Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.a (trivial) |
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: | yes |
Analytic conductor: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{73}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.77200 | −1.42568 | −0.712841 | − | 0.701325i | \(-0.752592\pi\) | ||||
−0.712841 | + | 0.701325i | \(0.752592\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77200 | 1.43881 | 0.719406 | − | 0.694589i | \(-0.244414\pi\) | ||||
0.719406 | + | 0.694589i | \(0.244414\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.77200 | −1.64245 | −0.821226 | − | 0.570603i | \(-0.806709\pi\) | ||||
−0.821226 | + | 0.570603i | \(0.806709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.77200 | 1.32419 | 0.662094 | − | 0.749421i | \(-0.269668\pi\) | ||||
0.662094 | + | 0.749421i | \(0.269668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.772002 | −0.160974 | −0.0804868 | − | 0.996756i | \(-0.525647\pi\) | ||||
−0.0804868 | + | 0.996756i | \(0.525647\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.77200 | −0.886139 | −0.443069 | − | 0.896487i | \(-0.646110\pi\) | ||||
−0.443069 | + | 0.896487i | \(0.646110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.7720 | 1.93471 | 0.967354 | − | 0.253428i | \(-0.0815580\pi\) | ||||
0.967354 | + | 0.253428i | \(0.0815580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.77200 | 0.637585 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.77200 | 1.27771 | 0.638855 | − | 0.769327i | \(-0.279409\pi\) | ||||
0.638855 | + | 0.769327i | \(0.279409\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.54400 | 1.17818 | 0.589088 | − | 0.808069i | \(-0.299487\pi\) | ||||
0.589088 | + | 0.808069i | \(0.299487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.77200 | 1.03272 | 0.516360 | − | 0.856371i | \(-0.327287\pi\) | ||||
0.516360 | + | 0.856371i | \(0.327287\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.77200 | −0.404338 | −0.202169 | − | 0.979351i | \(-0.564799\pi\) | ||||
−0.202169 | + | 0.979351i | \(0.564799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.22800 | 1.03257 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.54400 | 1.03625 | 0.518124 | − | 0.855305i | \(-0.326630\pi\) | ||||
0.518124 | + | 0.855305i | \(0.326630\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.77200 | −0.643457 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.77200 | −0.995103 | −0.497551 | − | 0.867434i | \(-0.665767\pi\) | ||||
−0.497551 | + | 0.867434i | \(0.665767\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.22800 | 0.760871 | 0.380436 | − | 0.924807i | \(-0.375774\pi\) | ||||
0.380436 | + | 0.924807i | \(0.375774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.54400 | −0.420596 | −0.210298 | − | 0.977637i | \(-0.567443\pi\) | ||||
−0.210298 | + | 0.977637i | \(0.567443\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.77200 | −0.441479 | −0.220740 | − | 0.975333i | \(-0.570847\pi\) | ||||
−0.220740 | + | 0.975333i | \(0.570847\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.0000 | −2.05129 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.77200 | 0.734527 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.00000 | 0.847998 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3160 | −1.18624 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.77200 | −0.592195 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.31601 | 0.742828 | 0.371414 | − | 0.928467i | \(-0.378873\pi\) | ||||
0.371414 | + | 0.928467i | \(0.378873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.7720 | −1.86788 | −0.933942 | − | 0.357425i | \(-0.883655\pi\) | ||||
−0.933942 | + | 0.357425i | \(0.883655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.22800 | 0.810729 | 0.405364 | − | 0.914155i | \(-0.367145\pi\) | ||||
0.405364 | + | 0.914155i | \(0.367145\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0000 | −1.35343 | −0.676716 | − | 0.736245i | \(-0.736597\pi\) | ||||
−0.676716 | + | 0.736245i | \(0.736597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.54400 | −0.722585 | −0.361292 | − | 0.932453i | \(-0.617664\pi\) | ||||
−0.361292 | + | 0.932453i | \(0.617664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3160 | −1.34674 | −0.673368 | − | 0.739307i | \(-0.735153\pi\) | ||||
−0.673368 | + | 0.739307i | \(0.735153\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.772002 | 0.0719895 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.5440 | 2.34161 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.7720 | 1.07018 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.54400 | 0.491951 | 0.245975 | − | 0.969276i | \(-0.420892\pi\) | ||||
0.245975 | + | 0.969276i | \(0.420892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.7720 | 1.29064 | 0.645318 | − | 0.763914i | \(-0.276725\pi\) | ||||
0.645318 | + | 0.763914i | \(0.276725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.7720 | −1.88787 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.0880 | 1.11818 | 0.559092 | − | 0.829106i | \(-0.311150\pi\) | ||||
0.559092 | + | 0.829106i | \(0.311150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.22800 | −0.358614 | −0.179307 | − | 0.983793i | \(-0.557386\pi\) | ||||
−0.179307 | + | 0.983793i | \(0.557386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.3160 | 1.19716 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.77200 | 0.396293 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.22800 | −0.100602 | −0.0503008 | − | 0.998734i | \(-0.516018\pi\) | ||||
−0.0503008 | + | 0.998734i | \(0.516018\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0880 | 0.820950 | 0.410475 | − | 0.911872i | \(-0.365363\pi\) | ||||
0.410475 | + | 0.911872i | \(0.365363\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.7720 | −0.865228 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.772002 | −0.0616125 | −0.0308062 | − | 0.999525i | \(-0.509807\pi\) | ||||
−0.0308062 | + | 0.999525i | \(0.509807\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.91199 | 0.229497 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.54400 | 0.669218 | 0.334609 | − | 0.942357i | \(-0.391396\pi\) | ||||
0.334609 | + | 0.942357i | \(0.391396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0880 | 0.858016 | 0.429008 | − | 0.903301i | \(-0.358863\pi\) | ||||
0.429008 | + | 0.903301i | \(0.358863\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.54400 | −0.725617 | −0.362809 | − | 0.931864i | \(-0.618182\pi\) | ||||
−0.362809 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.77200 | −0.285137 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.54400 | −0.563865 | −0.281933 | − | 0.959434i | \(-0.590975\pi\) | ||||
−0.281933 | + | 0.959434i | \(0.590975\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.31601 | 0.0978179 | 0.0489090 | − | 0.998803i | \(-0.484426\pi\) | ||||
0.0489090 | + | 0.998803i | \(0.484426\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.77200 | −0.571409 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32.3160 | −2.36318 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5440 | −0.980010 | −0.490005 | − | 0.871720i | \(-0.663005\pi\) | ||||
−0.490005 | + | 0.871720i | \(0.663005\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.22800 | −0.304338 | −0.152169 | − | 0.988354i | \(-0.548626\pi\) | ||||
−0.152169 | + | 0.988354i | \(0.548626\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.0000 | −1.42494 | −0.712470 | − | 0.701702i | \(-0.752424\pi\) | ||||
−0.712470 | + | 0.701702i | \(0.752424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.0000 | −1.06332 | −0.531661 | − | 0.846957i | \(-0.678432\pi\) | ||||
−0.531661 | + | 0.846957i | \(0.678432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.0000 | 1.26335 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.54400 | −0.526896 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.5440 | 1.90526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3160 | −0.779026 | −0.389513 | − | 0.921021i | \(-0.627357\pi\) | ||||
−0.389513 | + | 0.921021i | \(0.627357\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.77200 | −0.461847 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −40.6320 | −2.75828 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.3160 | −1.36660 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0880 | −1.27823 | −0.639114 | − | 0.769112i | \(-0.720699\pi\) | ||||
−0.639114 | + | 0.769112i | \(0.720699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5440 | −1.03169 | −0.515846 | − | 0.856681i | \(-0.672522\pi\) | ||||
−0.515846 | + | 0.856681i | \(0.672522\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.5440 | 1.82016 | 0.910080 | − | 0.414434i | \(-0.136020\pi\) | ||||
0.910080 | + | 0.414434i | \(0.136020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.5440 | 1.93549 | 0.967746 | − | 0.251928i | \(-0.0810646\pi\) | ||||
0.967746 | + | 0.251928i | \(0.0810646\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.77200 | 0.180825 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0880 | −1.68048 | −0.840238 | − | 0.542218i | \(-0.817585\pi\) | ||||
−0.840238 | + | 0.542218i | \(0.817585\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.22800 | −0.461780 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.3160 | 1.10179 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.77200 | 0.553684 | 0.276842 | − | 0.960915i | \(-0.410712\pi\) | ||||
0.276842 | + | 0.960915i | \(0.410712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.68399 | −0.231611 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.7720 | −0.671939 | −0.335970 | − | 0.941873i | \(-0.609064\pi\) | ||||
−0.335970 | + | 0.941873i | \(0.609064\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.3160 | −1.82161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | 0.739952 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.54400 | −0.463424 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.3160 | 1.23869 | 0.619344 | − | 0.785119i | \(-0.287398\pi\) | ||||
0.619344 | + | 0.785119i | \(0.287398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.22800 | −0.135341 | −0.0676706 | − | 0.997708i | \(-0.521557\pi\) | ||||
−0.0676706 | + | 0.997708i | \(0.521557\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.77200 | 0.287763 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0000 | 0.600842 | 0.300421 | − | 0.953807i | \(-0.402873\pi\) | ||||
0.300421 | + | 0.953807i | \(0.402873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.54400 | 0.330728 | 0.165364 | − | 0.986233i | \(-0.447120\pi\) | ||||
0.165364 | + | 0.986233i | \(0.447120\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.0880 | 1.37244 | 0.686220 | − | 0.727394i | \(-0.259269\pi\) | ||||
0.686220 | + | 0.727394i | \(0.259269\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.4560 | −1.67970 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.8600 | 1.69765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.08801 | 0.297245 | 0.148622 | − | 0.988894i | \(-0.452516\pi\) | ||||
0.148622 | + | 0.988894i | \(0.452516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | −0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.31601 | −0.133938 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.5440 | −1.47233 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.77200 | 0.445024 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.77200 | 0.158207 | 0.0791033 | − | 0.996866i | \(-0.474794\pi\) | ||||
0.0791033 | + | 0.996866i | \(0.474794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.68399 | −0.151708 | −0.0758542 | − | 0.997119i | \(-0.524168\pi\) | ||||
−0.0758542 | + | 0.997119i | \(0.524168\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.0880 | −1.29675 | −0.648376 | − | 0.761320i | \(-0.724551\pi\) | ||||
−0.648376 | + | 0.761320i | \(0.724551\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.7720 | −1.27499 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.0880 | −2.17491 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | 0.166410 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.4560 | 0.576458 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.7720 | 0.647048 | 0.323524 | − | 0.946220i | \(-0.395132\pi\) | ||||
0.323524 | + | 0.946220i | \(0.395132\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.22800 | −0.340272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.2280 | −0.992942 | −0.496471 | − | 0.868053i | \(-0.665371\pi\) | ||||
−0.496471 | + | 0.868053i | \(0.665371\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51.4040 | 2.78368 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.860009 | −0.0464361 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.6320 | −1.21495 | −0.607475 | − | 0.794339i | \(-0.707818\pi\) | ||||
−0.607475 | + | 0.794339i | \(0.707818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.4040 | 1.84160 | 0.920802 | − | 0.390030i | \(-0.127535\pi\) | ||||
0.920802 | + | 0.390030i | \(0.127535\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.7720 | 1.21203 | 0.606016 | − | 0.795453i | \(-0.292767\pi\) | ||||
0.606016 | + | 0.795453i | \(0.292767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.54400 | 0.188096 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.5440 | −1.03149 | −0.515747 | − | 0.856741i | \(-0.672485\pi\) | ||||
−0.515747 | + | 0.856741i | \(0.672485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.3160 | 0.753474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.77200 | 0.197436 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3160 | 0.799489 | 0.399744 | − | 0.916627i | \(-0.369099\pi\) | ||||
0.399744 | + | 0.916627i | \(0.369099\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.4560 | −1.47736 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0880 | −0.729449 | −0.364725 | − | 0.931115i | \(-0.618837\pi\) | ||||
−0.364725 | + | 0.931115i | \(0.618837\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.3160 | −0.737312 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.3160 | −1.30040 | −0.650198 | − | 0.759765i | \(-0.725314\pi\) | ||||
−0.650198 | + | 0.759765i | \(0.725314\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.22800 | −0.267138 | −0.133569 | − | 0.991040i | \(-0.542644\pi\) | ||||
−0.133569 | + | 0.991040i | \(0.542644\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | 0.917365 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.68399 | 0.186786 | 0.0933930 | − | 0.995629i | \(-0.470229\pi\) | ||||
0.0933930 | + | 0.995629i | \(0.470229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.22800 | 0.264391 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.00000 | 0.251577 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.68399 | 0.285272 | 0.142636 | − | 0.989775i | \(-0.454442\pi\) | ||||
0.142636 | + | 0.989775i | \(0.454442\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.5440 | 0.776231 | 0.388115 | − | 0.921611i | \(-0.373126\pi\) | ||||
0.388115 | + | 0.921611i | \(0.373126\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.3160 | 1.60977 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 37.0880 | 1.83838 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.45600 | 0.170888 | 0.0854440 | − | 0.996343i | \(-0.472769\pi\) | ||||
0.0854440 | + | 0.996343i | \(0.472769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −45.2640 | −2.22730 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.77200 | 0.330834 | 0.165417 | − | 0.986224i | \(-0.447103\pi\) | ||||
0.165417 | + | 0.986224i | \(0.447103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7720 | −0.671206 | −0.335603 | − | 0.942003i | \(-0.608940\pi\) | ||||
−0.335603 | + | 0.942003i | \(0.608940\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.77200 | −0.328490 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.3160 | 1.41870 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.6320 | 1.28282 | 0.641409 | − | 0.767199i | \(-0.278350\pi\) | ||||
0.641409 | + | 0.767199i | \(0.278350\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.0880 | −1.59011 | −0.795054 | − | 0.606539i | \(-0.792558\pi\) | ||||
−0.795054 | + | 0.606539i | \(0.792558\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.45600 | −0.213159 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.08801 | 0.336761 | 0.168381 | − | 0.985722i | \(-0.446146\pi\) | ||||
0.168381 | + | 0.985722i | \(0.446146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | −0.379236 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4560 | 0.493449 | 0.246724 | − | 0.969086i | \(-0.420646\pi\) | ||||
0.246724 | + | 0.969086i | \(0.420646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0000 | 1.69517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.3160 | 0.530503 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.455996 | 0.0213306 | 0.0106653 | − | 0.999943i | \(-0.496605\pi\) | ||||
0.0106653 | + | 0.999943i | \(0.496605\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.4560 | −0.859581 | −0.429791 | − | 0.902929i | \(-0.641413\pi\) | ||||
−0.429791 | + | 0.902929i | \(0.641413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.8600 | −1.62008 | −0.810041 | − | 0.586373i | \(-0.800555\pi\) | ||||
−0.810041 | + | 0.586373i | \(0.800555\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.0000 | −1.48078 | −0.740392 | − | 0.672176i | \(-0.765360\pi\) | ||||
−0.740392 | + | 0.672176i | \(0.765360\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.4920 | −1.08476 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.3160 | 1.48589 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.77200 | 0.264838 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.5440 | 1.25852 | 0.629259 | − | 0.777196i | \(-0.283359\pi\) | ||||
0.629259 | + | 0.777196i | \(0.283359\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.3160 | 1.06312 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.31601 | −0.332203 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.77200 | 0.0802971 | 0.0401485 | − | 0.999194i | \(-0.487217\pi\) | ||||
0.0401485 | + | 0.999194i | \(0.487217\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4560 | 0.742649 | 0.371324 | − | 0.928503i | \(-0.378904\pi\) | ||||
0.371324 | + | 0.928503i | \(0.378904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.3160 | 1.45544 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.3680 | 0.599636 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.0880 | −1.57075 | −0.785377 | − | 0.619017i | \(-0.787531\pi\) | ||||
−0.785377 | + | 0.619017i | \(0.787531\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.8600 | −1.06387 | −0.531933 | − | 0.846787i | \(-0.678534\pi\) | ||||
−0.531933 | + | 0.846787i | \(0.678534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.7720 | 0.835343 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.7720 | −0.743406 | −0.371703 | − | 0.928352i | \(-0.621226\pi\) | ||||
−0.371703 | + | 0.928352i | \(0.621226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.2280 | 0.629410 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.22800 | −0.362569 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.2280 | −0.581767 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 43.5440 | 1.90770 | 0.953849 | − | 0.300288i | \(-0.0970826\pi\) | ||||
0.953849 | + | 0.300288i | \(0.0970826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.5440 | 0.810873 | 0.405436 | − | 0.914123i | \(-0.367120\pi\) | ||||
0.405436 | + | 0.914123i | \(0.367120\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −72.9480 | −3.17767 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4040 | −0.974088 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.6320 | 0.980301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0000 | 0.605273 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.4920 | 1.48568 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.22800 | −0.353749 | −0.176875 | − | 0.984233i | \(-0.556599\pi\) | ||||
−0.176875 | + | 0.984233i | \(0.556599\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.54400 | 0.323150 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.5440 | 0.707371 | 0.353685 | − | 0.935364i | \(-0.384928\pi\) | ||||
0.353685 | + | 0.935364i | \(0.384928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.5440 | −1.17341 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.8600 | 0.802009 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.1760 | 1.27860 | 0.639299 | − | 0.768958i | \(-0.279224\pi\) | ||||
0.639299 | + | 0.768958i | \(0.279224\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.3160 | 0.859275 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.54400 | 0.402232 | 0.201116 | − | 0.979567i | \(-0.435543\pi\) | ||||
0.201116 | + | 0.979567i | \(0.435543\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.3160 | 0.602279 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0880 | −0.632522 | −0.316261 | − | 0.948672i | \(-0.602428\pi\) | ||||
−0.316261 | + | 0.948672i | \(0.602428\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.7720 | −1.16222 | −0.581111 | − | 0.813824i | \(-0.697382\pi\) | ||||
−0.581111 | + | 0.813824i | \(0.697382\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.772002 | −0.0321947 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.4040 | 1.68204 | 0.841021 | − | 0.541003i | \(-0.181955\pi\) | ||||
0.841021 | + | 0.541003i | \(0.181955\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.6320 | −0.938934 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.0000 | 1.49097 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.0880 | 1.53079 | 0.765393 | − | 0.643563i | \(-0.222545\pi\) | ||||
0.765393 | + | 0.643563i | \(0.222545\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 62.1760 | 2.56192 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.8600 | 1.14407 | 0.572037 | − | 0.820228i | \(-0.306153\pi\) | ||||
0.572037 | + | 0.820228i | \(0.306153\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.5440 | −1.04720 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.0880 | −1.18850 | −0.594252 | − | 0.804279i | \(-0.702552\pi\) | ||||
−0.594252 | + | 0.804279i | \(0.702552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.3160 | 1.88927 | 0.944635 | − | 0.328124i | \(-0.106416\pi\) | ||||
0.944635 | + | 0.328124i | \(0.106416\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.7720 | −0.478600 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.86001 | −0.116084 | −0.0580421 | − | 0.998314i | \(-0.518486\pi\) | ||||
−0.0580421 | + | 0.998314i | \(0.518486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.31601 | −0.336430 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5440 | 0.587427 | 0.293713 | − | 0.955894i | \(-0.405109\pi\) | ||||
0.293713 | + | 0.955894i | \(0.405109\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.3160 | 0.737375 | 0.368687 | − | 0.929553i | \(-0.379807\pi\) | ||||
0.368687 | + | 0.929553i | \(0.379807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.3160 | 1.25870 | 0.629348 | − | 0.777123i | \(-0.283322\pi\) | ||||
0.629348 | + | 0.777123i | \(0.283322\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.1760 | −1.20898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.6320 | −2.09858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.77200 | 0.229780 | 0.114890 | − | 0.993378i | \(-0.463348\pi\) | ||||
0.114890 | + | 0.993378i | \(0.463348\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.54400 | −0.220007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.6840 | 0.859151 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.6320 | −1.60487 | −0.802434 | − | 0.596741i | \(-0.796462\pi\) | ||||
−0.802434 | + | 0.596741i | \(0.796462\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.22800 | −0.0484275 | −0.0242138 | − | 0.999707i | \(-0.507708\pi\) | ||||
−0.0242138 | + | 0.999707i | \(0.507708\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.6320 | −0.889756 | −0.444878 | − | 0.895591i | \(-0.646753\pi\) | ||||
−0.444878 | + | 0.895591i | \(0.646753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.2640 | 2.24781 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.08801 | 0.277375 | 0.138688 | − | 0.990336i | \(-0.455712\pi\) | ||||
0.138688 | + | 0.990336i | \(0.455712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.7720 | −0.577190 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.0000 | −1.55818 | −0.779089 | − | 0.626913i | \(-0.784318\pi\) | ||||
−0.779089 | + | 0.626913i | \(0.784318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.7720 | −0.613460 | −0.306730 | − | 0.951797i | \(-0.599235\pi\) | ||||
−0.306730 | + | 0.951797i | \(0.599235\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.7720 | 0.844282 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.68399 | 0.142645 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.0880 | −1.43177 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.4040 | −1.78874 | −0.894372 | − | 0.447325i | \(-0.852377\pi\) | ||||
−0.894372 | + | 0.447325i | \(0.852377\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.0880 | 1.65601 | 0.828003 | − | 0.560723i | \(-0.189477\pi\) | ||||
0.828003 | + | 0.560723i | \(0.189477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.5960 | −1.05904 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.5440 | 1.05394 | 0.526971 | − | 0.849883i | \(-0.323328\pi\) | ||||
0.526971 | + | 0.849883i | \(0.323328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.0880 | −0.500067 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.6320 | 0.862211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6320 | −0.480544 | −0.240272 | − | 0.970706i | \(-0.577237\pi\) | ||||
−0.240272 | + | 0.970706i | \(0.577237\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.22800 | 0.160377 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.0880 | −1.93510 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.2280 | 0.424076 | 0.212038 | − | 0.977261i | \(-0.431990\pi\) | ||||
0.212038 | + | 0.977261i | \(0.431990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.8600 | 1.69193 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 70.8080 | 2.66301 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.13999 | 0.268148 | 0.134074 | − | 0.990971i | \(-0.457194\pi\) | ||||
0.134074 | + | 0.990971i | \(0.457194\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.31601 | −0.311437 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3160 | −0.535388 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.0000 | −0.671287 | −0.335643 | − | 0.941989i | \(-0.608954\pi\) | ||||
−0.335643 | + | 0.941989i | \(0.608954\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.0360 | −1.15584 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.77200 | −0.177228 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.0880 | −1.30134 | −0.650671 | − | 0.759360i | \(-0.725512\pi\) | ||||
−0.650671 | + | 0.759360i | \(0.725512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45.8600 | −1.69619 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.0880 | −1.51762 | −0.758810 | − | 0.651312i | \(-0.774219\pi\) | ||||
−0.758810 | + | 0.651312i | \(0.774219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.7200 | 1.09475 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.911993 | −0.0335482 | −0.0167741 | − | 0.999859i | \(-0.505340\pi\) | ||||
−0.0167741 | + | 0.999859i | \(0.505340\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.4040 | 0.565118 | 0.282559 | − | 0.959250i | \(-0.408817\pi\) | ||||
0.282559 | + | 0.959250i | \(0.408817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.22800 | 0.0449904 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 52.8080 | 1.92956 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.1760 | 1.06465 | 0.532324 | − | 0.846541i | \(-0.321319\pi\) | ||||
0.532324 | + | 0.846541i | \(0.321319\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0880 | −0.367140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.7200 | 1.40730 | 0.703652 | − | 0.710545i | \(-0.251552\pi\) | ||||
0.703652 | + | 0.710545i | \(0.251552\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.08801 | −0.184440 | −0.0922201 | − | 0.995739i | \(-0.529396\pi\) | ||||
−0.0922201 | + | 0.995739i | \(0.529396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.4560 | 1.03018 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.0000 | 1.29988 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.2640 | −1.95681 | −0.978405 | − | 0.206695i | \(-0.933729\pi\) | ||||
−0.978405 | + | 0.206695i | \(0.933729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.0880 | −1.62170 | −0.810851 | − | 0.585252i | \(-0.800996\pi\) | ||||
−0.810851 | + | 0.585252i | \(0.800996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.7720 | 0.386942 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.5440 | 1.56013 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.9120 | −0.605159 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.772002 | 0.0275539 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.1760 | −1.04001 | −0.520006 | − | 0.854162i | \(-0.674070\pi\) | ||||
−0.520006 | + | 0.854162i | \(0.674070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.0000 | 1.92002 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.3160 | −0.827976 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.1760 | −0.785515 | −0.392757 | − | 0.919642i | \(-0.628479\pi\) | ||||
−0.392757 | + | 0.919642i | \(0.628479\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.7720 | 0.664106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0000 | −0.635206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.91199 | −0.102634 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.0000 | −0.843795 | −0.421898 | − | 0.906644i | \(-0.638636\pi\) | ||||
−0.421898 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.4560 | −0.507619 | −0.253809 | − | 0.967254i | \(-0.581684\pi\) | ||||
−0.253809 | + | 0.967254i | \(0.581684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.54400 | −0.299283 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.0880 | 1.36752 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.45600 | −0.225316 | −0.112658 | − | 0.993634i | \(-0.535936\pi\) | ||||
−0.112658 | + | 0.993634i | \(0.535936\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.4040 | 0.711239 | 0.355620 | − | 0.934631i | \(-0.384270\pi\) | ||||
0.355620 | + | 0.934631i | \(0.384270\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.5440 | 0.470971 | 0.235486 | − | 0.971878i | \(-0.424332\pi\) | ||||
0.235486 | + | 0.971878i | \(0.424332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.2280 | 1.04986 | 0.524931 | − | 0.851145i | \(-0.324091\pi\) | ||||
0.524931 | + | 0.851145i | \(0.324091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −48.9480 | −1.69595 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.0880 | −0.383716 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.36799 | 0.116276 | 0.0581379 | − | 0.998309i | \(-0.481484\pi\) | ||||
0.0581379 | + | 0.998309i | \(0.481484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.22800 | −0.214759 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.00000 | 0.137604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.4040 | −1.52574 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.5440 | −1.11429 | −0.557143 | − | 0.830417i | \(-0.688102\pi\) | ||||
−0.557143 | + | 0.830417i | \(0.688102\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.91199 | 0.236109 | 0.118055 | − | 0.993007i | \(-0.462334\pi\) | ||||
0.118055 | + | 0.993007i | \(0.462334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.2280 | −0.553692 | −0.276846 | − | 0.960914i | \(-0.589289\pi\) | ||||
−0.276846 | + | 0.960914i | \(0.589289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.316006 | 0.0107570 | 0.00537848 | − | 0.999986i | \(-0.498288\pi\) | ||||
0.00537848 | + | 0.999986i | \(0.498288\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.54400 | 0.324506 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.8600 | −0.809395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.6840 | 0.633083 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.77200 | 0.127517 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0000 | −0.776655 | −0.388327 | − | 0.921521i | \(-0.626947\pi\) | ||||
−0.388327 | + | 0.921521i | \(0.626947\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.0880 | −1.38429 | −0.692145 | − | 0.721758i | \(-0.743334\pi\) | ||||
−0.692145 | + | 0.721758i | \(0.743334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.3160 | −0.448119 | −0.224060 | − | 0.974575i | \(-0.571931\pi\) | ||||
−0.224060 | + | 0.974575i | \(0.571931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.3160 | 1.08507 | 0.542533 | − | 0.840035i | \(-0.317465\pi\) | ||||
0.542533 | + | 0.840035i | \(0.317465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.9120 | −0.701366 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.54400 | 0.252168 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −51.4040 | −1.71442 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.0880 | −1.70199 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.31601 | −0.0437455 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.0000 | −1.16216 | −0.581078 | − | 0.813848i | \(-0.697369\pi\) | ||||
−0.581078 | + | 0.813848i | \(0.697369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.1760 | 0.999776 | 0.499888 | − | 0.866090i | \(-0.333375\pi\) | ||||
0.499888 | + | 0.866090i | \(0.333375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.6320 | 0.947581 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −55.7200 | −1.84004 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8600 | −1.24889 | −0.624443 | − | 0.781070i | \(-0.714674\pi\) | ||||
−0.624443 | + | 0.781070i | \(0.714674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.6320 | −0.349957 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.77200 | 0.255542 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.6320 | 1.13624 | 0.568120 | − | 0.822946i | \(-0.307671\pi\) | ||||
0.568120 | + | 0.822946i | \(0.307671\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.7200 | 1.36732 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.3160 | 1.05685 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.22800 | −0.268797 | −0.134398 | − | 0.990927i | \(-0.542910\pi\) | ||||
−0.134398 | + | 0.990927i | \(0.542910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.4040 | 1.21934 | 0.609668 | − | 0.792657i | \(-0.291303\pi\) | ||||
0.609668 | + | 0.792657i | \(0.291303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.82399 | −0.189655 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.5440 | 0.830069 | 0.415034 | − | 0.909806i | \(-0.363770\pi\) | ||||
0.415034 | + | 0.909806i | \(0.363770\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.3160 | −0.367333 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.13999 | −0.198894 | −0.0994469 | − | 0.995043i | \(-0.531707\pi\) | ||||
−0.0994469 | + | 0.995043i | \(0.531707\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.5440 | 0.438274 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.3680 | −1.59418 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 85.0360 | 2.74310 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.22800 | 0.136104 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.77200 | 0.121299 | 0.0606497 | − | 0.998159i | \(-0.480683\pi\) | ||||
0.0606497 | + | 0.998159i | \(0.480683\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.2280 | 0.937971 | 0.468986 | − | 0.883206i | \(-0.344620\pi\) | ||||
0.468986 | + | 0.883206i | \(0.344620\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.9480 | 0.511270 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.77200 | 0.280641 | 0.140321 | − | 0.990106i | \(-0.455187\pi\) | ||||
0.140321 | + | 0.990106i | \(0.455187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.1760 | 1.22011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.4040 | 1.44816 | 0.724082 | − | 0.689714i | \(-0.242264\pi\) | ||||
0.724082 | + | 0.689714i | \(0.242264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000 | 0.637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.22800 | −0.166241 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.0880 | −0.828713 | −0.414356 | − | 0.910115i | \(-0.635993\pi\) | ||||
−0.414356 | + | 0.910115i | \(0.635993\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.0000 | 0.475532 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.3160 | 1.21348 | 0.606740 | − | 0.794900i | \(-0.292477\pi\) | ||||
0.606740 | + | 0.794900i | \(0.292477\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.2.a.m.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1080.2.a.n.1.1 | yes | 2 | ||
4.3 | odd | 2 | 2160.2.a.z.1.2 | 2 | |||
5.2 | odd | 4 | 5400.2.f.be.649.2 | 4 | |||
5.3 | odd | 4 | 5400.2.f.be.649.3 | 4 | |||
5.4 | even | 2 | 5400.2.a.cb.1.2 | 2 | |||
8.3 | odd | 2 | 8640.2.a.db.1.2 | 2 | |||
8.5 | even | 2 | 8640.2.a.de.1.1 | 2 | |||
9.2 | odd | 6 | 3240.2.q.z.1081.2 | 4 | |||
9.4 | even | 3 | 3240.2.q.bc.2161.2 | 4 | |||
9.5 | odd | 6 | 3240.2.q.z.2161.2 | 4 | |||
9.7 | even | 3 | 3240.2.q.bc.1081.2 | 4 | |||
12.11 | even | 2 | 2160.2.a.bb.1.2 | 2 | |||
15.2 | even | 4 | 5400.2.f.bd.649.2 | 4 | |||
15.8 | even | 4 | 5400.2.f.bd.649.3 | 4 | |||
15.14 | odd | 2 | 5400.2.a.ca.1.2 | 2 | |||
24.5 | odd | 2 | 8640.2.a.cq.1.1 | 2 | |||
24.11 | even | 2 | 8640.2.a.cn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.a.m.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1080.2.a.n.1.1 | yes | 2 | 3.2 | odd | 2 | ||
2160.2.a.z.1.2 | 2 | 4.3 | odd | 2 | |||
2160.2.a.bb.1.2 | 2 | 12.11 | even | 2 | |||
3240.2.q.z.1081.2 | 4 | 9.2 | odd | 6 | |||
3240.2.q.z.2161.2 | 4 | 9.5 | odd | 6 | |||
3240.2.q.bc.1081.2 | 4 | 9.7 | even | 3 | |||
3240.2.q.bc.2161.2 | 4 | 9.4 | even | 3 | |||
5400.2.a.ca.1.2 | 2 | 15.14 | odd | 2 | |||
5400.2.a.cb.1.2 | 2 | 5.4 | even | 2 | |||
5400.2.f.bd.649.2 | 4 | 15.2 | even | 4 | |||
5400.2.f.bd.649.3 | 4 | 15.8 | even | 4 | |||
5400.2.f.be.649.2 | 4 | 5.2 | odd | 4 | |||
5400.2.f.be.649.3 | 4 | 5.3 | odd | 4 | |||
8640.2.a.cn.1.2 | 2 | 24.11 | even | 2 | |||
8640.2.a.cq.1.1 | 2 | 24.5 | odd | 2 | |||
8640.2.a.db.1.2 | 2 | 8.3 | odd | 2 | |||
8640.2.a.de.1.1 | 2 | 8.5 | even | 2 |