Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(191,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.p (of order \(6\), degree \(2\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 191.11 | ||
Character | \(\chi\) | \(=\) | 1152.191 |
Dual form | 1152.2.p.f.959.11 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.54472 | + | 0.783472i | 0.891847 | + | 0.452338i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.07112 | − | 1.85524i | −0.479020 | − | 0.829687i | 0.520690 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240584i | \(0.992341\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.13037 | − | 0.652621i | −0.427241 | − | 0.246668i | 0.270930 | − | 0.962599i | \(-0.412669\pi\) |
−0.698170 | + | 0.715932i | \(0.746002\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.77234 | + | 2.42050i | 0.590781 | + | 0.806832i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.36103 | + | 1.36314i | 0.711876 | + | 0.411002i | 0.811755 | − | 0.583998i | \(-0.198512\pi\) |
−0.0998790 | + | 0.995000i | \(0.531846\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.16603 | − | 0.673209i | 0.323399 | − | 0.186715i | −0.329507 | − | 0.944153i | \(-0.606883\pi\) |
0.652907 | + | 0.757438i | \(0.273549\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.201060 | − | 3.70502i | −0.0519135 | − | 0.956633i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.27575i | − | 1.03702i | −0.855071 | − | 0.518511i | \(-0.826487\pi\) | ||
0.855071 | − | 0.518511i | \(-0.173513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.16174 | 0.495937 | 0.247968 | − | 0.968768i | \(-0.420237\pi\) | ||||
0.247968 | + | 0.968768i | \(0.420237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.23480 | − | 1.89374i | −0.269456 | − | 0.413247i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.01947 | + | 1.76577i | 0.212573 | + | 0.368188i | 0.952519 | − | 0.304479i | \(-0.0984822\pi\) |
−0.739946 | + | 0.672666i | \(0.765149\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.205398 | − | 0.355759i | 0.0410796 | − | 0.0711519i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.841387 | + | 5.12758i | 0.161925 | + | 0.986803i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.72776 | − | 4.72461i | 0.506531 | − | 0.877338i | −0.493440 | − | 0.869780i | \(-0.664261\pi\) |
0.999971 | − | 0.00755840i | \(-0.00240594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.09216 | − | 3.51731i | 1.09418 | − | 0.631728i | 0.159497 | − | 0.987198i | \(-0.449013\pi\) |
0.934688 | + | 0.355470i | \(0.115679\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.57915 | + | 3.95547i | 0.448973 | + | 0.688559i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.79615i | 0.472635i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.3381i | 1.69957i | 0.527126 | + | 0.849787i | \(0.323269\pi\) | ||||
−0.527126 | + | 0.849787i | \(0.676731\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.32864 | − | 0.126368i | 0.372881 | − | 0.0202351i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.596355 | − | 0.344306i | 0.0931350 | − | 0.0537715i | −0.452709 | − | 0.891658i | \(-0.649542\pi\) |
0.545844 | + | 0.837887i | \(0.316209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.22839 | − | 2.12763i | 0.187327 | − | 0.324460i | −0.757031 | − | 0.653379i | \(-0.773351\pi\) |
0.944358 | + | 0.328919i | \(0.106684\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.59220 | − | 5.88076i | 0.386422 | − | 0.876652i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.56713 | − | 11.3746i | 0.957914 | − | 1.65916i | 0.230359 | − | 0.973106i | \(-0.426010\pi\) |
0.727555 | − | 0.686049i | \(-0.240657\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.64817 | − | 4.58677i | −0.378310 | − | 0.655252i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.34993 | − | 6.60485i | 0.469084 | − | 0.924864i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.56171 | −1.31340 | −0.656701 | − | 0.754151i | \(-0.728049\pi\) | ||||
−0.656701 | + | 0.754151i | \(0.728049\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.84035i | − | 0.787513i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.33929 | + | 1.69366i | 0.442299 | + | 0.224331i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.97985 | − | 5.18452i | 1.16908 | − | 0.674967i | 0.215615 | − | 0.976479i | \(-0.430825\pi\) |
0.953463 | + | 0.301512i | \(0.0974912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.68757 | + | 4.43842i | 0.984292 | + | 0.568281i | 0.903563 | − | 0.428455i | \(-0.140942\pi\) |
0.0807290 | + | 0.996736i | \(0.474275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.423741 | − | 3.89273i | −0.0533863 | − | 0.490438i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.49793 | − | 1.44218i | −0.309829 | − | 0.178880i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.23532 | + | 10.7999i | 0.761766 | + | 1.31942i | 0.941940 | + | 0.335782i | \(0.109001\pi\) |
−0.180174 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.191364 | + | 3.52635i | 0.0230375 | + | 0.424522i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.94992 | −0.587448 | −0.293724 | − | 0.955890i | \(-0.594895\pi\) | ||||
−0.293724 | + | 0.955890i | \(0.594895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8268 | −1.50126 | −0.750630 | − | 0.660723i | \(-0.770250\pi\) | ||||
−0.750630 | + | 0.660723i | \(0.770250\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.596010 | − | 0.388627i | 0.0688214 | − | 0.0448747i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.77923 | − | 3.08171i | −0.202762 | − | 0.351194i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.680856 | − | 0.393093i | −0.0766023 | − | 0.0442264i | 0.461210 | − | 0.887291i | \(-0.347416\pi\) |
−0.537812 | + | 0.843065i | \(0.680749\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.71761 | + | 8.57990i | −0.301956 | + | 0.953322i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.82152 | − | 1.05165i | −0.199938 | − | 0.115434i | 0.396689 | − | 0.917953i | \(-0.370159\pi\) |
−0.596626 | + | 0.802519i | \(0.703493\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.93253 | + | 4.57985i | −0.860404 | + | 0.496754i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.91523 | − | 5.16110i | 0.848602 | − | 0.553328i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 12.1722i | − | 1.29025i | −0.764077 | − | 0.645125i | \(-0.776805\pi\) | ||
0.764077 | − | 0.645125i | \(-0.223195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.75740 | −0.184226 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.1664 | − | 0.660234i | 1.26160 | − | 0.0684631i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.31548 | − | 4.01053i | −0.237564 | − | 0.411472i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.05440 | + | 13.9506i | −0.817801 | + | 1.41647i | 0.0894986 | + | 0.995987i | \(0.471474\pi\) |
−0.907299 | + | 0.420485i | \(0.861860\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.885074 | + | 8.13081i | 0.0889533 | + | 0.817177i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.26875 | + | 12.5898i | −0.723267 | + | 1.25274i | 0.236416 | + | 0.971652i | \(0.424027\pi\) |
−0.959683 | + | 0.281084i | \(0.909306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.14001 | − | 1.81289i | 0.309395 | − | 0.178629i | −0.337261 | − | 0.941411i | \(-0.609500\pi\) |
0.646656 | + | 0.762782i | \(0.276167\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.19070 | + | 4.31927i | −0.213791 | + | 0.421518i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6508i | 1.12632i | 0.826347 | + | 0.563161i | \(0.190415\pi\) | ||||
−0.826347 | + | 0.563161i | \(0.809585\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.96341i | 0.666974i | 0.942755 | + | 0.333487i | \(0.108225\pi\) | ||||
−0.942755 | + | 0.333487i | \(0.891775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.09962 | + | 15.9695i | −0.768782 | + | 1.51576i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.7540 | − | 6.78616i | 1.10572 | − | 0.638388i | 0.168003 | − | 0.985786i | \(-0.446268\pi\) |
0.937718 | + | 0.347398i | \(0.112935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.18394 | − | 3.78270i | 0.203654 | − | 0.352739i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.69611 | + | 1.62922i | 0.341705 | + | 0.150621i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.79045 | + | 4.83319i | −0.255800 | + | 0.443058i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.78370 | − | 3.08946i | −0.162155 | − | 0.280860i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.19096 | − | 0.0646296i | 0.107385 | − | 0.00582745i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.5912 | −1.03675 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.0340i | 1.95520i | 0.210465 | + | 0.977601i | \(0.432502\pi\) | ||||
−0.210465 | + | 0.977601i | \(0.567498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.56446 | − | 2.32419i | 0.313833 | − | 0.204634i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.64258 | + | 0.948346i | −0.143513 | + | 0.0828573i | −0.570037 | − | 0.821619i | \(-0.693071\pi\) |
0.426524 | + | 0.904476i | \(0.359738\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.44357 | − | 1.41080i | −0.211884 | − | 0.122331i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.61165 | − | 7.05323i | 0.741172 | − | 0.607046i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.63976 | + | 1.52407i | 0.225530 | + | 0.130210i | 0.608508 | − | 0.793548i | \(-0.291768\pi\) |
−0.382978 | + | 0.923757i | \(0.625102\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.82552 | + | 3.16190i | 0.154839 | + | 0.268189i | 0.933000 | − | 0.359875i | \(-0.117181\pi\) |
−0.778161 | + | 0.628064i | \(0.783848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.0561 | − | 12.4254i | 1.60481 | − | 1.04641i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.67071 | 0.306960 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6870 | −0.970555 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.497088 | − | 9.16006i | −0.0409991 | − | 0.755509i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.98401 | − | 12.0967i | −0.572153 | − | 0.990997i | −0.996345 | − | 0.0854250i | \(-0.972775\pi\) |
0.424192 | − | 0.905572i | \(-0.360558\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.4354 | − | 11.2211i | −1.58163 | − | 0.913156i | −0.994621 | − | 0.103578i | \(-0.966971\pi\) |
−0.587012 | − | 0.809578i | \(-0.699696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.3494 | − | 7.57809i | 0.836702 | − | 0.612653i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.0509 | − | 7.53494i | −1.04827 | − | 0.605221i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.67761 | − | 1.54592i | 0.213697 | − | 0.123378i | −0.389332 | − | 0.921098i | \(-0.627294\pi\) |
0.603028 | + | 0.797720i | \(0.293961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.7702 | − | 7.49133i | −1.17135 | − | 0.594101i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.66130i | − | 0.209740i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4313 | −0.817042 | −0.408521 | − | 0.912749i | \(-0.633955\pi\) | ||||
−0.408521 | + | 0.912749i | \(0.633955\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.57575 | − | 9.02173i | 0.356222 | − | 0.702341i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.50275 | + | 11.2631i | 0.503198 | + | 0.871564i | 0.999993 | + | 0.00369641i | \(0.00117661\pi\) |
−0.496795 | + | 0.867868i | \(0.665490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.59358 | + | 9.68836i | −0.430275 | + | 0.745259i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.83134 | + | 5.23248i | 0.292990 | + | 0.400138i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.69963 | − | 4.67590i | 0.205249 | − | 0.355502i | −0.744963 | − | 0.667106i | \(-0.767533\pi\) |
0.950212 | + | 0.311604i | \(0.100866\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.464352 | + | 0.268094i | −0.0351017 | + | 0.0202660i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.9333 | − | 0.973185i | 1.34795 | − | 0.0731491i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.69284i | − | 0.350759i | −0.984501 | − | 0.175380i | \(-0.943885\pi\) | ||
0.984501 | − | 0.175380i | \(-0.0561153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.33810i | 0.471108i | 0.971861 | + | 0.235554i | \(0.0756904\pi\) | ||||
−0.971861 | + | 0.235554i | \(0.924310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.39779 | + | 12.8791i | 0.620783 | + | 0.952053i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.1796 | − | 11.0734i | 1.41011 | − | 0.814130i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.82844 | − | 10.0952i | 0.426218 | − | 0.738231i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.39529 | − | 6.34518i | 0.174231 | − | 0.461544i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.26279 | + | 2.18721i | −0.0913720 | + | 0.158261i | −0.908089 | − | 0.418778i | \(-0.862459\pi\) |
0.816717 | + | 0.577039i | \(0.195792\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.77236 | − | 9.99802i | −0.415504 | − | 0.719673i | 0.579978 | − | 0.814632i | \(-0.303061\pi\) |
−0.995481 | + | 0.0949590i | \(0.969728\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.72870 | − | 4.18482i | −0.195406 | − | 0.299681i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.44368 | −0.174105 | −0.0870526 | − | 0.996204i | \(-0.527745\pi\) | ||||
−0.0870526 | + | 0.996204i | \(0.527745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.28327i | − | 0.374521i | −0.982310 | − | 0.187261i | \(-0.940039\pi\) | ||
0.982310 | − | 0.187261i | \(-0.0599609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.17043 | + | 21.5680i | 0.0825558 | + | 1.52129i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.16676 | + | 3.56038i | −0.432822 | + | 0.249890i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.27754 | − | 0.737586i | −0.0892270 | − | 0.0515153i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.46719 | + | 5.59716i | −0.171482 | + | 0.389029i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.10392 | + | 2.94675i | 0.353046 | + | 0.203831i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.23279 | − | 12.5276i | −0.497926 | − | 0.862432i | 0.502072 | − | 0.864826i | \(-0.332571\pi\) |
−0.999997 | + | 0.00239362i | \(0.999238\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.64626 | − | 3.87813i | −0.523913 | − | 0.265725i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.26300 | −0.358934 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.18189 | −0.623307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.8138 | − | 10.0494i | −1.33889 | − | 0.679076i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.87847 | − | 4.98566i | −0.193627 | − | 0.335372i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.6575 | + | 9.61719i | 1.11547 | + | 0.644015i | 0.940240 | − | 0.340513i | \(-0.110601\pi\) |
0.175227 | + | 0.984528i | \(0.443934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.22515 | − | 0.133363i | 0.0816766 | − | 0.00889086i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.503060 | + | 0.290442i | 0.0333893 | + | 0.0192773i | 0.516602 | − | 0.856226i | \(-0.327197\pi\) |
−0.483212 | + | 0.875503i | \(0.660530\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.78703 | + | 4.49584i | −0.514581 | + | 0.297094i | −0.734715 | − | 0.678376i | \(-0.762684\pi\) |
0.220134 | + | 0.975470i | \(0.429351\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.333978 | − | 6.15437i | −0.0219742 | − | 0.404928i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.68699i | 0.110518i | 0.998472 | + | 0.0552592i | \(0.0175985\pi\) | ||||
−0.998472 | + | 0.0552592i | \(0.982401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.1368 | −1.83544 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.743758 | − | 1.14065i | −0.0483122 | − | 0.0740933i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.75123 | − | 3.03323i | −0.113278 | − | 0.196203i | 0.803812 | − | 0.594883i | \(-0.202802\pi\) |
−0.917090 | + | 0.398680i | \(0.869468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.18735 | − | 2.05655i | 0.0764837 | − | 0.132474i | −0.825247 | − | 0.564772i | \(-0.808964\pi\) |
0.901731 | + | 0.432299i | \(0.142297\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.9201 | + | 11.1244i | −0.700522 | + | 0.713631i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.67303 | + | 9.82597i | −0.362436 | + | 0.627758i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.52066 | − | 1.45530i | 0.160386 | − | 0.0925986i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.98980 | − | 3.05163i | −0.126099 | − | 0.193389i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 16.4883i | − | 1.04073i | −0.853942 | − | 0.520367i | \(-0.825795\pi\) | ||
0.853942 | − | 0.520367i | \(-0.174205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.55870i | 0.349472i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.8417 | + | 0.859683i | −0.992049 | + | 0.0538354i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.98224 | − | 1.14444i | 0.123649 | − | 0.0713885i | −0.436900 | − | 0.899510i | \(-0.643924\pi\) |
0.560549 | + | 0.828122i | \(0.310590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.74687 | − | 11.6859i | 0.419230 | − | 0.726127i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.2704 | − | 1.77111i | 1.00711 | − | 0.109629i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.5336 | + | 25.1729i | −0.896179 | + | 1.55223i | −0.0638398 | + | 0.997960i | \(0.520335\pi\) |
−0.832339 | + | 0.554267i | \(0.812999\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.2417 | + | 17.7392i | 0.629146 | + | 1.08971i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.53658 | − | 18.8027i | 0.583629 | − | 1.15070i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.4025 | −0.695223 | −0.347612 | − | 0.937639i | \(-0.613007\pi\) | ||||
−0.347612 | + | 0.937639i | \(0.613007\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.9854i | 1.76074i | 0.474287 | + | 0.880370i | \(0.342706\pi\) | ||||
−0.474287 | + | 0.880370i | \(0.657294\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.71470 | − | 1.37688i | −0.164301 | − | 0.0833323i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.969899 | − | 0.559972i | 0.0584871 | − | 0.0337676i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1047 | + | 11.6075i | 1.20798 | + | 0.697425i | 0.962317 | − | 0.271931i | \(-0.0876622\pi\) |
0.245659 | + | 0.969356i | \(0.420996\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.3110 | + | 8.51218i | 1.15612 | + | 0.509611i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.7582 | − | 7.36593i | −0.761088 | − | 0.439415i | 0.0685980 | − | 0.997644i | \(-0.478147\pi\) |
−0.829686 | + | 0.558230i | \(0.811481\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.4785 | + | 21.6134i | 0.741770 | + | 1.28478i | 0.951689 | + | 0.307065i | \(0.0993468\pi\) |
−0.209919 | + | 0.977719i | \(0.567320\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.434639 | − | 8.00928i | −0.0257458 | − | 0.474429i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.898805 | −0.0530548 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.28204 | −0.0754142 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.3718 | + | 15.2395i | −1.37008 | + | 0.893354i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.0395 | − | 19.1210i | −0.644934 | − | 1.11706i | −0.984317 | − | 0.176410i | \(-0.943551\pi\) |
0.339382 | − | 0.940648i | \(-0.389782\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.2370 | − | 11.1065i | −1.12002 | − | 0.646645i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.00307 | + | 13.2533i | −0.290307 | + | 0.769033i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.37746 | + | 1.37263i | 0.137492 | + | 0.0793811i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.77707 | + | 1.60334i | −0.160068 | + | 0.0924151i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.0920 | + | 13.7530i | −1.21170 | + | 0.790087i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 19.0163i | − | 1.08887i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0180 | −1.59907 | −0.799535 | − | 0.600619i | \(-0.794921\pi\) | ||||
−0.799535 | + | 0.600619i | \(0.794921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.27080 | − | 0.340297i | 0.356733 | − | 0.0193588i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.78751 | + | 11.7563i | 0.384884 | + | 0.666639i | 0.991753 | − | 0.128163i | \(-0.0409080\pi\) |
−0.606869 | + | 0.794802i | \(0.707575\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.9417 | − | 24.1478i | 0.788034 | − | 1.36491i | −0.139136 | − | 0.990273i | \(-0.544433\pi\) |
0.927170 | − | 0.374641i | \(-0.122234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.76806 | + | 4.95573i | −0.381337 | + | 0.279224i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.15169 | − | 5.45888i | 0.177016 | − | 0.306601i | −0.763841 | − | 0.645405i | \(-0.776689\pi\) |
0.940857 | + | 0.338803i | \(0.110022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8806 | − | 7.43662i | 0.721176 | − | 0.416371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.12805 | + | 17.9972i | −0.509478 | + | 1.00451i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 9.24305i | − | 0.514297i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.553103i | − | 0.0306806i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.45564 | + | 10.7565i | −0.301698 | + | 0.594838i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.8466 | + | 8.57169i | −0.818520 | + | 0.472573i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.733725 | − | 1.27085i | 0.0403292 | − | 0.0698522i | −0.845156 | − | 0.534519i | \(-0.820493\pi\) |
0.885485 | + | 0.464667i | \(0.153826\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.0233 | + | 18.3227i | −1.37127 | + | 1.00408i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.3576 | − | 23.1360i | 0.729802 | − | 1.26405i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.25721 | − | 2.17756i | −0.0684848 | − | 0.118619i | 0.829750 | − | 0.558136i | \(-0.188483\pi\) |
−0.898235 | + | 0.439516i | \(0.855150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.4734 | − | 1.27383i | 1.27490 | − | 0.0691849i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.1783 | 1.03857 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0497i | 0.866603i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.33723 | − | 4.13217i | 0.341185 | − | 0.222468i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.4849 | + | 10.0949i | −0.938638 | + | 0.541923i | −0.889533 | − | 0.456871i | \(-0.848970\pi\) |
−0.0491051 | + | 0.998794i | \(0.515637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.58266 | + | 3.80050i | 0.352362 | + | 0.203436i | 0.665725 | − | 0.746197i | \(-0.268122\pi\) |
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.43302 | + | 5.41250i | 0.236617 | + | 0.288898i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.78534 | − | 5.07222i | −0.467596 | − | 0.269967i | 0.247637 | − | 0.968853i | \(-0.420346\pi\) |
−0.715233 | + | 0.698886i | \(0.753679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.30197 | + | 9.18328i | 0.281399 | + | 0.487398i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.09714 | + | 5.27971i | −0.428546 | + | 0.279432i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5983 | −1.08714 | −0.543570 | − | 0.839364i | \(-0.682928\pi\) | ||||
−0.543570 | + | 0.839364i | \(0.682928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3269 | −0.754047 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.334818 | − | 6.16985i | −0.0175734 | − | 0.323833i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.7390 | + | 23.7967i | 0.719133 | + | 1.24558i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1457 | − | 6.43498i | −0.581802 | − | 0.335903i | 0.180047 | − | 0.983658i | \(-0.442375\pi\) |
−0.761849 | + | 0.647755i | \(0.775708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.89034 | + | 0.833247i | 0.0984069 | + | 0.0433771i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8083 | + | 6.24017i | 0.561139 | + | 0.323974i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.12551 | − | 3.53656i | 0.317167 | − | 0.183116i | −0.332962 | − | 0.942940i | \(-0.608048\pi\) |
0.650129 | + | 0.759824i | \(0.274715\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.9053 | − | 9.08141i | −0.924624 | − | 0.468962i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.34540i | − | 0.378307i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0887 | 1.34009 | 0.670043 | − | 0.742322i | \(-0.266276\pi\) | ||||
0.670043 | + | 0.742322i | \(0.266276\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.2630 | + | 34.0365i | −0.884412 | + | 1.74374i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.84884 | − | 17.0587i | −0.503252 | − | 0.871659i | −0.999993 | − | 0.00375959i | \(-0.998803\pi\) |
0.496741 | − | 0.867899i | \(-0.334530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.81154 | + | 6.60178i | −0.194254 | + | 0.336458i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.32704 | − | 0.797580i | 0.372454 | − | 0.0405433i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.05645 | − | 12.2221i | 0.357776 | − | 0.619687i | −0.629813 | − | 0.776747i | \(-0.716868\pi\) |
0.987589 | + | 0.157060i | \(0.0502017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.54998 | − | 4.35898i | 0.381819 | − | 0.220443i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.28034 | + | 0.178014i | −0.165471 | + | 0.00897961i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.68420i | 0.0847413i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.1597i | 0.861220i | 0.902538 | + | 0.430610i | \(0.141702\pi\) | ||||
−0.902538 | + | 0.430610i | \(0.858298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.66932 | − | 4.09376i | −0.133633 | − | 0.204944i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.5726 | + | 12.4549i | −1.07728 | + | 0.621969i | −0.930162 | − | 0.367149i | \(-0.880334\pi\) |
−0.147120 | + | 0.989119i | \(0.547000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.73577 | − | 8.20260i | 0.235906 | − | 0.408601i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.8286 | − | 4.14831i | 0.935602 | − | 0.206131i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0923 | + | 24.4085i | −0.698528 | + | 1.20989i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.64539 | − | 13.2422i | −0.378040 | − | 0.654785i | 0.612737 | − | 0.790287i | \(-0.290069\pi\) |
−0.990777 | + | 0.135502i | \(0.956735\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.88364 | + | 4.42244i | 0.142239 | + | 0.218143i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.5341 | −0.665970 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.50580i | 0.221181i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.342669 | + | 6.31451i | 0.0167806 | + | 0.309223i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.38781 | − | 3.11065i | 0.263212 | − | 0.151965i | −0.362587 | − | 0.931950i | \(-0.618106\pi\) |
0.625799 | + | 0.779985i | \(0.284773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.60960 | + | 2.08400i | 0.175921 | + | 0.101568i | 0.585375 | − | 0.810763i | \(-0.300947\pi\) |
−0.409454 | + | 0.912331i | \(0.634281\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 39.1714 | − | 4.26397i | 1.90458 | − | 0.207321i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.52114 | − | 0.878230i | −0.0737861 | − | 0.0426004i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.79321 | − | 10.0341i | −0.280353 | − | 0.485586i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.67024 | + | 2.87590i | 0.273762 | + | 0.138850i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.3973 | 1.65686 | 0.828429 | − | 0.560094i | \(-0.189235\pi\) | ||||
0.828429 | + | 0.560094i | \(0.189235\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.7319 | 1.14048 | 0.570241 | − | 0.821478i | \(-0.306850\pi\) | ||||
0.570241 | + | 0.821478i | \(0.306850\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0532 | − | 9.15646i | −0.865586 | − | 0.439019i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.20382 | + | 3.81712i | 0.105423 | + | 0.182598i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.5367 | − | 16.4757i | −1.36198 | − | 0.786342i | −0.372096 | − | 0.928194i | \(-0.621361\pi\) |
−0.989888 | + | 0.141852i | \(0.954694\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.40879 | − | 14.5392i | 0.305180 | − | 0.692343i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.04392 | + | 1.75741i | 0.144621 | + | 0.0834969i | 0.570564 | − | 0.821253i | \(-0.306724\pi\) |
−0.425944 | + | 0.904750i | \(0.640058\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.5823 | + | 13.0379i | −1.07050 | + | 0.618056i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.31097 | − | 24.1578i | −0.0620066 | − | 1.14262i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.5711i | 1.30116i | 0.759437 | + | 0.650581i | \(0.225475\pi\) | ||||
−0.759437 | + | 0.650581i | \(0.774525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.87735 | 0.0884008 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.2310 | − | 32.5606i | −0.997519 | − | 1.52983i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.88239 | + | 3.26040i | 0.0882479 | + | 0.152850i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.69999 | + | 6.40857i | −0.173078 | + | 0.299780i | −0.939494 | − | 0.342564i | \(-0.888705\pi\) |
0.766416 | + | 0.642344i | \(0.222038\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.9242 | − | 3.59756i | 1.02334 | − | 0.167920i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.03604 | − | 10.4547i | 0.281126 | − | 0.486925i | −0.690536 | − | 0.723298i | \(-0.742625\pi\) |
0.971662 | + | 0.236373i | \(0.0759586\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.6479 | − | 6.72493i | 0.541325 | − | 0.312534i | −0.204291 | − | 0.978910i | \(-0.565489\pi\) |
0.745616 | + | 0.666376i | \(0.232155\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.2566 | − | 21.8644i | −0.661134 | − | 1.01394i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.9746i | 0.600391i | 0.953878 | + | 0.300196i | \(0.0970519\pi\) | ||||
−0.953878 | + | 0.300196i | \(0.902948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 16.2772i | − | 0.751612i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.34735 | − | 0.290184i | 0.246393 | − | 0.0133710i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.80051 | − | 3.34892i | 0.266708 | − | 0.153984i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.444016 | − | 0.769058i | 0.0203729 | − | 0.0352868i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.9466 | − | 23.1441i | −0.775932 | − | 1.05969i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.54472 | − | 13.0678i | 0.344727 | − | 0.597085i | −0.640577 | − | 0.767894i | \(-0.721305\pi\) |
0.985304 | + | 0.170809i | \(0.0546381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.95971 | + | 12.0546i | 0.317335 | + | 0.549641i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.08505 | − | 4.11097i | 0.0948733 | − | 0.187056i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.5090 | 1.56697 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.93710i | 0.404979i | 0.979284 | + | 0.202489i | \(0.0649032\pi\) | ||||
−0.979284 | + | 0.202489i | \(0.935097\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.1135 | − | 8.17263i | −0.728676 | − | 0.369579i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0926 | + | 5.82696i | −0.455472 | + | 0.262967i | −0.710138 | − | 0.704062i | \(-0.751368\pi\) |
0.254666 | + | 0.967029i | \(0.418034\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.2013 | − | 11.6632i | −0.909819 | − | 0.525284i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.1365 | − | 10.3511i | 0.635391 | − | 0.465247i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.59526 | + | 3.23043i | 0.250982 | + | 0.144904i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.6569 | + | 21.9224i | 0.566601 | + | 0.981381i | 0.996899 | + | 0.0786941i | \(0.0250750\pi\) |
−0.430298 | + | 0.902687i | \(0.641592\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.22063 | + | 22.4931i | 0.0545337 | + | 1.00492i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.4640 | 1.22456 | 0.612279 | − | 0.790642i | \(-0.290253\pi\) | ||||
0.612279 | + | 0.790642i | \(0.290253\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.1428 | 1.38584 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.2311 | + | 10.5834i | −0.720848 | + | 0.470027i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.31530 | + | 16.1346i | 0.412894 | + | 0.715153i | 0.995205 | − | 0.0978134i | \(-0.0311848\pi\) |
−0.582311 | + | 0.812966i | \(0.697851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.4990 | + | 8.37102i | 0.641399 | + | 0.370312i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.81886 | + | 11.0845i | 0.0803046 | + | 0.489392i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.72667 | − | 3.88364i | −0.296412 | − | 0.171134i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.0103 | − | 17.9038i | 1.36383 | − | 0.787409i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.83362 | − | 5.10788i | 0.343858 | − | 0.224211i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.1019i | 1.05593i | 0.849268 | + | 0.527963i | \(0.177044\pi\) | ||||
−0.849268 | + | 0.527963i | \(0.822956\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.9903 | −1.48629 | −0.743146 | − | 0.669129i | \(-0.766667\pi\) | ||||
−0.743146 | + | 0.669129i | \(0.766667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.927340 | + | 0.0503239i | −0.0404724 | + | 0.00219631i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0391 | − | 26.0486i | −0.655116 | − | 1.13469i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.42138 | − | 16.3183i | 0.409625 | − | 0.709492i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.4645 | + | 12.5470i | 1.23525 | + | 0.544491i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.463580 | − | 0.802943i | 0.0200799 | − | 0.0347793i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.6149 | − | 12.4794i | 0.934494 | − | 0.539530i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.67671 | − | 7.24914i | 0.158662 | − | 0.312823i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 14.4393i | − | 0.621945i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 38.0055i | − | 1.63399i | −0.576648 | − | 0.816993i | \(-0.695639\pi\) | ||
0.576648 | − | 0.816993i | \(-0.304361\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.96573 | + | 9.79062i | −0.213100 | + | 0.420156i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.9188 | − | 7.45866i | 0.553380 | − | 0.319494i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0534 | − | 20.8771i | 0.515367 | − | 0.892642i | −0.484474 | − | 0.874806i | \(-0.660989\pi\) |
0.999841 | − | 0.0178365i | \(-0.00567782\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.88182 | + | 26.4741i | 0.122993 | + | 1.12989i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.89669 | − | 10.2134i | 0.251207 | − | 0.435104i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.513081 | + | 0.888682i | 0.0218184 | + | 0.0377906i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 38.3029 | − | 2.07858i | 1.62587 | − | 0.0882308i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.9729 | −1.56659 | −0.783295 | − | 0.621650i | \(-0.786463\pi\) | ||||
−0.783295 | + | 0.621650i | \(0.786463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.30784i | − | 0.139907i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.9126 | − | 11.0278i | 0.714051 | − | 0.465594i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.5859 | + | 7.84380i | −0.572576 | + | 0.330577i | −0.758177 | − | 0.652048i | \(-0.773910\pi\) |
0.185602 | + | 0.982625i | \(0.440577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.1799 | − | 14.5376i | −1.05933 | − | 0.611602i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.67133 | − | 7.92492i | 0.364162 | − | 0.332815i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.9567 | + | 16.7181i | 1.21393 | + | 0.700861i | 0.963612 | − | 0.267304i | \(-0.0861327\pi\) |
0.250314 | + | 0.968165i | \(0.419466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1141 | + | 31.3746i | 0.758053 | + | 1.31299i | 0.943842 | + | 0.330397i | \(0.107183\pi\) |
−0.185788 | + | 0.982590i | \(0.559484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.66427 | + | 2.38928i | −0.153077 | + | 0.0998135i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.837584 | 0.0349297 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.34600 | 0.180926 | 0.0904631 | − | 0.995900i | \(-0.471165\pi\) | ||||
0.0904631 | + | 0.995900i | \(0.471165\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.08353 | − | 19.9667i | −0.0450299 | − | 0.829786i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.37266 | + | 2.37752i | 0.0569477 | + | 0.0986363i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.5754 | − | 13.0339i | −0.934979 | − | 0.539811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.936393 | − | 8.60225i | −0.0387151 | − | 0.355659i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.0281 | + | 20.2235i | 1.44576 | + | 0.834711i | 0.998225 | − | 0.0595537i | \(-0.0189678\pi\) |
0.447538 | + | 0.894265i | \(0.352301\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.1697 | − | 7.60351i | 0.542646 | − | 0.313297i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.77481 | − | 1.91456i | −0.155275 | − | 0.0787543i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9.69635i | − | 0.398181i | −0.979981 | − | 0.199091i | \(-0.936201\pi\) | ||
0.979981 | − | 0.199091i | \(-0.0637988\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9556 | 0.490133 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.13930 | − | 8.16119i | 0.169410 | − | 0.334015i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.8663 | − | 36.1415i | −0.852574 | − | 1.47670i | −0.878878 | − | 0.477047i | \(-0.841707\pi\) |
0.0263039 | − | 0.999654i | \(-0.491626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.58836 | + | 2.75112i | −0.0647905 | + | 0.112220i | −0.896601 | − | 0.442839i | \(-0.853971\pi\) |
0.831811 | + | 0.555060i | \(0.187305\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.0900 | + | 34.2337i | −0.614511 | + | 1.39410i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.82112 | + | 6.61838i | −0.155351 | + | 0.269075i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.14402 | − | 2.39255i | 0.168201 | − | 0.0971107i | −0.413536 | − | 0.910488i | \(-0.635707\pi\) |
0.581737 | + | 0.813377i | \(0.302373\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.3154 | + | 0.668319i | −0.499045 | + | 0.0270816i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 17.6842i | − | 0.715426i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 37.8359i | − | 1.52818i | −0.645111 | − | 0.764089i | \(-0.723189\pi\) | ||
0.645111 | − | 0.764089i | \(-0.276811\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.39556 | − | 2.14028i | −0.0562745 | − | 0.0863045i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.4083 | + | 19.8657i | −1.38523 | + | 0.799761i | −0.992773 | − | 0.120011i | \(-0.961707\pi\) |
−0.392454 | + | 0.919772i | \(0.628374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.1582 | − | 31.4510i | 0.729840 | − | 1.26412i | −0.227110 | − | 0.973869i | \(-0.572928\pi\) |
0.956950 | − | 0.290252i | \(-0.0937390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.19634 | + | 6.71309i | −0.328908 | + | 0.269387i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.94383 | + | 13.7591i | −0.318263 | + | 0.551247i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.3886 | + | 19.7257i | 0.455545 | + | 0.789028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.57545 | + | 8.55069i | 0.222662 | + | 0.341482i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.2032 | 1.76250 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.0129i | − | 1.19480i | −0.801945 | − | 0.597398i | \(-0.796201\pi\) | ||
0.801945 | − | 0.597398i | \(-0.203799\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.35767 | − | 25.0183i | −0.0539624 | − | 0.994388i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 40.8783 | − | 23.6011i | 1.62221 | − | 0.936581i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.17571 | − | 3.56555i | −0.244690 | − | 0.141272i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.77296 | − | 11.9813i | −0.347053 | − | 0.473972i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.8537 | + | 7.42111i | 0.507692 | + | 0.293116i | 0.731885 | − | 0.681429i | \(-0.238641\pi\) |
−0.224192 | + | 0.974545i | \(0.571974\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.9226 | + | 29.3107i | 0.667361 | + | 1.15590i | 0.978639 | + | 0.205584i | \(0.0659093\pi\) |
−0.311279 | + | 0.950319i | \(0.600757\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.12989 | − | 4.12342i | −0.320114 | − | 0.162359i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.5923 | 0.691624 | 0.345812 | − | 0.938304i | \(-0.387603\pi\) | ||||
0.345812 | + | 0.938304i | \(0.387603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.2689 | 1.10965 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.1835 | − | 7.19376i | −0.555894 | − | 0.281946i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.9079 | + | 22.3571i | 0.505124 | + | 0.874900i | 0.999982 | + | 0.00592671i | \(0.00188654\pi\) |
−0.494859 | + | 0.868974i | \(0.664780\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.51881 | + | 2.03159i | 0.137491 | + | 0.0793807i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.7334 | − | 31.0471i | −0.886915 | − | 1.21126i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.1802 | + | 11.0737i | 0.747153 | + | 0.431369i | 0.824664 | − | 0.565622i | \(-0.191364\pi\) |
−0.0775113 | + | 0.996991i | \(0.524697\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.8395 | − | 9.72232i | 0.654983 | − | 0.378154i | −0.135380 | − | 0.990794i | \(-0.543226\pi\) |
0.790363 | + | 0.612639i | \(0.209892\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.540318 | − | 9.95668i | −0.0209842 | − | 0.386685i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.04453i | 0.234397i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1234 | 0.430700 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.1964 | + | 27.9066i | 0.703513 | + | 1.07893i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.1004 | + | 20.9585i | 0.467130 | + | 0.809092i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6142 | − | 20.1164i | 0.447695 | − | 0.775431i | −0.550540 | − | 0.834808i | \(-0.685578\pi\) |
0.998236 | + | 0.0593778i | \(0.0189117\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.99700 | + | 0.753862i | 0.0768647 | + | 0.0290162i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.3138 | + | 24.7922i | −0.550123 | + | 0.952841i | 0.448142 | + | 0.893962i | \(0.352086\pi\) |
−0.998265 | + | 0.0588787i | \(0.981247\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.2090 | − | 10.5129i | 0.698796 | − | 0.403450i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.549536 | + | 0.842786i | 0.0210583 | + | 0.0322956i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.7625i | 1.40668i | 0.710855 | + | 0.703339i | \(0.248308\pi\) | ||||
−0.710855 | + | 0.703339i | \(0.751692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.52984i | − | 0.249492i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.5512 | + | 0.843914i | −0.593314 | + | 0.0321973i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1493 | + | 6.43703i | −0.424753 | + | 0.245231i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.7269 | + | 32.4360i | −0.712407 | + | 1.23392i | 0.251545 | + | 0.967846i | \(0.419061\pi\) |
−0.963951 | + | 0.266079i | \(0.914272\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.30587 | − | 9.76846i | 0.163567 | − | 0.371073i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.91071 | − | 6.77355i | 0.148342 | − | 0.256936i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.47216 | − | 2.54986i | −0.0557622 | − | 0.0965830i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.32171 | + | 2.60594i | −0.0499917 | + | 0.0985655i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.9693 | 0.527615 | 0.263807 | − | 0.964575i | \(-0.415022\pi\) | ||||
0.263807 | + | 0.964575i | \(0.415022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.3483i | 0.842881i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −43.4635 | − | 22.0444i | −1.63693 | − | 0.830239i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.4328 | − | 9.48747i | 0.618019 | − | 0.356813i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.0480 | − | 12.1521i | −0.790476 | − | 0.456381i | 0.0496543 | − | 0.998766i | \(-0.484188\pi\) |
−0.840130 | + | 0.542385i | \(0.817521\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.255231 | − | 2.34470i | −0.00957192 | − | 0.0879333i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.4215 | + | 7.17156i | 0.465189 | + | 0.268577i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.93178 | − | 6.81004i | −0.147040 | − | 0.254681i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.328724 | − | 6.05754i | −0.0122764 | − | 0.226223i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.8725 | −1.30052 | −0.650262 | − | 0.759710i | \(-0.725341\pi\) | ||||
−0.650262 | + | 0.759710i | \(0.725341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.73251 | −0.176248 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.44537 | − | 2.24654i | 0.128135 | − | 0.0835497i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.12055 | − | 1.94085i | −0.0416162 | − | 0.0720813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1521 | + | 13.9443i | 0.895754 | + | 0.517164i | 0.875820 | − | 0.482638i | \(-0.160321\pi\) |
0.0199335 | + | 0.999801i | \(0.493655\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.5841 | + | 8.62856i | −0.947561 | + | 0.319576i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.09721 | − | 5.25227i | −0.336472 | − | 0.194262i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.4750 | + | 15.8627i | −1.01481 | + | 0.585902i | −0.912597 | − | 0.408860i | \(-0.865926\pi\) |
−0.102215 | + | 0.994762i | \(0.532593\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.4616 | + | 10.7337i | −0.607196 | + | 0.395920i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.9984i | 1.25235i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.80482 | 0.0663913 | 0.0331957 | − | 0.999449i | \(-0.489432\pi\) | ||||
0.0331957 | + | 0.999449i | \(0.489432\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.03391 | − | 0.273174i | 0.184925 | − | 0.0100353i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.84368 | + | 11.8536i | 0.251070 | + | 0.434866i | 0.963821 | − | 0.266551i | \(-0.0858842\pi\) |
−0.712751 | + | 0.701418i | \(0.752551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.9614 | + | 25.9140i | −0.548145 | + | 0.949415i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.682829 | − | 6.27287i | −0.0249834 | − | 0.229512i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.60353 | − | 13.1697i | 0.277827 | − | 0.481210i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.8511 | − | 12.0384i | 0.760868 | − | 0.439287i | −0.0687396 | − | 0.997635i | \(-0.521898\pi\) |
0.829607 | + | 0.558348i | \(0.188564\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.9182 | − | 25.4699i | 0.470764 | − | 0.928176i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 48.0764i | 1.74968i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11.0608i | − | 0.402013i | −0.979590 | − | 0.201007i | \(-0.935579\pi\) | ||
0.979590 | − | 0.201007i | \(-0.0644213\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.35508 | + | 8.58665i | −0.158080 | + | 0.311676i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.392113 | + | 0.226386i | −0.0142141 | + | 0.00820650i | −0.507090 | − | 0.861893i | \(-0.669279\pi\) |
0.492876 | + | 0.870099i | \(0.335946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.54447 | − | 7.87125i | 0.164521 | − | 0.284958i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.1447 | − | 11.0836i | −0.909107 | − | 0.400728i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.98053 | − | 12.0906i | 0.252052 | − | 0.436568i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.71970 | + | 2.97861i | 0.0620139 | + | 0.107411i | 0.895366 | − | 0.445332i | \(-0.146914\pi\) |
−0.833352 | + | 0.552743i | \(0.813581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.95865 | − | 0.214824i | 0.142567 | − | 0.00773668i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.5126 | 0.989558 | 0.494779 | − | 0.869019i | \(-0.335249\pi\) | ||||
0.494779 | + | 0.869019i | \(0.335249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.88979i | − | 0.103804i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.5776 | − | 12.7655i | 0.702344 | − | 0.457961i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.28916 | − | 0.744298i | 0.0461890 | − | 0.0266673i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6869 | − | 6.74744i | −0.418190 | − | 0.241442i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.5209 | + | 10.0116i | 0.947780 | + | 0.357784i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.73609 | − | 3.31173i | −0.204730 | − | 0.118201i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.03995 | − | 5.26534i | −0.108362 | − | 0.187689i | 0.806745 | − | 0.590900i | \(-0.201227\pi\) |
−0.915107 | + | 0.403211i | \(0.867894\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −42.1726 | + | 27.4985i | −1.50139 | + | 0.978973i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.7152 | −0.629879 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.9519 | 0.424426 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.92248 | + | 35.4263i | 0.0681832 | + | 1.25644i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.0930 | + | 41.7303i | 0.853418 | + | 1.47816i | 0.878105 | + | 0.478468i | \(0.158808\pi\) |
−0.0246874 | + | 0.999695i | \(0.507859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.6349 | − | 28.0794i | −1.72058 | − | 0.993377i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.4627 | − | 21.5733i | 1.04101 | − | 0.762255i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.2843 | − | 17.4847i | −1.06871 | − | 0.617021i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.93734 | + | 2.85058i | −0.174018 | + | 0.100470i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.6137 | − | 8.93355i | −0.620033 | − | 0.314476i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.1846i | 1.27218i | 0.771614 | + | 0.636092i | \(0.219450\pi\) | ||||
−0.771614 | + | 0.636092i | \(0.780550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6514 | −1.21678 | −0.608388 | − | 0.793640i | \(-0.708183\pi\) | ||||
−0.608388 | + | 0.793640i | \(0.708183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.7093 | + | 44.7745i | −0.796450 | + | 1.57031i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.1732 | + | 19.3525i | 0.391380 | + | 0.677889i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.65545 | − | 4.59937i | 0.0929024 | − | 0.160912i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.11472 | − | 4.25379i | −0.108837 | − | 0.148639i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0803 | + | 17.4596i | −0.351806 | + | 0.609345i | −0.986566 | − | 0.163364i | \(-0.947766\pi\) |
0.634760 | + | 0.772709i | \(0.281099\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.63955 | + | 5.56539i | −0.336013 | + | 0.193997i | −0.658508 | − | 0.752574i | \(-0.728812\pi\) |
0.322494 | + | 0.946571i | \(0.395479\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.93695 | − | 0.105112i | 0.0674359 | − | 0.00365954i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 54.2010i | − | 1.88475i | −0.334554 | − | 0.942376i | \(-0.608586\pi\) | ||
0.334554 | − | 0.942376i | \(-0.391414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13.2828i | − | 0.461331i | −0.973033 | − | 0.230665i | \(-0.925910\pi\) | ||
0.973033 | − | 0.230665i | \(-0.0740903\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.9621 | + | 33.6818i | 0.761858 | + | 1.16841i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.6119 | + | 11.3229i | −0.679511 | + | 0.392316i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.9305 | − | 24.1283i | 0.482084 | − | 0.834993i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.1612 | + | 28.2786i | 0.800567 | + | 0.977452i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.0812 | − | 24.3894i | 0.486138 | − | 0.842016i | −0.513735 | − | 0.857949i | \(-0.671738\pi\) |
0.999873 | + | 0.0159329i | \(0.00507181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.381300 | − | 0.660432i | −0.0131483 | − | 0.0227735i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.9368 | − | 21.3740i | −0.480010 | − | 0.736160i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.9656 | 0.824442 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.65633i | 0.159993i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.34234 | + | 43.1633i | 0.0803888 | + | 1.48136i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.2547 | + | 10.5393i | −0.625762 | + | 0.361284i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.57043 | − | 2.06139i | −0.122249 | − | 0.0705806i | 0.437628 | − | 0.899156i | \(-0.355819\pi\) |
−0.559878 | + | 0.828575i | \(0.689152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.60366 | − | 12.7127i | 0.191641 | − | 0.434764i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.2719 | − | 27.2924i | −1.61478 | − | 0.932292i | −0.988242 | − | 0.152899i | \(-0.951139\pi\) |
−0.626535 | − | 0.779393i | \(-0.715528\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.19815 | − | 5.53937i | −0.109120 | − | 0.189001i | 0.806294 | − | 0.591515i | \(-0.201470\pi\) |
−0.915414 | + | 0.402514i | \(0.868136\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.38840 | − | 0.704188i | −0.0473167 | − | 0.0239987i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.4752 | 0.696985 | 0.348493 | − | 0.937312i | \(-0.386694\pi\) | ||||
0.348493 | + | 0.937312i | \(0.386694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5665 | −0.393274 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.98040 | − | 1.00444i | −0.0672579 | − | 0.0341127i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.07168 | − | 1.85620i | −0.0363542 | − | 0.0629674i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.5412 | + | 8.39535i | 0.492709 | + | 0.284466i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −48.0426 | + | 5.22965i | −1.62600 | + | 0.176997i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.1024 | + | 7.56469i | 0.442943 | + | 0.255733i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.2059 | − | 27.2544i | 1.59403 | − | 0.920314i | 0.601426 | − | 0.798928i | \(-0.294599\pi\) |
0.992605 | − | 0.121386i | \(-0.0387339\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.07222 | − | 38.1858i | −0.0698943 | − | 1.28797i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.0171i | 0.943919i | 0.881620 | + | 0.471960i | \(0.156453\pi\) | ||||
−0.881620 | + | 0.471960i | \(0.843547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.4423 | −0.553327 | −0.276663 | − | 0.960967i | \(-0.589229\pi\) | ||||
−0.276663 | + | 0.960967i | \(0.589229\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.0143 | − | 32.2281i | −0.706386 | − | 1.08334i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.6877 | + | 25.4398i | 0.493164 | + | 0.854185i | 0.999969 | − | 0.00787590i | \(-0.00250700\pi\) |
−0.506805 | + | 0.862061i | \(0.669174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3799 | − | 24.9067i | 0.482285 | − | 0.835343i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.1119 | + | 16.5529i | −0.606773 | + | 0.554543i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.1964 | − | 24.5889i | 0.475064 | − | 0.822836i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.70632 | + | 5.02660i | −0.291020 | + | 0.168021i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.59710 | + | 3.98301i | 0.0867148 | + | 0.132989i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 38.3775i | − | 1.27996i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.8835i | 1.36203i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.54598 | + | 0.300963i | −0.184559 | + | 0.0100154i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.7587 | − | 6.78888i | 0.390872 | − | 0.225670i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.99859 | + | 17.3181i | −0.331998 | + | 0.575037i | −0.982903 | − | 0.184122i | \(-0.941056\pi\) |
0.650906 | + | 0.759158i | \(0.274389\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −43.3564 | + | 4.71953i | −1.43804 | + | 0.156537i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4921 | + | 18.1729i | −0.347620 | + | 0.602096i | −0.985826 | − | 0.167770i | \(-0.946343\pi\) |
0.638206 | + | 0.769866i | \(0.279677\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.86710 | − | 4.96597i | −0.0948873 | − | 0.164350i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.8988 | − | 29.3750i | 0.492538 | − | 0.971108i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.47564 | 0.0817529 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.9502i | 1.21888i | 0.792834 | + | 0.609438i | \(0.208605\pi\) | ||||
−0.792834 | + | 0.609438i | \(0.791395\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.2800 | − | 21.9513i | −1.42613 | − | 0.723320i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.77177 | + | 3.33233i | −0.189980 | + | 0.109685i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.67788 | + | 2.12342i | 0.120928 | + | 0.0698177i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.95326 | + | 4.38733i | 0.326908 | + | 0.144099i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.2952 | − | 16.3362i | −0.928336 | − | 0.535975i | −0.0420509 | − | 0.999115i | \(-0.513389\pi\) |
−0.886285 | + | 0.463141i | \(0.846722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.72465 | − | 9.91539i | −0.187618 | − | 0.324964i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.27408 | + | 23.4781i | 0.0417116 | + | 0.768637i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.9719 | −0.816668 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.8176 | 1.03944 | 0.519718 | − | 0.854338i | \(-0.326037\pi\) | ||||
0.519718 | + | 0.854338i | \(0.326037\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.4553 | − | 26.3787i | 1.32021 | − | 0.860837i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.26311 | − | 5.65188i | −0.106374 | − | 0.184246i | 0.807924 | − | 0.589286i | \(-0.200591\pi\) |
−0.914299 | + | 0.405040i | \(0.867258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.21593 | + | 0.702016i | 0.0395960 | + | 0.0228608i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.3375 | + | 2.35264i | −0.466398 | + | 0.0765314i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.6572 | − | 14.8132i | −0.833747 | − | 0.481364i | 0.0213869 | − | 0.999771i | \(-0.493192\pi\) |
−0.855134 | + | 0.518407i | \(0.826525\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9564 | + | 8.63510i | −0.485506 | + | 0.280307i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.14536 | − | 5.96320i | 0.296559 | − | 0.193370i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.03621i | 0.0335660i | 0.999859 | + | 0.0167830i | \(0.00534244\pi\) | ||||
−0.999859 | + | 0.0167830i | \(0.994658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.41039 | 0.175076 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.7234 | − | 1.39593i | 0.831518 | − | 0.0451239i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.98928 | − | 3.44553i | −0.0642371 | − | 0.111262i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.24297 | − | 16.0093i | 0.298160 | − | 0.516429i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.2006 | + | 20.6491i | −0.908752 | + | 0.665409i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.3658 | + | 21.4182i | −0.398069 | + | 0.689476i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.37695 | + | 4.25908i | −0.237227 | + | 0.136963i | −0.613901 | − | 0.789383i | \(-0.710401\pi\) |
0.376675 | + | 0.926346i | \(0.377067\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.24167 | − | 14.2780i | 0.232636 | − | 0.458674i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.7663i | 1.43662i | 0.695724 | + | 0.718309i | \(0.255084\pi\) | ||||
−0.695724 | + | 0.718309i | \(0.744916\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.76550i | − | 0.152775i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.433341 | − | 0.854391i | 0.0138780 | − | 0.0273624i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0647 | + | 10.4296i | −0.577940 | + | 0.333674i | −0.760314 | − | 0.649555i | \(-0.774955\pi\) |
0.182374 | + | 0.983229i | \(0.441622\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.5924 | − | 28.7389i | 0.530295 | − | 0.918498i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8549 | + | 12.3415i | −0.538136 | + | 0.394035i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.56941 | − | 6.18241i | 0.113847 | − | 0.197188i | −0.803471 | − | 0.595343i | \(-0.797016\pi\) |
0.917318 | + | 0.398155i | \(0.130349\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.61748 | + | 4.53361i | 0.0833998 | + | 0.144453i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −29.6496 | + | 1.60899i | −0.943757 | + | 0.0512147i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.00919 | 0.159283 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.1928i | − | 0.387317i | −0.981069 | − | 0.193658i | \(-0.937965\pi\) | ||
0.981069 | − | 0.193658i | \(-0.0620354\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.12908 | − | 1.38826i | 0.0675642 | − | 0.0440550i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.80172 | + | 5.65902i | −0.310735 | + | 0.179403i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.9482 | + | 6.89832i | 0.378405 | + | 0.218472i | 0.677124 | − | 0.735869i | \(-0.263226\pi\) |
−0.298719 | + | 0.954341i | \(0.596559\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −53.0094 | + | 8.69835i | −1.67714 | + | 0.275204i |
(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 | 1152.2.p.f.191.11 | yes | 24 | |
3.2 | odd | 2 | 3456.2.p.f.575.10 | 24 | |||
4.3 | odd | 2 | 1152.2.p.g.191.2 | yes | 24 | ||
8.3 | odd | 2 | 1152.2.p.g.191.11 | yes | 24 | ||
8.5 | even | 2 | inner | 1152.2.p.f.191.2 | ✓ | 24 | |
9.4 | even | 3 | 3456.2.p.g.2879.3 | 24 | |||
9.5 | odd | 6 | 1152.2.p.g.959.11 | yes | 24 | ||
12.11 | even | 2 | 3456.2.p.g.575.10 | 24 | |||
24.5 | odd | 2 | 3456.2.p.f.575.3 | 24 | |||
24.11 | even | 2 | 3456.2.p.g.575.3 | 24 | |||
36.23 | even | 6 | inner | 1152.2.p.f.959.2 | yes | 24 | |
36.31 | odd | 6 | 3456.2.p.f.2879.3 | 24 | |||
72.5 | odd | 6 | 1152.2.p.g.959.2 | yes | 24 | ||
72.13 | even | 6 | 3456.2.p.g.2879.10 | 24 | |||
72.59 | even | 6 | inner | 1152.2.p.f.959.11 | yes | 24 | |
72.67 | odd | 6 | 3456.2.p.f.2879.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.p.f.191.2 | ✓ | 24 | 8.5 | even | 2 | inner | |
1152.2.p.f.191.11 | yes | 24 | 1.1 | even | 1 | trivial | |
1152.2.p.f.959.2 | yes | 24 | 36.23 | even | 6 | inner | |
1152.2.p.f.959.11 | yes | 24 | 72.59 | even | 6 | inner | |
1152.2.p.g.191.2 | yes | 24 | 4.3 | odd | 2 | ||
1152.2.p.g.191.11 | yes | 24 | 8.3 | odd | 2 | ||
1152.2.p.g.959.2 | yes | 24 | 72.5 | odd | 6 | ||
1152.2.p.g.959.11 | yes | 24 | 9.5 | odd | 6 | ||
3456.2.p.f.575.3 | 24 | 24.5 | odd | 2 | |||
3456.2.p.f.575.10 | 24 | 3.2 | odd | 2 | |||
3456.2.p.f.2879.3 | 24 | 36.31 | odd | 6 | |||
3456.2.p.f.2879.10 | 24 | 72.67 | odd | 6 | |||
3456.2.p.g.575.3 | 24 | 24.11 | even | 2 | |||
3456.2.p.g.575.10 | 24 | 12.11 | even | 2 | |||
3456.2.p.g.2879.3 | 24 | 9.4 | even | 3 | |||
3456.2.p.g.2879.10 | 24 | 72.13 | even | 6 |