Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-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 | ||||||||
\(5\) | −1.82843 | −0.817697 | −0.408849 | − | 0.912602i | \(-0.634070\pi\) | ||||
−0.408849 | + | 0.912602i | \(0.634070\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843 | 0.784465 | 0.392232 | − | 0.919866i | \(-0.371703\pi\) | ||||
0.392232 | + | 0.919866i | \(0.371703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.171573 | −0.0416125 | −0.0208063 | − | 0.999784i | \(-0.506623\pi\) | ||||
−0.0208063 | + | 0.999784i | \(0.506623\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.82843 | −1.56655 | −0.783274 | − | 0.621676i | \(-0.786452\pi\) | ||||
−0.783274 | + | 0.621676i | \(0.786452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.65685 | −0.331371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82843 | −0.525226 | −0.262613 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.82843 | 1.22642 | 0.613211 | − | 0.789919i | \(-0.289878\pi\) | ||||
0.613211 | + | 0.789919i | \(0.289878\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.82843 | 0.309061 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.65685 | 0.436784 | 0.218392 | − | 0.975861i | \(-0.429919\pi\) | ||||
0.218392 | + | 0.975861i | \(0.429919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.82843 | −0.597900 | −0.298950 | − | 0.954269i | \(-0.596636\pi\) | ||||
−0.298950 | + | 0.954269i | \(0.596636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.82843 | −1.19382 | −0.596912 | − | 0.802307i | \(-0.703606\pi\) | ||||
−0.596912 | + | 0.802307i | \(0.703606\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.65685 | 1.26273 | 0.631366 | − | 0.775485i | \(-0.282495\pi\) | ||||
0.631366 | + | 0.775485i | \(0.282495\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.82843 | −1.19042 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.656854 | 0.0855151 | 0.0427576 | − | 0.999085i | \(-0.486386\pi\) | ||||
0.0427576 | + | 0.999085i | \(0.486386\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.17157 | 0.406078 | 0.203039 | − | 0.979171i | \(-0.434918\pi\) | ||||
0.203039 | + | 0.979171i | \(0.434918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.17157 | −0.641455 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.65685 | 0.196632 | 0.0983162 | − | 0.995155i | \(-0.468654\pi\) | ||||
0.0983162 | + | 0.995155i | \(0.468654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.65685 | −0.662085 | −0.331042 | − | 0.943616i | \(-0.607400\pi\) | ||||
−0.331042 | + | 0.943616i | \(0.607400\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.82843 | −0.550250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.82843 | 0.205714 | 0.102857 | − | 0.994696i | \(-0.467202\pi\) | ||||
0.102857 | + | 0.994696i | \(0.467202\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.34315 | −0.586486 | −0.293243 | − | 0.956038i | \(-0.594735\pi\) | ||||
−0.293243 | + | 0.956038i | \(0.594735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.313708 | 0.0340265 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.4853 | 1.28096 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.1421 | −1.84205 | −0.921027 | − | 0.389498i | \(-0.872649\pi\) | ||||
−0.921027 | + | 0.389498i | \(0.872649\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.9706 | 1.88764 | 0.943821 | − | 0.330458i | \(-0.107203\pi\) | ||||
0.943821 | + | 0.330458i | \(0.107203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.34315 | −0.230877 | −0.115439 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.65685 | −0.546869 | −0.273434 | − | 0.961891i | \(-0.588160\pi\) | ||||
−0.273434 | + | 0.961891i | \(0.588160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6569 | −1.02074 | −0.510371 | − | 0.859954i | \(-0.670492\pi\) | ||||
−0.510371 | + | 0.859954i | \(0.670492\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.17157 | 0.674645 | 0.337322 | − | 0.941389i | \(-0.390479\pi\) | ||||
0.337322 | + | 0.941389i | \(0.390479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.31371 | 0.682007 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.171573 | 0.0157281 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1716 | 1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.1716 | −1.08005 | −0.540026 | − | 0.841648i | \(-0.681586\pi\) | ||||
−0.540026 | + | 0.841648i | \(0.681586\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.82843 | 0.592100 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.8284 | −1.26688 | −0.633439 | − | 0.773793i | \(-0.718357\pi\) | ||||
−0.633439 | + | 0.773793i | \(0.718357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1716 | −0.947560 | −0.473780 | − | 0.880643i | \(-0.657111\pi\) | ||||
−0.473780 | + | 0.880643i | \(0.657111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.6569 | 1.14204 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.17157 | 0.429476 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.1421 | 1.65011 | 0.825054 | − | 0.565054i | \(-0.191145\pi\) | ||||
0.825054 | + | 0.565054i | \(0.191145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8284 | −1.45086 | −0.725428 | − | 0.688298i | \(-0.758358\pi\) | ||||
−0.725428 | + | 0.688298i | \(0.758358\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.4853 | −1.00284 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.82843 | 0.225733 | 0.112867 | − | 0.993610i | \(-0.463997\pi\) | ||||
0.112867 | + | 0.993610i | \(0.463997\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.48528 | 0.116336 | 0.0581681 | − | 0.998307i | \(-0.481474\pi\) | ||||
0.0581681 | + | 0.998307i | \(0.481474\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.9706 | −1.39060 | −0.695302 | − | 0.718718i | \(-0.744729\pi\) | ||||
−0.695302 | + | 0.718718i | \(0.744729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000 | 0.152057 | 0.0760286 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760286 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.65685 | 0.125246 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.14214 | −0.309598 | −0.154799 | − | 0.987946i | \(-0.549473\pi\) | ||||
−0.154799 | + | 0.987946i | \(0.549473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.6569 | 1.46108 | 0.730541 | − | 0.682869i | \(-0.239268\pi\) | ||||
0.730541 | + | 0.682869i | \(0.239268\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.85786 | −0.357157 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.828427 | −0.0605806 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.6274 | −1.78198 | −0.890989 | − | 0.454026i | \(-0.849987\pi\) | ||||
−0.890989 | + | 0.454026i | \(0.849987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.3137 | 0.742397 | 0.371198 | − | 0.928554i | \(-0.378947\pi\) | ||||
0.371198 | + | 0.928554i | \(0.378947\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.7990 | −0.840643 | −0.420322 | − | 0.907375i | \(-0.638083\pi\) | ||||
−0.420322 | + | 0.907375i | \(0.638083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.9706 | −1.34479 | −0.672394 | − | 0.740194i | \(-0.734734\pi\) | ||||
−0.672394 | + | 0.740194i | \(0.734734\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.82843 | 0.198517 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.00000 | 0.488901 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.9706 | −2.28062 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9706 | −1.16830 | −0.584151 | − | 0.811645i | \(-0.698572\pi\) | ||||
−0.584151 | + | 0.811645i | \(0.698572\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.3137 | 0.976187 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.82843 | −0.463544 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.485281 | −0.0326436 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.1421 | −1.21489 | −0.607444 | − | 0.794363i | \(-0.707805\pi\) | ||||
−0.607444 | + | 0.794363i | \(0.707805\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.6569 | 1.17193 | 0.585963 | − | 0.810338i | \(-0.300716\pi\) | ||||
0.585963 | + | 0.810338i | \(0.300716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.31371 | 0.0868123 | 0.0434062 | − | 0.999058i | \(-0.486179\pi\) | ||||
0.0434062 | + | 0.999058i | \(0.486179\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.1421 | 0.664433 | 0.332217 | − | 0.943203i | \(-0.392203\pi\) | ||||
0.332217 | + | 0.943203i | \(0.392203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8284 | −1.03253 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.1421 | −0.785409 | −0.392705 | − | 0.919665i | \(-0.628461\pi\) | ||||
−0.392705 | + | 0.919665i | \(0.628461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.1421 | −1.16864 | −0.584319 | − | 0.811524i | \(-0.698638\pi\) | ||||
−0.584319 | + | 0.811524i | \(0.698638\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.82843 | −0.116814 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.3137 | −1.22890 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.97056 | −0.250620 | −0.125310 | − | 0.992118i | \(-0.539992\pi\) | ||||
−0.125310 | + | 0.992118i | \(0.539992\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.3137 | −1.21424 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.65685 | −0.165089 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.8284 | −0.667709 | −0.333855 | − | 0.942625i | \(-0.608349\pi\) | ||||
−0.333855 | + | 0.942625i | \(0.608349\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.65685 | −0.224639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1421 | 0.923232 | 0.461616 | − | 0.887080i | \(-0.347270\pi\) | ||||
0.461616 | + | 0.887080i | \(0.347270\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.00000 | 0.364474 | 0.182237 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182237 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.00000 | −0.482418 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.6569 | −1.48149 | −0.740743 | − | 0.671788i | \(-0.765527\pi\) | ||||
−0.740743 | + | 0.671788i | \(0.765527\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.9706 | −1.96686 | −0.983429 | − | 0.181291i | \(-0.941972\pi\) | ||||
−0.983429 | + | 0.181291i | \(0.941972\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.1716 | −1.37741 | −0.688704 | − | 0.725043i | \(-0.741820\pi\) | ||||
−0.688704 | + | 0.725043i | \(0.741820\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.82843 | 0.225985 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9706 | −0.998268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1716 | 0.711071 | 0.355535 | − | 0.934663i | \(-0.384299\pi\) | ||||
0.355535 | + | 0.934663i | \(0.384299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.20101 | −0.0699255 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.3137 | −0.654289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.82843 | 0.451223 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.79899 | −0.332049 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.2843 | 1.38598 | 0.692988 | − | 0.720949i | \(-0.256294\pi\) | ||||
0.692988 | + | 0.720949i | \(0.256294\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.97056 | −0.565379 | −0.282689 | − | 0.959212i | \(-0.591227\pi\) | ||||
−0.282689 | + | 0.959212i | \(0.591227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.6274 | 1.39202 | 0.696012 | − | 0.718030i | \(-0.254956\pi\) | ||||
0.696012 | + | 0.718030i | \(0.254956\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.6569 | −1.66569 | −0.832847 | − | 0.553503i | \(-0.813291\pi\) | ||||
−0.832847 | + | 0.553503i | \(0.813291\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6569 | −0.764637 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.17157 | 0.0651881 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.68629 | −0.259949 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.65685 | −0.477268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.7990 | −1.58294 | −0.791468 | − | 0.611211i | \(-0.790683\pi\) | ||||
−0.791468 | + | 0.611211i | \(0.790683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.31371 | 0.399591 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.3137 | −1.10656 | −0.553279 | − | 0.832996i | \(-0.686624\pi\) | ||||
−0.553279 | + | 0.832996i | \(0.686624\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.9706 | 1.78546 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.14214 | 0.329727 | 0.164864 | − | 0.986316i | \(-0.447282\pi\) | ||||
0.164864 | + | 0.986316i | \(0.447282\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.2843 | −1.08579 | −0.542896 | − | 0.839800i | \(-0.682672\pi\) | ||||
−0.542896 | + | 0.839800i | \(0.682672\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.85786 | −0.258558 | −0.129279 | − | 0.991608i | \(-0.541266\pi\) | ||||
−0.129279 | + | 0.991608i | \(0.541266\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.02944 | −0.160786 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.3431 | −0.862558 | −0.431279 | − | 0.902219i | \(-0.641938\pi\) | ||||
−0.431279 | + | 0.902219i | \(0.641938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.6274 | 1.45407 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.3431 | 0.541385 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.0000 | −1.14839 | −0.574195 | − | 0.818718i | \(-0.694685\pi\) | ||||
−0.574195 | + | 0.818718i | \(0.694685\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | −0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.68629 | 0.190869 | 0.0954345 | − | 0.995436i | \(-0.469576\pi\) | ||||
0.0954345 | + | 0.995436i | \(0.469576\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.4853 | 0.898159 | 0.449079 | − | 0.893492i | \(-0.351752\pi\) | ||||
0.449079 | + | 0.893492i | \(0.351752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.00000 | −0.0510976 | −0.0255488 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255488 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.82843 | 0.449938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.79899 | −0.0912124 | −0.0456062 | − | 0.998959i | \(-0.514522\pi\) | ||||
−0.0456062 | + | 0.998959i | \(0.514522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.686292 | 0.0347073 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.34315 | −0.168212 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3431 | 0.719862 | 0.359931 | − | 0.932979i | \(-0.382800\pi\) | ||||
0.359931 | + | 0.932979i | \(0.382800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.3137 | 1.26411 | 0.632053 | − | 0.774925i | \(-0.282212\pi\) | ||||
0.632053 | + | 0.774925i | \(0.282212\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.3137 | 0.962084 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.8284 | 0.635882 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.02944 | −0.149796 | −0.0748980 | − | 0.997191i | \(-0.523863\pi\) | ||||
−0.0748980 | + | 0.997191i | \(0.523863\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.656854 | −0.0323217 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.76955 | 0.479568 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.6569 | 0.911447 | 0.455723 | − | 0.890121i | \(-0.349381\pi\) | ||||
0.455723 | + | 0.890121i | \(0.349381\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.9706 | 0.729621 | 0.364810 | − | 0.931082i | \(-0.381134\pi\) | ||||
0.364810 | + | 0.931082i | \(0.381134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.284271 | 0.0137892 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.17157 | −0.153483 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.9706 | −1.20279 | −0.601395 | − | 0.798952i | \(-0.705388\pi\) | ||||
−0.601395 | + | 0.798952i | \(0.705388\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.4853 | 1.65726 | 0.828628 | − | 0.559799i | \(-0.189122\pi\) | ||||
0.828628 | + | 0.559799i | \(0.189122\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.3137 | 1.30659 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0000 | −1.05000 | −0.525001 | − | 0.851101i | \(-0.675935\pi\) | ||||
−0.525001 | + | 0.851101i | \(0.675935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.8284 | 1.65475 | 0.827374 | − | 0.561651i | \(-0.189834\pi\) | ||||
0.827374 | + | 0.561651i | \(0.189834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9706 | −0.520055 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.17157 | 0.0552899 | 0.0276450 | − | 0.999618i | \(-0.491199\pi\) | ||||
0.0276450 | + | 0.999618i | \(0.491199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.4853 | −0.870438 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.17157 | 0.242447 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.3137 | 1.93257 | 0.966287 | − | 0.257468i | \(-0.0828881\pi\) | ||||
0.966287 | + | 0.257468i | \(0.0828881\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.514719 | −0.0239728 | −0.0119864 | − | 0.999928i | \(-0.503815\pi\) | ||||
−0.0119864 | + | 0.999928i | \(0.503815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1716 | 0.844505 | 0.422252 | − | 0.906478i | \(-0.361240\pi\) | ||||
0.422252 | + | 0.906478i | \(0.361240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.2843 | −1.86413 | −0.932067 | − | 0.362286i | \(-0.881996\pi\) | ||||
−0.932067 | + | 0.362286i | \(0.881996\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −37.7990 | −1.73800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3137 | 0.519109 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.00000 | 0.0456912 | 0.0228456 | − | 0.999739i | \(-0.492727\pi\) | ||||
0.0228456 | + | 0.999739i | \(0.492727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.51472 | 0.342642 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.1716 | 1.50624 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.1421 | 1.36030 | 0.680148 | − | 0.733075i | \(-0.261916\pi\) | ||||
0.680148 | + | 0.733075i | \(0.261916\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.485281 | 0.0218560 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.65685 | −0.0743201 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.7696 | −1.95939 | −0.979697 | − | 0.200483i | \(-0.935749\pi\) | ||||
−0.979697 | + | 0.200483i | \(0.935749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.62742 | 0.429265 | 0.214633 | − | 0.976695i | \(-0.431145\pi\) | ||||
0.214633 | + | 0.976695i | \(0.431145\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.6863 | −1.54352 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.48528 | 0.243131 | 0.121565 | − | 0.992583i | \(-0.461209\pi\) | ||||
0.121565 | + | 0.992583i | \(0.461209\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.65685 | 0.250244 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.28427 | 0.188788 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.7990 | 1.83832 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.4558 | 1.68478 | 0.842391 | − | 0.538867i | \(-0.181148\pi\) | ||||
0.842391 | + | 0.538867i | \(0.181148\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.4264 | −1.76772 | −0.883862 | − | 0.467748i | \(-0.845065\pi\) | ||||
−0.883862 | + | 0.467748i | \(0.845065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.17157 | −0.0510345 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.8284 | −0.469031 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.3431 | 0.447173 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.82843 | 0.207975 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.2843 | −1.17304 | −0.586521 | − | 0.809934i | \(-0.699503\pi\) | ||||
−0.586521 | + | 0.809934i | \(0.699503\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.4853 | 0.834658 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.48528 | −0.234534 | −0.117267 | − | 0.993100i | \(-0.537413\pi\) | ||||
−0.117267 | + | 0.993100i | \(0.537413\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.3137 | 0.822792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.82843 | −0.0777526 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.3137 | 1.49629 | 0.748145 | − | 0.663535i | \(-0.230945\pi\) | ||||
0.748145 | + | 0.663535i | \(0.230945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.1421 | −0.936513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.3137 | −1.65688 | −0.828438 | − | 0.560081i | \(-0.810770\pi\) | ||||
−0.828438 | + | 0.560081i | \(0.810770\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1127 | −0.551655 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.3431 | −1.10436 | −0.552181 | − | 0.833724i | \(-0.686204\pi\) | ||||
−0.552181 | + | 0.833724i | \(0.686204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.7696 | 1.32951 | 0.664757 | − | 0.747059i | \(-0.268535\pi\) | ||||
0.664757 | + | 0.747059i | \(0.268535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.62742 | 0.276382 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9706 | 0.456711 | 0.228355 | − | 0.973578i | \(-0.426665\pi\) | ||||
0.228355 | + | 0.973578i | \(0.426665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.34315 | 0.221671 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.65685 | 0.399946 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.97056 | −0.205157 | −0.102579 | − | 0.994725i | \(-0.532709\pi\) | ||||
−0.102579 | + | 0.994725i | \(0.532709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −46.6274 | −1.92125 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.4853 | −0.471644 | −0.235822 | − | 0.971796i | \(-0.575778\pi\) | ||||
−0.235822 | + | 0.971796i | \(0.575778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.313708 | −0.0128608 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.1716 | 1.11020 | 0.555100 | − | 0.831783i | \(-0.312680\pi\) | ||||
0.555100 | + | 0.831783i | \(0.312680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.1127 | 0.779623 | 0.389812 | − | 0.920895i | \(-0.372540\pi\) | ||||
0.389812 | + | 0.920895i | \(0.372540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.5147 | −0.915353 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.14214 | 0.168124 | 0.0840620 | − | 0.996461i | \(-0.473211\pi\) | ||||
0.0840620 | + | 0.996461i | \(0.473211\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.4853 | 0.990568 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.3137 | −1.42168 | −0.710838 | − | 0.703356i | \(-0.751684\pi\) | ||||
−0.710838 | + | 0.703356i | \(0.751684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.17157 | 0.0470895 | 0.0235447 | − | 0.999723i | \(-0.492505\pi\) | ||||
0.0235447 | + | 0.999723i | \(0.492505\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.455844 | −0.0181757 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.1127 | 1.11915 | 0.559574 | − | 0.828780i | \(-0.310965\pi\) | ||||
0.559574 | + | 0.828780i | \(0.310965\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.2548 | 0.883156 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.82843 | 0.112066 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.4558 | 0.452479 | 0.226239 | − | 0.974072i | \(-0.427357\pi\) | ||||
0.226239 | + | 0.974072i | \(0.427357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.6569 | 0.851419 | 0.425709 | − | 0.904860i | \(-0.360025\pi\) | ||||
0.425709 | + | 0.904860i | \(0.360025\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.17157 | 0.124495 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.48528 | 0.253789 | 0.126894 | − | 0.991916i | \(-0.459499\pi\) | ||||
0.126894 | + | 0.991916i | \(0.459499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.31371 | −0.285770 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.3431 | −0.480821 | −0.240410 | − | 0.970671i | \(-0.577282\pi\) | ||||
−0.240410 | + | 0.970671i | \(0.577282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1127 | −0.665607 | −0.332803 | − | 0.942996i | \(-0.607995\pi\) | ||||
−0.332803 | + | 0.942996i | \(0.607995\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.4853 | −0.484158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3137 | 0.438069 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3137 | 0.591179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.6569 | −1.37447 | −0.687235 | − | 0.726435i | \(-0.741176\pi\) | ||||
−0.687235 | + | 0.726435i | \(0.741176\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.3137 | −0.972885 | −0.486442 | − | 0.873713i | \(-0.661706\pi\) | ||||
−0.486442 | + | 0.873713i | \(0.661706\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.1421 | 0.696231 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.1716 | −0.810108 | −0.405054 | − | 0.914293i | \(-0.632747\pi\) | ||||
−0.405054 | + | 0.914293i | \(0.632747\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.1127 | 1.03592 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.65685 | 0.215509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.8284 | 0.792351 | 0.396175 | − | 0.918175i | \(-0.370337\pi\) | ||||
0.396175 | + | 0.918175i | \(0.370337\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.4264 | 0.774818 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.656854 | 0.0248801 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.4853 | 1.75572 | 0.877862 | − | 0.478913i | \(-0.158969\pi\) | ||||
0.877862 | + | 0.478913i | \(0.158969\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.1421 | −0.684244 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.9706 | −0.713461 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.2843 | 1.17491 | 0.587453 | − | 0.809258i | \(-0.300131\pi\) | ||||
0.587453 | + | 0.809258i | \(0.300131\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.3137 | −1.02291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.9706 | −0.933846 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.34315 | 0.0500909 | 0.0250454 | − | 0.999686i | \(-0.492027\pi\) | ||||
0.0250454 | + | 0.999686i | \(0.492027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.34315 | 0.0872633 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.68629 | 0.174044 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1421 | −0.376151 | −0.188075 | − | 0.982155i | \(-0.560225\pi\) | ||||
−0.188075 | + | 0.982155i | \(0.560225\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.34315 | 0.0496780 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.68629 | 0.0992204 | 0.0496102 | − | 0.998769i | \(-0.484202\pi\) | ||||
0.0496102 | + | 0.998769i | \(0.484202\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.3137 | −0.711430 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.9411 | −1.39569 | −0.697843 | − | 0.716250i | \(-0.745857\pi\) | ||||
−0.697843 | + | 0.716250i | \(0.745857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.17157 | −0.0429808 | −0.0214904 | − | 0.999769i | \(-0.506841\pi\) | ||||
−0.0214904 | + | 0.999769i | \(0.506841\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.8284 | −1.34929 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.65685 | 0.206697 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | 0.875772 | 0.437886 | − | 0.899030i | \(-0.355727\pi\) | ||||
0.437886 | + | 0.899030i | \(0.355727\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.5980 | 1.18636 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.6274 | −1.29490 | −0.647450 | − | 0.762108i | \(-0.724165\pi\) | ||||
−0.647450 | + | 0.762108i | \(0.724165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.17157 | −0.0787195 | −0.0393597 | − | 0.999225i | \(-0.512532\pi\) | ||||
−0.0393597 | + | 0.999225i | \(0.512532\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6569 | 0.385804 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.85786 | 0.0670836 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.34315 | 0.156618 | 0.0783089 | − | 0.996929i | \(-0.475048\pi\) | ||||
0.0783089 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.8284 | 1.36059 | 0.680297 | − | 0.732937i | \(-0.261851\pi\) | ||||
0.680297 | + | 0.732937i | \(0.261851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.3137 | −0.406400 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.1421 | 0.936639 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.17157 | −0.184581 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.9411 | 0.924701 | 0.462351 | − | 0.886697i | \(-0.347006\pi\) | ||||
0.462351 | + | 0.886697i | \(0.347006\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.17157 | −0.254992 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.97056 | 0.318554 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.3137 | −0.471596 | −0.235798 | − | 0.971802i | \(-0.575770\pi\) | ||||
−0.235798 | + | 0.971802i | \(0.575770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.48528 | −0.0525455 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.3137 | −0.963880 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.31371 | −0.257774 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.9411 | −1.12299 | −0.561495 | − | 0.827480i | \(-0.689774\pi\) | ||||
−0.561495 | + | 0.827480i | \(0.689774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.7696 | 1.50184 | 0.750921 | − | 0.660392i | \(-0.229610\pi\) | ||||
0.750921 | + | 0.660392i | \(0.229610\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.71573 | −0.0951278 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.4558 | 1.87018 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.6569 | 0.755829 | 0.377915 | − | 0.925840i | \(-0.376641\pi\) | ||||
0.377915 | + | 0.925840i | \(0.376641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.1716 | 0.912284 | 0.456142 | − | 0.889907i | \(-0.349231\pi\) | ||||
0.456142 | + | 0.889907i | \(0.349231\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.17157 | 0.110286 | 0.0551432 | − | 0.998478i | \(-0.482438\pi\) | ||||
0.0551432 | + | 0.998478i | \(0.482438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.17157 | 0.318542 | 0.159271 | − | 0.987235i | \(-0.449086\pi\) | ||||
0.159271 | + | 0.987235i | \(0.449086\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.171573 | −0.00594465 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.8579 | 1.13709 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.3137 | −0.839402 | −0.419701 | − | 0.907662i | \(-0.637865\pi\) | ||||
−0.419701 | + | 0.907662i | \(0.637865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.14214 | 0.314499 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3137 | −0.423104 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.6274 | −0.364303 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.9706 | 0.512582 | 0.256291 | − | 0.966600i | \(-0.417499\pi\) | ||||
0.256291 | + | 0.966600i | \(0.417499\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.1421 | −1.47371 | −0.736854 | − | 0.676052i | \(-0.763689\pi\) | ||||
−0.736854 | + | 0.676052i | \(0.763689\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.6569 | 0.397727 | 0.198863 | − | 0.980027i | \(-0.436275\pi\) | ||||
0.198863 | + | 0.980027i | \(0.436275\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.6863 | 0.636089 | 0.318044 | − | 0.948076i | \(-0.396974\pi\) | ||||
0.318044 | + | 0.948076i | \(0.396974\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.65685 | −0.124337 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.82843 | 0.299484 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.3137 | −0.383350 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1716 | −0.411474 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.9706 | −1.07957 | −0.539785 | − | 0.841803i | \(-0.681494\pi\) | ||||
−0.539785 | + | 0.841803i | \(0.681494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.9706 | 0.908661 | 0.454331 | − | 0.890833i | \(-0.349878\pi\) | ||||
0.454331 | + | 0.890833i | \(0.349878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.7990 | −1.03647 | −0.518234 | − | 0.855239i | \(-0.673410\pi\) | ||||
−0.518234 | + | 0.855239i | \(0.673410\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −52.5980 | −1.76607 | −0.883034 | − | 0.469310i | \(-0.844503\pi\) | ||||
−0.883034 | + | 0.469310i | \(0.844503\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.1716 | 0.408221 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −59.1127 | −1.97813 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.57359 | 0.253157 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.3137 | −0.644148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.343146 | −0.0114318 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35.9411 | −1.19472 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.7696 | 0.988482 | 0.494241 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494241 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.4853 | −1.01002 | −0.505011 | − | 0.863113i | \(-0.668512\pi\) | ||||
−0.505011 | + | 0.863113i | \(0.668512\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.7990 | −0.853822 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.0833 | 1.48716 | 0.743580 | − | 0.668647i | \(-0.233126\pi\) | ||||
0.743580 | + | 0.668647i | \(0.233126\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.68629 | 0.154251 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.40202 | −0.144738 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.8284 | −0.519314 | −0.259657 | − | 0.965701i | \(-0.583609\pi\) | ||||
−0.259657 | + | 0.965701i | \(0.583609\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.82843 | −0.223793 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.51472 | 0.0495366 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.1716 | 1.08367 | 0.541834 | − | 0.840486i | \(-0.317730\pi\) | ||||
0.541834 | + | 0.840486i | \(0.317730\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.7990 | −1.39521 | −0.697604 | − | 0.716484i | \(-0.745750\pi\) | ||||
−0.697604 | + | 0.716484i | \(0.745750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.3137 | 0.498683 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.9411 | 1.88283 | 0.941417 | − | 0.337245i | \(-0.109495\pi\) | ||||
0.941417 | + | 0.337245i | \(0.109495\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.0000 | −0.519382 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.31371 | 0.107342 | 0.0536708 | − | 0.998559i | \(-0.482908\pi\) | ||||
0.0536708 | + | 0.998559i | \(0.482908\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0294 | 1.45712 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.8284 | 0.478835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.8579 | −0.607056 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.65685 | 0.181912 | 0.0909561 | − | 0.995855i | \(-0.471008\pi\) | ||||
0.0909561 | + | 0.995855i | \(0.471008\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.6569 | 0.341995 | 0.170997 | − | 0.985271i | \(-0.445301\pi\) | ||||
0.170997 | + | 0.985271i | \(0.445301\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.1716 | 0.358144 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.9706 | 1.37475 | 0.687375 | − | 0.726303i | \(-0.258763\pi\) | ||||
0.687375 | + | 0.726303i | \(0.258763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.9706 | 0.925903 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.71573 | 0.0866183 | 0.0433091 | − | 0.999062i | \(-0.486210\pi\) | ||||
0.0433091 | + | 0.999062i | \(0.486210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.5736 | 0.687392 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.3137 | 0.995718 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.4264 | −0.871229 | −0.435614 | − | 0.900133i | \(-0.643469\pi\) | ||||
−0.435614 | + | 0.900133i | \(0.643469\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.6863 | 1.09963 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.8579 | −0.565564 | −0.282782 | − | 0.959184i | \(-0.591257\pi\) | ||||
−0.282782 | + | 0.959184i | \(0.591257\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.a.bh.1.1 | yes | 2 | |
3.2 | odd | 2 | 6048.2.a.y.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 6048.2.a.bi.1.1 | yes | 2 | ||
12.11 | even | 2 | 6048.2.a.bb.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.y.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
6048.2.a.bb.1.2 | yes | 2 | 12.11 | even | 2 | ||
6048.2.a.bh.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
6048.2.a.bi.1.1 | yes | 2 | 4.3 | odd | 2 |