Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2432,2,Mod(1217,2432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2432.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2432 = 2^{7} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2432.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.4196177716\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3182656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{3} + 25x^{2} - 10x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.5 | ||
Root | \(-1.67298 + 1.67298i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2432.1217 |
Dual form | 2432.2.c.g.1217.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2432\mathbb{Z}\right)^\times\).
\(n\) | \(1407\) | \(1921\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.59774i | 1.49980i | 0.661549 | + | 0.749902i | \(0.269899\pi\) | ||||
−0.661549 | + | 0.749902i | \(0.730101\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.59774i | 0.714529i | 0.934003 | + | 0.357264i | \(0.116291\pi\) | ||||
−0.934003 | + | 0.357264i | \(0.883709\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.34596 | 1.64262 | 0.821310 | − | 0.570482i | \(-0.193244\pi\) | ||||
0.821310 | + | 0.570482i | \(0.193244\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.74823 | −1.24941 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.74823i | − 0.527111i | −0.964644 | − | 0.263555i | \(-0.915105\pi\) | ||||
0.964644 | − | 0.263555i | \(-0.0848951\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.748228i | − 0.207521i | −0.994602 | − | 0.103761i | \(-0.966912\pi\) | ||||
0.994602 | − | 0.103761i | \(-0.0330876\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.15049 | −1.07165 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.2897i | 2.46361i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.94370 | −0.405289 | −0.202645 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202645 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.44724 | 0.489448 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.94370i | − 0.374065i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.28966i | 1.35366i | 0.736141 | + | 0.676828i | \(0.236646\pi\) | ||||
−0.736141 | + | 0.676828i | \(0.763354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.654037 | −0.117468 | −0.0587342 | − | 0.998274i | \(-0.518706\pi\) | ||||
−0.0587342 | + | 0.998274i | \(0.518706\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.54143 | 0.790562 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.94370i | 1.17370i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.84951i | 0.632855i | 0.948617 | + | 0.316428i | \(0.102483\pi\) | ||||
−0.948617 | + | 0.316428i | \(0.897517\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.94370 | 0.311241 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.54143 | −0.709253 | −0.354626 | − | 0.935008i | \(-0.615392\pi\) | ||||
−0.354626 | + | 0.935008i | \(0.615392\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4402i | 1.59211i | 0.605225 | + | 0.796054i | \(0.293083\pi\) | ||||
−0.605225 | + | 0.796054i | \(0.706917\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 5.98868i | − 0.892739i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.59774 | −1.10824 | −0.554122 | − | 0.832436i | \(-0.686946\pi\) | ||||
−0.554122 | + | 0.832436i | \(0.686946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.8874 | 1.69820 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.79321i | 1.09127i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.59774i | 0.906269i | 0.891442 | + | 0.453134i | \(0.149694\pi\) | ||||
−0.891442 | + | 0.453134i | \(0.850306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.79321 | 0.376636 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.59774 | 0.344078 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.74823i | 0.878544i | 0.898354 | + | 0.439272i | \(0.144764\pi\) | ||||
−0.898354 | + | 0.439272i | \(0.855236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 9.09419i | − 1.16439i | −0.813049 | − | 0.582196i | \(-0.802194\pi\) | ||||
0.813049 | − | 0.582196i | \(-0.197806\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −16.2897 | −2.05230 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.19547 | 0.148280 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.40226i | 0.904331i | 0.891934 | + | 0.452165i | \(0.149348\pi\) | ||||
−0.891934 | + | 0.452165i | \(0.850652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 5.04921i | − 0.607854i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.69901 | −0.201636 | −0.100818 | − | 0.994905i | \(-0.532146\pi\) | ||||
−0.100818 | + | 0.994905i | \(0.532146\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.6848 | 1.95281 | 0.976406 | − | 0.215941i | \(-0.0692820\pi\) | ||||
0.976406 | + | 0.215941i | \(0.0692820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.35729i | 0.734076i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.59774i | − 0.865842i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.654037 | −0.0735849 | −0.0367924 | − | 0.999323i | \(-0.511714\pi\) | ||||
−0.0367924 | + | 0.999323i | \(0.511714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.19547 | −0.688386 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 12.5793i | − 1.38076i | −0.723447 | − | 0.690380i | \(-0.757443\pi\) | ||||
0.723447 | − | 0.690380i | \(-0.242557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.79321i | 0.519896i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.9366 | −2.03022 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.5414 | 1.54139 | 0.770694 | − | 0.637205i | \(-0.219909\pi\) | ||||
0.770694 | + | 0.637205i | \(0.219909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.25177i | − 0.340878i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1.69901i | − 0.176180i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.59774 | 0.163924 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5793 | −1.07417 | −0.537084 | − | 0.843529i | \(-0.680474\pi\) | ||||
−0.537084 | + | 0.843529i | \(0.680474\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.55276i | 0.658577i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4.80453i | − 0.478069i | −0.971011 | − | 0.239034i | \(-0.923169\pi\) | ||||
0.971011 | − | 0.239034i | \(-0.0768308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.5793 | −1.23948 | −0.619739 | − | 0.784808i | \(-0.712761\pi\) | ||||
−0.619739 | + | 0.784808i | \(0.712761\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.0379 | −1.76032 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 5.44015i | − 0.525920i | −0.964807 | − | 0.262960i | \(-0.915301\pi\) | ||||
0.964807 | − | 0.262960i | \(-0.0846987\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 14.7861i | − 1.41625i | −0.706085 | − | 0.708127i | \(-0.749541\pi\) | ||||
0.706085 | − | 0.708127i | \(-0.250459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0379 | 1.32057 | 0.660287 | − | 0.751014i | \(-0.270435\pi\) | ||||
0.660287 | + | 0.751014i | \(0.270435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.10552i | − 0.289591i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.80453i | 0.259279i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.0379 | 1.19518 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.94370 | 0.722154 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 11.7974i | − 1.06374i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8987i | 1.06425i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.54852 | −0.669823 | −0.334911 | − | 0.942250i | \(-0.608706\pi\) | ||||
−0.334911 | + | 0.942250i | \(0.608706\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −27.1208 | −2.38785 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0492139i | 0.00429984i | 0.999998 | + | 0.00214992i | \(0.000684342\pi\) | ||||
−0.999998 | + | 0.00214992i | \(0.999316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.34596i | − 0.376843i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.10552 | 0.267280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.3909 | −1.48581 | −0.742904 | − | 0.669398i | \(-0.766552\pi\) | ||||
−0.742904 | + | 0.669398i | \(0.766552\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.25177i | 0.699906i | 0.936767 | + | 0.349953i | \(0.113802\pi\) | ||||
−0.936767 | + | 0.349953i | \(0.886198\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 19.7369i | − 1.66215i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.30807 | −0.109387 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6469 | −0.967226 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 30.8803i | 2.54696i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 6.28966i | − 0.515269i | −0.966242 | − | 0.257635i | \(-0.917057\pi\) | ||||
0.966242 | − | 0.257635i | \(-0.0829431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.1884 | 1.80566 | 0.902832 | − | 0.429992i | \(-0.141484\pi\) | ||||
0.902832 | + | 0.429992i | \(0.141484\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.2447 | −0.909079 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.04498i | − 0.0839346i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.99291i | 0.717713i | 0.933393 | + | 0.358856i | \(0.116833\pi\) | ||||
−0.933393 | + | 0.358856i | \(0.883167\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.1392 | −1.35922 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.44724 | −0.665736 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.9929i | − 1.33099i | −0.746403 | − | 0.665494i | \(-0.768221\pi\) | ||||
0.746403 | − | 0.665494i | \(-0.231779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.25601i | 0.564879i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.3389 | −1.26434 | −0.632170 | − | 0.774830i | \(-0.717836\pi\) | ||||
−0.632170 | + | 0.774830i | \(0.717836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4402 | 0.956935 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.74823i | 0.286634i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.3839i | 1.77784i | 0.458061 | + | 0.888921i | \(0.348544\pi\) | ||||
−0.458061 | + | 0.888921i | \(0.651456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.6356 | 0.803978 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.5301 | −1.31764 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4.54143i | − 0.339443i | −0.985492 | − | 0.169721i | \(-0.945713\pi\) | ||||
0.985492 | − | 0.169721i | \(-0.0542868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 12.0900i | − 0.898639i | −0.893371 | − | 0.449320i | \(-0.851666\pi\) | ||||
0.893371 | − | 0.449320i | \(-0.148334\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.6243 | 1.74636 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.15049 | −0.452193 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.24468i | − 0.383529i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 8.44724i | − 0.614446i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.5485 | −0.907979 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7298 | 0.772349 | 0.386175 | − | 0.922426i | \(-0.373796\pi\) | ||||
0.386175 | + | 0.922426i | \(0.373796\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.10552i | 0.222391i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.38385i | 0.668572i | 0.942472 | + | 0.334286i | \(0.108495\pi\) | ||||
−0.942472 | + | 0.334286i | \(0.891505\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2404 | 0.796814 | 0.398407 | − | 0.917209i | \(-0.369563\pi\) | ||||
0.398407 | + | 0.917209i | \(0.369563\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.2291 | −1.35632 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 31.6806i | 2.22354i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 7.25601i | − 0.506782i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.28543 | 0.506372 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.74823 | −0.120927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 5.44015i | − 0.374516i | −0.982311 | − | 0.187258i | \(-0.940040\pi\) | ||||
0.982311 | − | 0.187258i | \(-0.0599600\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 4.41359i | − 0.302414i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.6806 | −1.13761 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.84242 | −0.192956 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 43.3428i | 2.92883i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.24468i | − 0.150994i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.4217 | −1.70237 | −0.851183 | − | 0.524869i | \(-0.824114\pi\) | ||||
−0.851183 | + | 0.524869i | \(0.824114\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.17282 | −0.611521 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.74114i | 0.248308i | 0.992263 | + | 0.124154i | \(0.0396217\pi\) | ||||
−0.992263 | + | 0.124154i | \(0.960378\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5.29675i | − 0.350019i | −0.984567 | − | 0.175010i | \(-0.944004\pi\) | ||||
0.984567 | − | 0.175010i | \(-0.0559956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.7369 | 1.29859 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.93661 | −0.650969 | −0.325485 | − | 0.945547i | \(-0.605527\pi\) | ||||
−0.325485 | + | 0.945547i | \(0.605527\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 12.1392i | − 0.791872i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.69901i | − 0.110363i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.8424 | −1.80098 | −0.900488 | − | 0.434880i | \(-0.856791\pi\) | ||||
−0.900488 | + | 0.434880i | \(0.856791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.84951 | 0.376800 | 0.188400 | − | 0.982092i | \(-0.439670\pi\) | ||||
0.188400 | + | 0.982092i | \(0.439670\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 21.9253i | − 1.40651i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.9929i | 1.21341i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.748228 | −0.0476086 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 32.6778 | 2.07087 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 15.2447i | − 0.962236i | −0.876656 | − | 0.481118i | \(-0.840231\pi\) | ||||
0.876656 | − | 0.481118i | \(-0.159769\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.39803i | 0.213632i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.4515 | −0.779742 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.58641 | 0.473227 | 0.236614 | − | 0.971604i | \(-0.423962\pi\) | ||||
0.236614 | + | 0.971604i | \(0.423962\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.7298i | 1.03954i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 27.3233i | − 1.69127i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.79321 | −0.172236 | −0.0861182 | − | 0.996285i | \(-0.527446\pi\) | ||||
−0.0861182 | + | 0.996285i | \(0.527446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5414 | −0.647555 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 37.7748i | 2.31178i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 25.0308i | − 1.52615i | −0.646307 | − | 0.763077i | \(-0.723687\pi\) | ||||
0.646307 | − | 0.763077i | \(-0.276313\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.5301 | 1.67234 | 0.836168 | − | 0.548474i | \(-0.184791\pi\) | ||||
0.836168 | + | 0.548474i | \(0.184791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.44724 | 0.511250 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.27834i | − 0.257993i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 10.4023i | − 0.625012i | −0.949916 | − | 0.312506i | \(-0.898832\pi\) | ||||
0.949916 | − | 0.312506i | \(-0.101168\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.45148 | 0.146766 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8874 | 0.828453 | 0.414226 | − | 0.910174i | \(-0.364052\pi\) | ||||
0.414226 | + | 0.910174i | \(0.364052\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 27.3346i | − 1.62488i | −0.583048 | − | 0.812438i | \(-0.698140\pi\) | ||||
0.583048 | − | 0.812438i | \(-0.301860\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.15049i | 0.245854i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.7369 | −1.16503 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 27.4823i | − 1.61104i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 10.1321i | − 0.591923i | −0.955200 | − | 0.295961i | \(-0.904360\pi\) | ||||
0.955200 | − | 0.295961i | \(-0.0956399\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.7819 | −0.627745 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.39803 | −0.197174 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.45433i | 0.0841061i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 45.3725i | 2.61523i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.4809 | 0.717009 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.5301 | 0.831992 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1208i | 0.977133i | 0.872527 | + | 0.488567i | \(0.162480\pi\) | ||||
−0.872527 | + | 0.488567i | \(0.837520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 32.6778i | − 1.85897i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.2404 | 1.77148 | 0.885742 | − | 0.464179i | \(-0.153650\pi\) | ||||
0.885742 | + | 0.464179i | \(0.153650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.2291 | 1.42603 | 0.713017 | − | 0.701147i | \(-0.247328\pi\) | ||||
0.713017 | + | 0.701147i | \(0.247328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 26.0266i | − 1.46643i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.6427i | 0.653920i | 0.945038 | + | 0.326960i | \(0.106024\pi\) | ||||
−0.945038 | + | 0.326960i | \(0.893976\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.7440 | 0.713527 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.1321 | 0.788776 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.00000i | − 0.166924i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.83110i | − 0.101571i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 38.4104 | 2.12410 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −33.0195 | −1.82042 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 12.5977i | − 0.692434i | −0.938154 | − | 0.346217i | \(-0.887466\pi\) | ||||
0.938154 | − | 0.346217i | \(-0.112534\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 14.4288i | − 0.790695i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.8269 | −0.646170 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.49646 | −0.299411 | −0.149706 | − | 0.988731i | \(-0.547833\pi\) | ||||
−0.149706 | + | 0.988731i | \(0.547833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.4667i | 1.98060i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.14341i | 0.0619189i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.2404 | 1.14688 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.06731 | 0.434329 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 10.3417i | − 0.555173i | −0.960701 | − | 0.277586i | \(-0.910465\pi\) | ||||
0.960701 | − | 0.277586i | \(-0.0895345\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.6806i | 1.64230i | 0.570716 | + | 0.821148i | \(0.306666\pi\) | ||||
−0.570716 | + | 0.821148i | \(0.693334\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.45433 | −0.0776264 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.3276 | 1.24160 | 0.620800 | − | 0.783969i | \(-0.286808\pi\) | ||||
0.620800 | + | 0.783969i | \(0.286808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.71457i | − 0.144075i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 33.8690i | 1.79254i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1576 | 0.641653 | 0.320826 | − | 0.947138i | \(-0.396039\pi\) | ||||
0.320826 | + | 0.947138i | \(0.396039\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.6356i | 1.08309i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.6580i | 1.39534i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.08287 | −0.474122 | −0.237061 | − | 0.971495i | \(-0.576184\pi\) | ||||
−0.237061 | + | 0.971495i | \(0.576184\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.0223 | 0.886147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.6735i | 1.48865i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 18.1321i | − 0.938844i | −0.882974 | − | 0.469422i | \(-0.844462\pi\) | ||||
0.882974 | − | 0.469422i | \(-0.155538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −30.9097 | −1.59617 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.45433 | 0.280912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 23.6427i | − 1.21444i | −0.794532 | − | 0.607222i | \(-0.792284\pi\) | ||||
0.794532 | − | 0.607222i | \(-0.207716\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 19.6091i | − 1.00460i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.9253 | 1.12033 | 0.560165 | − | 0.828381i | \(-0.310738\pi\) | ||||
0.560165 | + | 0.828381i | \(0.310738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.1392 | 0.618669 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 39.1321i | − 1.98920i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 29.2599i | − 1.48354i | −0.670656 | − | 0.741769i | \(-0.733987\pi\) | ||||
0.670656 | − | 0.741769i | \(-0.266013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.83110 | −0.294891 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.127845 | −0.00644892 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.04498i | − 0.0525785i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.10128i | 0.306214i | 0.988210 | + | 0.153107i | \(0.0489280\pi\) | ||||
−0.988210 | + | 0.153107i | \(0.951072\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.2897 | 0.565190 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.0379 | 0.800894 | 0.400447 | − | 0.916320i | \(-0.368855\pi\) | ||||
0.400447 | + | 0.916320i | \(0.368855\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.489369i | 0.0243772i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 9.89872i | − 0.491871i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.72982 | 0.333585 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.5343 | 1.26259 | 0.631296 | − | 0.775542i | \(-0.282523\pi\) | ||||
0.631296 | + | 0.775542i | \(0.282523\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 45.1771i | − 2.22842i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.3276i | 1.44311i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.0984 | 0.986593 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.4359 | −1.04972 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 35.1586i | − 1.71761i | −0.512301 | − | 0.858806i | \(-0.671207\pi\) | ||||
0.512301 | − | 0.858806i | \(-0.328793\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.89872i | 0.141275i | 0.997502 | + | 0.0706375i | \(0.0225034\pi\) | ||||
−0.997502 | + | 0.0706375i | \(0.977497\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.4780 | 1.38465 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.34173 | 0.356126 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 39.5230i | − 1.91265i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3.39803i | − 0.164058i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.9774 | −1.25129 | −0.625643 | − | 0.780110i | \(-0.715163\pi\) | ||||
−0.625643 | + | 0.780110i | \(0.715163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.9324 | 1.48652 | 0.743258 | − | 0.669005i | \(-0.233280\pi\) | ||||
0.743258 | + | 0.669005i | \(0.233280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 30.2557i | − 1.45065i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.94370i | 0.0929797i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1278 | 0.483376 | 0.241688 | − | 0.970354i | \(-0.422299\pi\) | ||||
0.241688 | + | 0.970354i | \(0.422299\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −44.5567 | −2.12175 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.3276i | 0.680723i | 0.940295 | + | 0.340361i | \(0.110549\pi\) | ||||
−0.940295 | + | 0.340361i | \(0.889451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.2334i | 1.10137i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.3389 | 0.772802 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.61615 | 0.312235 | 0.156118 | − | 0.987738i | \(-0.450102\pi\) | ||||
0.156118 | + | 0.987738i | \(0.450102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.93946i | 0.373855i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 57.6395i | 2.70814i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.19547 | 0.243567 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.5864 | −1.80500 | −0.902498 | − | 0.430694i | \(-0.858269\pi\) | ||||
−0.902498 | + | 0.430694i | \(0.858269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 5.83110i | − 0.272172i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.1841i | 1.54554i | 0.634686 | + | 0.772770i | \(0.281129\pi\) | ||||
−0.634686 | + | 0.772770i | \(0.718871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2826 | −0.617294 | −0.308647 | − | 0.951177i | \(-0.599876\pi\) | ||||
−0.308647 | + | 0.951177i | \(0.599876\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.71457 | 0.125885 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.8311i | 0.963948i | 0.876185 | + | 0.481974i | \(0.160080\pi\) | ||||
−0.876185 | + | 0.481974i | \(0.839920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.1700i | 1.48547i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.3612 | −1.07643 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.2518 | 0.839217 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.44724i | − 0.112287i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 24.7298i | − 1.13230i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.6848 | −1.17357 | −0.586785 | − | 0.809743i | \(-0.699607\pi\) | ||||
−0.586785 | + | 0.809743i | \(0.699607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.88031 | 0.131331 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 21.9437i | − 0.998473i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 16.9030i | − 0.767524i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.51063 | 0.430968 | 0.215484 | − | 0.976507i | \(-0.430867\pi\) | ||||
0.215484 | + | 0.976507i | \(0.430867\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 44.1431 | 1.99622 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.89448i | 0.311144i | 0.987825 | + | 0.155572i | \(0.0497220\pi\) | ||||
−0.987825 | + | 0.155572i | \(0.950278\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.8690i | 0.984930i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.4696 | −0.470572 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.38385 | −0.331211 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 29.1321i | − 1.30413i | −0.758163 | − | 0.652066i | \(-0.773903\pi\) | ||||
0.758163 | − | 0.652066i | \(-0.226097\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 42.4441i | − 1.89626i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1533 | 0.586479 | 0.293239 | − | 0.956039i | \(-0.405267\pi\) | ||||
0.293239 | + | 0.956039i | \(0.405267\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.67637 | 0.341594 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.3162i | 1.43521i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 32.5651i | − 1.44342i | −0.692193 | − | 0.721712i | \(-0.743355\pi\) | ||||
0.692193 | − | 0.721712i | \(-0.256645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 72.5117 | 3.20773 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.94370 | −0.0858164 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 20.0984i | − 0.885643i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2826i | 0.584167i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −60.7451 | −2.66641 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0450 | −0.571511 | −0.285755 | − | 0.958303i | \(-0.592244\pi\) | ||||
−0.285755 | + | 0.958303i | \(0.592244\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9437i | 0.522261i | 0.965303 | + | 0.261131i | \(0.0840954\pi\) | ||||
−0.965303 | + | 0.261131i | \(0.915905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27.6285i | 1.20581i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.96211 | −0.0854709 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2220 | −0.835741 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 25.2939i | − 1.09766i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.39803i | 0.147185i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.69193 | 0.375785 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.7974 | 0.509097 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 20.7819i | − 0.895139i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.48513i | − 0.0638508i | −0.999490 | − | 0.0319254i | \(-0.989836\pi\) | ||||
0.999490 | − | 0.0319254i | \(-0.0101639\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.4065 | 1.34778 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.6243 | 1.01195 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6.01418i | − 0.257148i | −0.991700 | − | 0.128574i | \(-0.958960\pi\) | ||||
0.991700 | − | 0.128574i | \(-0.0410399\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 34.0871i | 1.45480i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.28966 | 0.310550 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.84242 | −0.120872 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 15.9774i | − 0.678201i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.3584i | 1.15921i | 0.814897 | + | 0.579605i | \(0.196793\pi\) | ||||
−0.814897 | + | 0.579605i | \(0.803207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.81162 | 0.330396 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.6243 | 0.575218 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.1434i | 0.891088i | 0.895260 | + | 0.445544i | \(0.146990\pi\) | ||||
−0.895260 | + | 0.445544i | \(0.853010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.4288i | 0.943588i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.9253 | −1.13076 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.0000 | −1.00613 | −0.503066 | − | 0.864248i | \(-0.667795\pi\) | ||||
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.18130i | 0.384225i | 0.981373 | + | 0.192113i | \(0.0615339\pi\) | ||||
−0.981373 | + | 0.192113i | \(0.938466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 32.5977i | − 1.36179i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.75670 | −0.198368 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.79744 | −0.199720 | −0.0998601 | − | 0.995001i | \(-0.531840\pi\) | ||||
−0.0998601 | + | 0.995001i | \(0.531840\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.8732i | 1.15837i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 54.6693i | − 2.26806i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.5343 | 0.477704 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.48090 | −0.185262 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.64980i | − 0.0680945i | −0.999420 | − | 0.0340473i | \(-0.989160\pi\) | ||||
0.999420 | − | 0.0340473i | \(-0.0108397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.654037i | 0.0269491i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.3768 | −1.00273 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.8874 | −0.816678 | −0.408339 | − | 0.912830i | \(-0.633892\pi\) | ||||
−0.408339 | + | 0.912830i | \(0.633892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.8311i | 0.853992i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.1997i | 1.19506i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.25462 | −0.0921214 | −0.0460607 | − | 0.998939i | \(-0.514667\pi\) | ||||
−0.0460607 | + | 0.998939i | \(0.514667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.7677 | −1.01030 | −0.505148 | − | 0.863033i | \(-0.668562\pi\) | ||||
−0.505148 | + | 0.863033i | \(0.668562\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 27.7454i | − 1.12988i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.6919i | 0.516000i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.9774 | 1.86616 | 0.933082 | − | 0.359665i | \(-0.117109\pi\) | ||||
0.933082 | + | 0.359665i | \(0.117109\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −82.2978 | −3.33488 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.68484i | 0.229984i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 0.326485i | − 0.0131866i | −0.999978 | − | 0.00659330i | \(-0.997901\pi\) | ||||
0.999978 | − | 0.00659330i | \(-0.00209873\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.8492 | 0.760073 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.9140 | 1.52636 | 0.763179 | − | 0.646187i | \(-0.223637\pi\) | ||||
0.763179 | + | 0.646187i | \(0.223637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4.76771i | − 0.191630i | −0.995399 | − | 0.0958151i | \(-0.969454\pi\) | ||||
0.995399 | − | 0.0958151i | \(-0.0305458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.77796i | 0.151604i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 63.1965 | 2.53192 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.77479 | −0.270992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.54143i | − 0.181367i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.5485i | 0.460470i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9958 | 0.437734 | 0.218867 | − | 0.975755i | \(-0.429764\pi\) | ||||
0.218867 | + | 0.975755i | \(0.429764\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.1321 | 0.561700 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 12.0605i | − 0.478608i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8.89448i | − 0.352412i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.36829 | 0.251926 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.1586 | −0.993707 | −0.496853 | − | 0.867834i | \(-0.665511\pi\) | ||||
−0.496853 | + | 0.867834i | \(0.665511\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9069i | 1.45547i | 0.685861 | + | 0.727733i | \(0.259426\pi\) | ||||
−0.685861 | + | 0.727733i | \(0.740574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 43.3318i | − 1.70619i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.3531 | 0.682219 | 0.341109 | − | 0.940024i | \(-0.389197\pi\) | ||||
0.341109 | + | 0.940024i | \(0.389197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.7974 | 0.463090 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 7.38385i | − 0.289396i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 14.4780i | − 0.566570i | −0.959036 | − | 0.283285i | \(-0.908576\pi\) | ||||
0.959036 | − | 0.283285i | \(-0.0914242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0786309 | −0.00307236 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −62.5386 | −2.43986 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.5301i | 1.85151i | 0.378124 | + | 0.925755i | \(0.376569\pi\) | ||||
−0.378124 | + | 0.925755i | \(0.623431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 8.22204i | − 0.319800i | −0.987133 | − | 0.159900i | \(-0.948883\pi\) | ||||
0.987133 | − | 0.159900i | \(-0.0511172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.83110 | 0.226461 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.94370 | 0.269265 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 14.1689i | − 0.548622i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 66.0390i | − 2.55321i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.8987 | −0.613763 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.9016 | 0.612961 | 0.306480 | − | 0.951877i | \(-0.400849\pi\) | ||||
0.306480 | + | 0.951877i | \(0.400849\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 4.75670i | − 0.183086i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.9816i | 0.844821i | 0.906405 | + | 0.422411i | \(0.138816\pi\) | ||||
−0.906405 | + | 0.422411i | \(0.861184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.9774 | −1.76445 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.71849 | −0.372413 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.30807i | − 0.0500520i | −0.999687 | − | 0.0250260i | \(-0.992033\pi\) | ||||
0.999687 | − | 0.0250260i | \(-0.00796686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 27.7861i | − 1.06165i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.7596 | 0.524960 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.93661 | 0.188070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 44.2291i | − 1.68256i | −0.540603 | − | 0.841278i | \(-0.681804\pi\) | ||||
0.540603 | − | 0.841278i | \(-0.318196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.4780i | 1.08179i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.1841 | −0.500103 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.6243 | −0.516057 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 25.8127i | − 0.976325i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 24.5793i | − 0.928348i | −0.885744 | − | 0.464174i | \(-0.846351\pi\) | ||||
0.885744 | − | 0.464174i | \(-0.153649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.84951 | 0.145187 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.5343 | 1.18765 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 20.8803i | − 0.785285i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.39803i | 0.352950i | 0.984305 | + | 0.176475i | \(0.0564695\pi\) | ||||
−0.984305 | + | 0.176475i | \(0.943530\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.45148 | 0.0919376 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.27125 | 0.0476087 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.08995i | − 0.0781599i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 72.3272i | − 2.70111i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.3460 | −0.907951 | −0.453976 | − | 0.891014i | \(-0.649995\pi\) | ||||
−0.453976 | + | 0.891014i | \(0.649995\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.6693 | −2.03599 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.1955i | 0.565126i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.8396i | 0.662545i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1137 | −1.07977 | −0.539883 | − | 0.841740i | \(-0.681532\pi\) | ||||
−0.539883 | + | 0.841740i | \(0.681532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.3697 | 1.42110 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.3205i | 1.15843i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.91713i | − 0.181618i | −0.995868 | − | 0.0908092i | \(-0.971055\pi\) | ||||
0.995868 | − | 0.0908092i | \(-0.0289453\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −49.3386 | −1.81988 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9408 | 0.476682 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 51.7114i | − 1.90223i | −0.308830 | − | 0.951117i | \(-0.599937\pi\) | ||||
0.308830 | − | 0.951117i | \(-0.400063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.94370i | − 0.0714035i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0379 | 0.661746 | 0.330873 | − | 0.943675i | \(-0.392657\pi\) | ||||
0.330873 | + | 0.943675i | \(0.392657\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0492 | 0.368175 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 47.1502i | 1.72513i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 23.6427i | − 0.863886i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9171 | 0.398372 | 0.199186 | − | 0.979962i | \(-0.436170\pi\) | ||||
0.199186 | + | 0.979962i | \(0.436170\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.6017 | 1.44316 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.4512i | 1.29020i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 33.4710i | − 1.21652i | −0.793737 | − | 0.608261i | \(-0.791867\pi\) | ||||
0.793737 | − | 0.608261i | \(-0.208133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.82718 | −0.320406 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.3399 | 1.86107 | 0.930536 | − | 0.366201i | \(-0.119342\pi\) | ||||
0.930536 | + | 0.366201i | \(0.119342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 64.2599i | − 2.32637i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 17.9660i | − 0.649563i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.04921 | 0.182317 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.7974 | 0.605731 | 0.302866 | − | 0.953033i | \(-0.402057\pi\) | ||||
0.302866 | + | 0.953033i | \(0.402057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.7075i | 0.709748i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 8.62145i | − 0.310092i | −0.987907 | − | 0.155046i | \(-0.950447\pi\) | ||||
0.987907 | − | 0.155046i | \(-0.0495526\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.60059 | −0.0574948 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −43.4596 | −1.55911 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.54143i | 0.162714i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.97026i | 0.106284i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1689 | 0.506355 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.3683 | −0.512826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 25.0124i | − 0.891595i | −0.895134 | − | 0.445798i | \(-0.852920\pi\) | ||||
0.895134 | − | 0.445798i | \(-0.147080\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 7.25601i | − 0.258321i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.0082 | 2.16920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.80453 | −0.241636 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 27.3839i | − 0.971205i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 48.0574i | − 1.70228i | −0.524939 | − | 0.851140i | \(-0.675912\pi\) | ||||
0.524939 | − | 0.851140i | \(-0.324088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.7932 | −0.806366 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −54.5046 | −1.92583 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 29.1689i | − 1.02935i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 13.4965i | − 0.475688i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 65.0234 | 2.28893 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.20965 | −0.218320 | −0.109160 | − | 0.994024i | \(-0.534816\pi\) | ||||
−0.109160 | + | 0.994024i | \(0.534816\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.6130i | 0.934508i | 0.884123 | + | 0.467254i | \(0.154757\pi\) | ||||
−0.884123 | + | 0.467254i | \(0.845243\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 71.5159i | 2.50817i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.1502 | 0.951029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4402 | 0.365255 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.1884i | 0.425897i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 25.4993i | − 0.889932i | −0.895547 | − | 0.444966i | \(-0.853216\pi\) | ||||
0.895547 | − | 0.444966i | \(-0.146784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.0166 | 1.18575 | 0.592873 | − | 0.805296i | \(-0.297994\pi\) | ||||
0.592873 | + | 0.805296i | \(0.297994\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.1140 | 0.386939 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.6048i | 0.890367i | 0.895439 | + | 0.445183i | \(0.146862\pi\) | ||||
−0.895439 | + | 0.445183i | \(0.853138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0350i | 0.661114i | 0.943786 | + | 0.330557i | \(0.107237\pi\) | ||||
−0.943786 | + | 0.330557i | \(0.892763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.0223 | 0.937394 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.6622 | 1.23562 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 26.1052i | − 0.903408i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.27125i | 0.0439408i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.6848 | −0.541501 | −0.270750 | − | 0.962650i | \(-0.587272\pi\) | ||||
−0.270750 | + | 0.962650i | \(0.587272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1392 | −0.832385 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36.0758i | 1.24252i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.8761i | 0.683758i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.5230 | 1.18623 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 71.0082 | 2.43699 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 7.48228i | − 0.256489i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.57224i | − 0.122311i | −0.998128 | − | 0.0611555i | \(-0.980521\pi\) | ||||
0.998128 | − | 0.0611555i | \(-0.0194786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.98868 | −0.204808 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.7309 | −1.93789 | −0.968945 | − | 0.247276i | \(-0.920464\pi\) | ||||
−0.968945 | + | 0.247276i | \(0.920464\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.6059i | 0.634825i | 0.948288 | + | 0.317412i | \(0.102814\pi\) | ||||
−0.948288 | + | 0.317412i | \(0.897186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 51.2713i | − 1.74732i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.9395 | 0.610666 | 0.305333 | − | 0.952246i | \(-0.401232\pi\) | ||||
0.305333 | + | 0.952246i | \(0.401232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.3612 | −1.27032 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 20.7819i | − 0.705790i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.14341i | 0.0387874i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.53858 | 0.187668 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.6537 | 1.34208 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.7114i | 1.74816i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 57.6201i | − 1.94569i | −0.231455 | − | 0.972846i | \(-0.574349\pi\) | ||||
0.231455 | − | 0.972846i | \(-0.425651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.3205 | 0.887767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.3431 | 0.516923 | 0.258461 | − | 0.966022i | \(-0.416785\pi\) | ||||
0.258461 | + | 0.966022i | \(0.416785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 17.8608i | − 0.601065i | −0.953772 | − | 0.300532i | \(-0.902836\pi\) | ||||
0.953772 | − | 0.300532i | \(-0.0971644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 28.0085i | − 0.941495i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.1445 | −1.65011 | −0.825055 | − | 0.565053i | \(-0.808856\pi\) | ||||
−0.825055 | + | 0.565053i | \(0.808856\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.8056 | −1.10026 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.8311i | 0.362855i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.59774i | 0.254249i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.25601 | 0.242542 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.77796 | −0.126143 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 4.76771i | − 0.159012i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7932i | 0.659407i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −117.866 | −3.92233 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.3165 | 0.642104 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 9.19971i | − 0.305471i | −0.988267 | − | 0.152736i | \(-0.951192\pi\) | ||||
0.988267 | − | 0.152736i | \(-0.0488083\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.0085i | 0.597303i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.2939 | −0.838024 | −0.419012 | − | 0.907981i | \(-0.637624\pi\) | ||||
−0.419012 | + | 0.907981i | \(0.637624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9915 | −0.727813 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 37.7454i | 1.24782i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.213882i | 0.00706301i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.8155 | 1.47833 | 0.739164 | − | 0.673525i | \(-0.235221\pi\) | ||||
0.739164 | + | 0.673525i | \(0.235221\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −44.4752 | −1.46551 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.27125i | 0.0418437i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.42068i | 0.309750i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.1502 | 1.54861 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.65119 | −0.185409 | −0.0927047 | − | 0.995694i | \(-0.529551\pi\) | ||||
−0.0927047 | + | 0.995694i | \(0.529551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 11.8874i | − 0.389594i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 81.1544i | 2.65688i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.37962 | 0.274043 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.58641 | 0.280506 | 0.140253 | − | 0.990116i | \(-0.455208\pi\) | ||||
0.140253 | + | 0.990116i | \(0.455208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 65.5386i | 2.13877i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 34.8155i | − 1.13495i | −0.823389 | − | 0.567477i | \(-0.807920\pi\) | ||||
0.823389 | − | 0.567477i | \(-0.192080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.82718 | 0.287452 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.4965 | 0.439040 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 18.6551i | − 0.606209i | −0.952957 | − | 0.303105i | \(-0.901977\pi\) | ||||
0.952957 | − | 0.303105i | \(-0.0980232\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 12.4841i | − 0.405250i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.2447 | −0.980751 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.7227 | −1.22196 | −0.610980 | − | 0.791646i | \(-0.709224\pi\) | ||||
−0.610980 | + | 0.791646i | \(0.709224\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 20.0492i | − 0.648777i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.1055i | 1.07015i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −75.5804 | −2.44062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5722 | −0.986201 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.3909i | 0.657089i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.1434i | 0.551866i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.3683 | −0.847947 | −0.423974 | − | 0.905675i | \(-0.639365\pi\) | ||||
−0.423974 | + | 0.905675i | \(0.639365\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.79321 | 0.250354 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 0.978737i | − 0.0314092i | −0.999877 | − | 0.0157046i | \(-0.995001\pi\) | ||||
0.999877 | − | 0.0157046i | \(-0.00499913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.8619i | 1.14968i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.75670 | 0.152336 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.254623 | −0.00814611 | −0.00407306 | − | 0.999992i | \(-0.501296\pi\) | ||||
−0.00407306 | + | 0.999992i | \(0.501296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 25.4217i | − 0.812482i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 55.4217i | 1.76948i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49.3754 | −1.57483 | −0.787415 | − | 0.616423i | \(-0.788581\pi\) | ||||
−0.787415 | + | 0.616423i | \(0.788581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.9929 | −0.477714 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 85.7759i | − 2.73028i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 20.2925i | − 0.645264i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.6101 | −1.19473 | −0.597363 | − | 0.801971i | \(-0.703785\pi\) | ||||
−0.597363 | + | 0.801971i | \(0.703785\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.7256 | 1.03851 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.9593i | 0.569347i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.3867i | 0.613983i | 0.951712 | + | 0.306992i | \(0.0993223\pi\) | ||||
−0.951712 | + | 0.306992i | \(0.900678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.48228 | 0.236729 |
(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 | 2432.2.c.g.1217.5 | yes | 6 | |
4.3 | odd | 2 | 2432.2.c.f.1217.2 | ✓ | 6 | ||
8.3 | odd | 2 | 2432.2.c.f.1217.5 | yes | 6 | ||
8.5 | even | 2 | inner | 2432.2.c.g.1217.2 | yes | 6 | |
16.3 | odd | 4 | 4864.2.a.be.1.3 | 3 | |||
16.5 | even | 4 | 4864.2.a.bf.1.3 | 3 | |||
16.11 | odd | 4 | 4864.2.a.bd.1.1 | 3 | |||
16.13 | even | 4 | 4864.2.a.bc.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.f.1217.2 | ✓ | 6 | 4.3 | odd | 2 | ||
2432.2.c.f.1217.5 | yes | 6 | 8.3 | odd | 2 | ||
2432.2.c.g.1217.2 | yes | 6 | 8.5 | even | 2 | inner | |
2432.2.c.g.1217.5 | yes | 6 | 1.1 | even | 1 | trivial | |
4864.2.a.bc.1.1 | 3 | 16.13 | even | 4 | |||
4864.2.a.bd.1.1 | 3 | 16.11 | odd | 4 | |||
4864.2.a.be.1.3 | 3 | 16.3 | odd | 4 | |||
4864.2.a.bf.1.3 | 3 | 16.5 | even | 4 |