.163397i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.0530i | 1.29719i | 0.761132 | + | 0.648597i | \(0.224644\pi\) | ||||
−0.761132 | + | 0.648597i | \(0.775356\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.384189 | 0.0197867 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 15.2282i | − 0.782222i | −0.920344 | − | 0.391111i | \(-0.872091\pi\) | ||||
0.920344 | − | 0.391111i | \(-0.127909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.5703 | −1.51097 | −0.755487 | − | 0.655164i | \(-0.772600\pi\) | ||||
−0.755487 | + | 0.655164i | \(0.772600\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.3244 | 0.577143 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.90315i | 0.0964934i | 0.998835 | + | 0.0482467i | \(0.0153634\pi\) | ||||
−0.998835 | + | 0.0482467i | \(0.984637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.7015 | −0.844629 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 38.5085i | − 1.93757i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7660i | 0.841462i | 0.907185 | + | 0.420731i | \(0.138226\pi\) | ||||
−0.907185 | + | 0.420731i | \(0.861774\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.2567 | −0.861759 | −0.430880 | − | 0.902409i | \(-0.641797\pi\) | ||||
−0.430880 | + | 0.902409i | \(0.641797\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.235671i | − 0.0117396i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.1395 | 1.94007 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.55671 | 0.0769744 | 0.0384872 | − | 0.999259i | \(-0.487746\pi\) | ||||
0.0384872 | + | 0.999259i | \(0.487746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.90515i | − 0.290573i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.8537 | −1.17093 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.1570i | 1.27785i | 0.769268 | + | 0.638926i | \(0.220621\pi\) | ||||
−0.769268 | + | 0.638926i | \(0.779379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.696870i | 0.0339634i | 0.999856 | + | 0.0169817i | \(0.00540570\pi\) | ||||
−0.999856 | + | 0.0169817i | \(0.994594\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.14608 | −0.298128 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.19577i | 0.106261i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.65116 | −0.368543 | −0.184272 | − | 0.982875i | \(-0.558993\pi\) | ||||
−0.184272 | + | 0.982875i | \(0.558993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0860 | 0.821101 | 0.410550 | − | 0.911838i | \(-0.365337\pi\) | ||||
0.410550 | + | 0.911838i | \(0.365337\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.83721i | 0.183559i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.23837 | 0.154559 | 0.0772796 | − | 0.997009i | \(-0.475377\pi\) | ||||
0.0772796 | + | 0.997009i | \(0.475377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.42501i | 0.162727i | 0.996684 | + | 0.0813636i | \(0.0259275\pi\) | ||||
−0.996684 | + | 0.0813636i | \(0.974073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5810i | 0.643800i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.7647 | 1.87661 | 0.938305 | − | 0.345808i | \(-0.112395\pi\) | ||||
0.938305 | + | 0.345808i | \(0.112395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 6.24920i | − 0.294263i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.126512 | 0.00593098 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.46983 | 0.349424 | 0.174712 | − | 0.984620i | \(-0.444101\pi\) | ||||
0.174712 | + | 0.984620i | \(0.444101\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 15.0075i | − 0.698967i | −0.936942 | − | 0.349484i | \(-0.886357\pi\) | ||||
0.936942 | − | 0.349484i | \(-0.113643\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.29553 | 0.199630 | 0.0998150 | − | 0.995006i | \(-0.468175\pi\) | ||||
0.0998150 | + | 0.995006i | \(0.468175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 26.3945i | − 1.22139i | −0.791865 | − | 0.610696i | \(-0.790890\pi\) | ||||
0.791865 | − | 0.610696i | \(-0.209110\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8.55452i | − 0.395011i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −38.0686 | −1.75039 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.41208i | 0.0647906i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.66267 | −0.304425 | −0.152213 | − | 0.988348i | \(-0.548640\pi\) | ||||
−0.152213 | + | 0.988348i | \(0.548640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.437254 | 0.0199371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 32.0960i | − 1.45740i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.6813 | 1.66219 | 0.831095 | − | 0.556131i | \(-0.187715\pi\) | ||||
0.831095 | + | 0.556131i | \(0.187715\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.38460i | − 0.197874i | −0.995094 | − | 0.0989371i | \(-0.968456\pi\) | ||||
0.995094 | − | 0.0989371i | \(-0.0315443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 25.3048i | − 1.13967i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.86725 | −0.173470 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 35.6754i | − 1.59705i | −0.601961 | − | 0.798525i | \(-0.705614\pi\) | ||||
0.601961 | − | 0.798525i | \(-0.294386\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.3657 | 0.506770 | 0.253385 | − | 0.967365i | \(-0.418456\pi\) | ||||
0.253385 | + | 0.967365i | \(0.418456\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4691 | 0.510369 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.78884i | 0.123613i | 0.998088 | + | 0.0618066i | \(0.0196862\pi\) | ||||
−0.998088 | + | 0.0618066i | \(0.980314\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.56044 | −0.334454 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 32.4676i | − 1.43069i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 39.6673i | − 1.74457i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.3056 | 1.76582 | 0.882910 | − | 0.469542i | \(-0.155581\pi\) | ||||
0.882910 | + | 0.469542i | \(0.155581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 35.9726i | − 1.57297i | −0.617608 | − | 0.786486i | \(-0.711898\pi\) | ||||
0.617608 | − | 0.786486i | \(-0.288102\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.5226 | −0.676175 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.89387 | 0.212777 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 0.0698140i | − 0.00302398i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.5352 | −1.10398 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.29757i | 0.185109i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.1931i | 0.438234i | 0.975699 | + | 0.219117i | \(0.0703177\pi\) | ||||
−0.975699 | + | 0.219117i | \(0.929682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.9501 | −1.02591 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 12.3063i | − 0.526182i | −0.964771 | − | 0.263091i | \(-0.915258\pi\) | ||||
0.964771 | − | 0.263091i | \(-0.0847419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.81385 | −0.247679 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.6139 | 0.621445 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.2392i | 1.15416i | 0.816687 | + | 0.577082i | \(0.195809\pi\) | ||||
−0.816687 | + | 0.577082i | \(0.804191\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.425290 | −0.0179878 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.9187i | 1.38736i | 0.720285 | + | 0.693678i | \(0.244011\pi\) | ||||
−0.720285 | + | 0.693678i | \(0.755989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 35.6274i | − 1.49886i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.9554 | 1.08811 | 0.544053 | − | 0.839051i | \(-0.316889\pi\) | ||||
0.544053 | + | 0.839051i | \(0.316889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.527977i | 0.0220951i | 0.999939 | + | 0.0110476i | \(0.00351662\pi\) | ||||
−0.999939 | + | 0.0110476i | \(0.996483\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2648 | 0.428073 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.1860 | 1.79786 | 0.898929 | − | 0.438094i | \(-0.144346\pi\) | ||||
0.898929 | + | 0.438094i | \(0.144346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 9.05240i | − 0.375557i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5256 | 0.560171 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 20.5375i | − 0.847675i | −0.905738 | − | 0.423837i | \(-0.860683\pi\) | ||||
0.905738 | − | 0.423837i | \(-0.139317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.56636i | 0.146949i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −47.4930 | −1.95030 | −0.975152 | − | 0.221537i | \(-0.928893\pi\) | ||||
−0.975152 | + | 0.221537i | \(0.928893\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 8.33280i | − 0.341612i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.31521 | 0.217174 | 0.108587 | − | 0.994087i | \(-0.465367\pi\) | ||||
0.108587 | + | 0.994087i | \(0.465367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.9137 | 1.22020 | 0.610102 | − | 0.792323i | \(-0.291129\pi\) | ||||
0.610102 | + | 0.792323i | \(0.291129\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.6816i | 0.800171i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3429 | 0.703927 | 0.351964 | − | 0.936014i | \(-0.385514\pi\) | ||||
0.351964 | + | 0.936014i | \(0.385514\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 0.443150i | − 0.0179279i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 17.8469i | − 0.720830i | −0.932792 | − | 0.360415i | \(-0.882635\pi\) | ||||
0.932792 | − | 0.360415i | \(-0.117365\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.51870 | 0.141658 | 0.0708289 | − | 0.997488i | \(-0.477436\pi\) | ||||
0.0708289 | + | 0.997488i | \(0.477436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.33557i | 0.214455i | 0.994235 | + | 0.107227i | \(0.0341973\pi\) | ||||
−0.994235 | + | 0.107227i | \(0.965803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.15394 | −0.206488 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9404 | −1.23761 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 28.8000i | − 1.14833i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.1520 | −0.523574 | −0.261787 | − | 0.965126i | \(-0.584312\pi\) | ||||
−0.261787 | + | 0.965126i | \(0.584312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 28.9308i | − 1.14808i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0480111i | 0.00190227i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.20177 | 0.323950 | 0.161975 | − | 0.986795i | \(-0.448214\pi\) | ||||
0.161975 | + | 0.986795i | \(0.448214\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 32.8167i | − 1.29416i | −0.762421 | − | 0.647082i | \(-0.775989\pi\) | ||||
0.762421 | − | 0.647082i | \(-0.224011\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.7207 | 1.52227 | 0.761134 | − | 0.648595i | \(-0.224643\pi\) | ||||
0.761134 | + | 0.648595i | \(0.224643\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.3778 | 0.996166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.7630i | 1.12558i | 0.826598 | + | 0.562792i | \(0.190273\pi\) | ||||
−0.826598 | + | 0.562792i | \(0.809727\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.03115 | 0.0793637 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.6124i | 1.19249i | 0.802803 | + | 0.596244i | \(0.203341\pi\) | ||||
−0.802803 | + | 0.596244i | \(0.796659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.1975i | 1.71908i | 0.511066 | + | 0.859541i | \(0.329251\pi\) | ||||
−0.511066 | + | 0.859541i | \(0.670749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.91449 | −0.0742406 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.2627i | 1.63642i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.43649 | −0.364292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0117 | 0.655754 | 0.327877 | − | 0.944720i | \(-0.393667\pi\) | ||||
0.327877 | + | 0.944720i | \(0.393667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.4750i | 1.74775i | 0.486155 | + | 0.873873i | \(0.338399\pi\) | ||||
−0.486155 | + | 0.873873i | \(0.661601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.1803 | 0.467439 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.4287i | 1.31738i | 0.752416 | + | 0.658689i | \(0.228889\pi\) | ||||
−0.752416 | + | 0.658689i | \(0.771111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.9283i | 1.10529i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.151103 | 0.00575657 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 28.9692i | − 1.10204i | −0.834491 | − | 0.551021i | \(-0.814238\pi\) | ||||
0.834491 | − | 0.551021i | \(-0.185762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −58.0213 | −2.20087 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.59834 | −0.174175 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.9846i | 0.490421i | 0.969470 | + | 0.245211i | \(0.0788571\pi\) | ||||
−0.969470 | + | 0.245211i | \(0.921143\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.61688 | −0.249560 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.35250i | 0.163693i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.62511i | 0.211255i | 0.994406 | + | 0.105628i | \(0.0336852\pi\) | ||||
−0.994406 | + | 0.105628i | \(0.966315\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.9250 | 0.970899 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.543695i | 0.0203330i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3194 | 0.496732 | 0.248366 | − | 0.968666i | \(-0.420106\pi\) | ||||
0.248366 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3214 | 0.458871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.5525i | 0.577606i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0614 | −0.744037 | −0.372019 | − | 0.928225i | \(-0.621334\pi\) | ||||
−0.372019 | + | 0.928225i | \(0.621334\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.0120i | 1.03606i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.06695i | − 0.150216i | −0.997175 | − | 0.0751081i | \(-0.976070\pi\) | ||||
0.997175 | − | 0.0751081i | \(-0.0239302\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.7637 | 1.35421 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.22283i | 0.0817680i | 0.999164 | + | 0.0408840i | \(0.0130174\pi\) | ||||
−0.999164 | + | 0.0408840i | \(0.986983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.6763 | −1.05203 | −0.526015 | − | 0.850475i | \(-0.676314\pi\) | ||||
−0.526015 | + | 0.850475i | \(0.676314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.3504 | −0.489120 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 9.69053i | − 0.354084i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.61386 | −0.314324 | −0.157162 | − | 0.987573i | \(-0.550235\pi\) | ||||
−0.157162 | + | 0.987573i | \(0.550235\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 18.2888i | − 0.665596i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.8835i | 1.01344i | 0.862109 | + | 0.506722i | \(0.169143\pi\) | ||||
−0.862109 | + | 0.506722i | \(0.830857\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.20889 | 0.152572 | 0.0762861 | − | 0.997086i | \(-0.475694\pi\) | ||||
0.0762861 | + | 0.997086i | \(0.475694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9.08902i | − 0.329045i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.283512 | 0.0102370 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.5187 | 0.775986 | 0.387993 | − | 0.921662i | \(-0.373168\pi\) | ||||
0.387993 | + | 0.921662i | \(0.373168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 30.1139i | − 1.08312i | −0.840661 | − | 0.541562i | \(-0.817833\pi\) | ||||
0.840661 | − | 0.541562i | \(-0.182167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.54031 | 0.342698 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.05648i | 0.0378524i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 16.6198i | − 0.594703i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.5328 | 1.73221 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 48.9845i | − 1.74611i | −0.487624 | − | 0.873054i | \(-0.662136\pi\) | ||||
0.487624 | − | 0.873054i | \(-0.337864\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.5205 | 0.480734 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.105421 | −0.00374363 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 47.5262i | − 1.68347i | −0.539894 | − | 0.841733i | \(-0.681536\pi\) | ||||
0.539894 | − | 0.841733i | \(-0.318464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.1883 | −1.03261 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 32.4915i | − 1.14660i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.9170i | 0.490510i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.1063 | 1.05848 | 0.529240 | − | 0.848472i | \(-0.322477\pi\) | ||||
0.529240 | + | 0.848472i | \(0.322477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.2492i | 1.06219i | 0.847311 | + | 0.531096i | \(0.178220\pi\) | ||||
−0.847311 | + | 0.531096i | \(0.821780\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.9183 | −0.977935 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.43583 | 0.225161 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 15.4111i | − 0.537851i | −0.963161 | − | 0.268926i | \(-0.913331\pi\) | ||||
0.963161 | − | 0.268926i | \(-0.0866686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0591 | 0.699217 | 0.349608 | − | 0.936896i | \(-0.386315\pi\) | ||||
0.349608 | + | 0.936896i | \(0.386315\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.3363i | 1.22876i | 0.789009 | + | 0.614382i | \(0.210594\pi\) | ||||
−0.789009 | + | 0.614382i | \(0.789406\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.3976i | 1.81985i | 0.414778 | + | 0.909923i | \(0.363859\pi\) | ||||
−0.414778 | + | 0.909923i | \(0.636141\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.16228 | 0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.7973i | 1.58488i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.5132 | −1.50224 | −0.751121 | − | 0.660164i | \(-0.770487\pi\) | ||||
−0.751121 | + | 0.660164i | \(0.770487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.0334 | −1.20805 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 34.2498i | − 1.17823i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.46912 | −0.256642 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.1002i | 1.64885i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.8647i | 0.988310i | 0.869374 | + | 0.494155i | \(0.164522\pi\) | ||||
−0.869374 | + | 0.494155i | \(0.835478\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.7856 | −0.368429 | −0.184214 | − | 0.982886i | \(-0.558974\pi\) | ||||
−0.184214 | + | 0.982886i | \(0.558974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.7595i | 1.62953i | 0.579789 | + | 0.814767i | \(0.303135\pi\) | ||||
−0.579789 | + | 0.814767i | \(0.696865\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.2620 | 1.40457 | 0.702287 | − | 0.711894i | \(-0.252162\pi\) | ||||
0.702287 | + | 0.711894i | \(0.252162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.3635 | −2.05242 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 62.8041i | 2.13048i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.410712 | 0.0139164 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 8.05391i | − 0.272272i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 34.8776i | − 1.17773i | −0.808230 | − | 0.588867i | \(-0.799574\pi\) | ||||
0.808230 | − | 0.588867i | \(-0.200426\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.15123 | −0.207240 | −0.103620 | − | 0.994617i | \(-0.533043\pi\) | ||||
−0.103620 | + | 0.994617i | \(0.533043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 24.2713i | − 0.816796i | −0.912804 | − | 0.408398i | \(-0.866088\pi\) | ||||
0.912804 | − | 0.408398i | \(-0.133912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.8061 | 0.429987 | 0.214994 | − | 0.976615i | \(-0.431027\pi\) | ||||
0.214994 | + | 0.976615i | \(0.431027\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9792 | 0.368229 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.70611i | 0.224411i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56.9878 | −1.90489 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.2797i | 1.31005i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 9.95250i | − 0.331566i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.2397 | 1.10492 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 26.7650i | − 0.888717i | −0.895849 | − | 0.444358i | \(-0.853432\pi\) | ||||
0.895849 | − | 0.444358i | \(-0.146568\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.9594 | 1.15826 | 0.579128 | − | 0.815237i | \(-0.303393\pi\) | ||||
0.579128 | + | 0.815237i | \(0.303393\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.9034 | 1.28751 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.770817i | 0.0254546i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.3058 | −0.570867 | −0.285433 | − | 0.958399i | \(-0.592138\pi\) | ||||
−0.285433 | + | 0.958399i | \(0.592138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 0.185671i | − 0.00611143i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.7007i | 0.581995i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.69526 | −0.285282 | −0.142641 | − | 0.989774i | \(-0.545559\pi\) | ||||
−0.142641 | + | 0.989774i | \(0.545559\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 0.726543i | − 0.0238115i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35.8108 | 1.17114 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.8633 | 0.812249 | 0.406125 | − | 0.913818i | \(-0.366880\pi\) | ||||
0.406125 | + | 0.913818i | \(0.366880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.1562i | 0.494078i | 0.969006 | + | 0.247039i | \(0.0794575\pi\) | ||||
−0.969006 | + | 0.247039i | \(0.920542\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.67990 | 0.250092 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.6626i | 0.833922i | 0.908924 | + | 0.416961i | \(0.136905\pi\) | ||||
−0.908924 | + | 0.416961i | \(0.863095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 0.362985i | − 0.0117830i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.66478 | 0.313073 | 0.156536 | − | 0.987672i | \(-0.449967\pi\) | ||||
0.156536 | + | 0.987672i | \(0.449967\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.7256i | 1.15605i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.9782 | −0.354505 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.90488 | −0.222738 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 68.6735i | 2.21068i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.28949 | −0.202256 | −0.101128 | − | 0.994873i | \(-0.532245\pi\) | ||||
−0.101128 | + | 0.994873i | \(0.532245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 28.3396i | − 0.909462i | −0.890629 | − | 0.454731i | \(-0.849735\pi\) | ||||
0.890629 | − | 0.454731i | \(-0.150265\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 22.0189i | − 0.705895i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.0973 | 0.898911 | 0.449455 | − | 0.893303i | \(-0.351618\pi\) | ||||
0.449455 | + | 0.893303i | \(0.351618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 22.1494i | − 0.707899i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.4571 | 1.22659 | 0.613296 | − | 0.789853i | \(-0.289843\pi\) | ||||
0.613296 | + | 0.789853i | \(0.289843\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.40380 | 0.267767 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 46.7841i | − 1.48765i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.2448 | 0.960759 | 0.480380 | − | 0.877061i | \(-0.340499\pi\) | ||||
0.480380 | + | 0.877061i | \(0.340499\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 66.4376i | 2.10621i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 17.2007i | − 0.544751i | −0.962191 | − | 0.272375i | \(-0.912191\pi\) | ||||
0.962191 | − | 0.272375i | \(-0.0878093\pi\) | |||||||
\(998\) | 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.c.d.3025.4 | 16 | ||
3.2 | odd | 2 | inner | 6048.2.c.d.3025.14 | 16 | ||
4.3 | odd | 2 | 1512.2.c.d.757.15 | yes | 16 | ||
8.3 | odd | 2 | 1512.2.c.d.757.14 | yes | 16 | ||
8.5 | even | 2 | inner | 6048.2.c.d.3025.13 | 16 | ||
12.11 | even | 2 | 1512.2.c.d.757.2 | ✓ | 16 | ||
24.5 | odd | 2 | inner | 6048.2.c.d.3025.3 | 16 | ||
24.11 | even | 2 | 1512.2.c.d.757.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.d.757.2 | ✓ | 16 | 12.11 | even | 2 | ||
1512.2.c.d.757.3 | yes | 16 | 24.11 | even | 2 | ||
1512.2.c.d.757.14 | yes | 16 | 8.3 | odd | 2 | ||
1512.2.c.d.757.15 | yes | 16 | 4.3 | odd | 2 | ||
6048.2.c.d.3025.3 | 16 | 24.5 | odd | 2 | inner | ||
6048.2.c.d.3025.4 | 16 | 1.1 | even | 1 | trivial | ||
6048.2.c.d.3025.13 | 16 | 8.5 | even | 2 | inner | ||
6048.2.c.d.3025.14 | 16 | 3.2 | odd | 2 | inner |