Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6840,2,Mod(1,6840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6840.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: | \(54.6176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.321637\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6840.1 |
$q$-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 | ||||||||
\(7\) | −4.21819 | −1.59432 | −0.797162 | − | 0.603765i | \(-0.793667\pi\) | ||||
−0.797162 | + | 0.603765i | \(0.793667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.57491 | −1.68090 | −0.840450 | − | 0.541890i | \(-0.817709\pi\) | ||||
−0.840450 | + | 0.541890i | \(0.817709\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.21819 | −0.615214 | −0.307607 | − | 0.951513i | \(-0.599528\pi\) | ||||
−0.307607 | + | 0.951513i | \(0.599528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.643274 | −0.156017 | −0.0780085 | − | 0.996953i | \(-0.524856\pi\) | ||||
−0.0780085 | + | 0.996953i | \(0.524856\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.35673 | −0.282897 | −0.141448 | − | 0.989946i | \(-0.545176\pi\) | ||||
−0.141448 | + | 0.989946i | \(0.545176\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.86146 | −0.902751 | −0.451375 | − | 0.892334i | \(-0.649066\pi\) | ||||
−0.451375 | + | 0.892334i | \(0.649066\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.64327 | 0.474746 | 0.237373 | − | 0.971419i | \(-0.423714\pi\) | ||||
0.237373 | + | 0.971419i | \(0.423714\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.21819 | −0.713004 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.21819 | −0.364668 | −0.182334 | − | 0.983237i | \(-0.558365\pi\) | ||||
−0.182334 | + | 0.983237i | \(0.558365\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.57491 | −0.558308 | −0.279154 | − | 0.960246i | \(-0.590054\pi\) | ||||
−0.279154 | + | 0.960246i | \(0.590054\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.218187 | −0.0332732 | −0.0166366 | − | 0.999862i | \(-0.505296\pi\) | ||||
−0.0166366 | + | 0.999862i | \(0.505296\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.35673 | 0.197899 | 0.0989494 | − | 0.995092i | \(-0.468452\pi\) | ||||
0.0989494 | + | 0.995092i | \(0.468452\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.7931 | 1.54187 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.643274 | −0.0883605 | −0.0441803 | − | 0.999024i | \(-0.514068\pi\) | ||||
−0.0441803 | + | 0.999024i | \(0.514068\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.57491 | −0.751721 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.43637 | 0.577567 | 0.288783 | − | 0.957394i | \(-0.406749\pi\) | ||||
0.288783 | + | 0.957394i | \(0.406749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0796 | 1.67468 | 0.837339 | − | 0.546685i | \(-0.184110\pi\) | ||||
0.837339 | + | 0.546685i | \(0.184110\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.21819 | −0.275132 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.28655 | 0.157177 | 0.0785885 | − | 0.996907i | \(-0.474959\pi\) | ||||
0.0785885 | + | 0.996907i | \(0.474959\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.1498 | −1.32324 | −0.661620 | − | 0.749839i | \(-0.730131\pi\) | ||||
−0.661620 | + | 0.749839i | \(0.730131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.5160 | 2.67990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.28655 | −0.144748 | −0.0723740 | − | 0.997378i | \(-0.523058\pi\) | ||||
−0.0723740 | + | 0.997378i | \(0.523058\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3662 | −1.35737 | −0.678683 | − | 0.734431i | \(-0.737449\pi\) | ||||
−0.678683 | + | 0.734431i | \(0.737449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.643274 | −0.0697729 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0113 | −1.27319 | −0.636597 | − | 0.771197i | \(-0.719658\pi\) | ||||
−0.636597 | + | 0.771197i | \(0.719658\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.35673 | 0.980851 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.78181 | 0.587054 | 0.293527 | − | 0.955951i | \(-0.405171\pi\) | ||||
0.293527 | + | 0.955951i | \(0.405171\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.43637 | 0.640443 | 0.320222 | − | 0.947343i | \(-0.396243\pi\) | ||||
0.320222 | + | 0.947343i | \(0.396243\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.28655 | −0.126767 | −0.0633837 | − | 0.997989i | \(-0.520189\pi\) | ||||
−0.0633837 | + | 0.997989i | \(0.520189\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.28655 | 0.124375 | 0.0621877 | − | 0.998064i | \(-0.480192\pi\) | ||||
0.0621877 | + | 0.998064i | \(0.480192\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.4364 | 1.76588 | 0.882942 | − | 0.469482i | \(-0.155559\pi\) | ||||
0.882942 | + | 0.469482i | \(0.155559\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0796 | −1.23043 | −0.615215 | − | 0.788359i | \(-0.710931\pi\) | ||||
−0.615215 | + | 0.788359i | \(0.710931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.35673 | −0.126515 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.71345 | 0.248742 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.0796 | 1.82542 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.28655 | −0.824048 | −0.412024 | − | 0.911173i | \(-0.635178\pi\) | ||||
−0.412024 | + | 0.911173i | \(0.635178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.86146 | −0.250007 | −0.125004 | − | 0.992156i | \(-0.539894\pi\) | ||||
−0.125004 | + | 0.992156i | \(0.539894\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.21819 | 0.365763 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.8727 | 1.27066 | 0.635332 | − | 0.772239i | \(-0.280863\pi\) | ||||
0.635332 | + | 0.772239i | \(0.280863\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.850175 | 0.0721109 | 0.0360555 | − | 0.999350i | \(-0.488521\pi\) | ||||
0.0360555 | + | 0.999350i | \(0.488521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.3662 | 1.03411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.86146 | −0.403722 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.1593 | 1.65151 | 0.825757 | − | 0.564026i | \(-0.190748\pi\) | ||||
0.825757 | + | 0.564026i | \(0.190748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5160 | 0.937161 | 0.468580 | − | 0.883421i | \(-0.344766\pi\) | ||||
0.468580 | + | 0.883421i | \(0.344766\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.64327 | 0.212313 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.14982 | 0.730236 | 0.365118 | − | 0.930961i | \(-0.381029\pi\) | ||||
0.365118 | + | 0.930961i | \(0.381029\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.72292 | 0.451029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50474 | −0.431164 | −0.215582 | − | 0.976486i | \(-0.569165\pi\) | ||||
−0.215582 | + | 0.976486i | \(0.569165\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.920352 | 0.0712190 | 0.0356095 | − | 0.999366i | \(-0.488663\pi\) | ||||
0.0356095 | + | 0.999366i | \(0.488663\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.07965 | −0.621511 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.6658 | 1.26708 | 0.633540 | − | 0.773710i | \(-0.281601\pi\) | ||||
0.633540 | + | 0.773710i | \(0.281601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.21819 | −0.318865 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.0226 | 1.79553 | 0.897766 | − | 0.440473i | \(-0.145189\pi\) | ||||
0.897766 | + | 0.440473i | \(0.145189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.14982 | −0.680101 | −0.340051 | − | 0.940407i | \(-0.610444\pi\) | ||||
−0.340051 | + | 0.940407i | \(0.610444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.21819 | −0.163084 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.58620 | 0.262249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.2884 | 1.17858 | 0.589292 | − | 0.807920i | \(-0.299407\pi\) | ||||
0.589292 | + | 0.807920i | \(0.299407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5047 | 1.40398 | 0.701991 | − | 0.712186i | \(-0.252295\pi\) | ||||
0.701991 | + | 0.712186i | \(0.252295\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.51602 | −0.677988 | −0.338994 | − | 0.940788i | \(-0.610087\pi\) | ||||
−0.338994 | + | 0.940788i | \(0.610087\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.27708 | −0.161418 | −0.0807089 | − | 0.996738i | \(-0.525718\pi\) | ||||
−0.0807089 | + | 0.996738i | \(0.525718\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.5066 | 1.43928 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.57491 | −0.249683 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.57491 | 0.385625 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.42690 | 0.0982320 | 0.0491160 | − | 0.998793i | \(-0.484360\pi\) | ||||
0.0491160 | + | 0.998793i | \(0.484360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.218187 | −0.0148802 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.1498 | −0.756899 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.42690 | 0.0959839 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.71345 | −0.449566 | −0.224783 | − | 0.974409i | \(-0.572167\pi\) | ||||
−0.224783 | + | 0.974409i | \(0.572167\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7931 | 0.915480 | 0.457740 | − | 0.889086i | \(-0.348659\pi\) | ||||
0.457740 | + | 0.889086i | \(0.348659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5066 | −0.958620 | −0.479310 | − | 0.877646i | \(-0.659113\pi\) | ||||
−0.479310 | + | 0.877646i | \(0.659113\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.2996 | −1.59192 | −0.795961 | − | 0.605347i | \(-0.793034\pi\) | ||||
−0.795961 | + | 0.605347i | \(0.793034\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.35673 | 0.0885030 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.57491 | 0.360611 | 0.180306 | − | 0.983611i | \(-0.442291\pi\) | ||||
0.180306 | + | 0.983611i | \(0.442291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.2996 | 1.56528 | 0.782639 | − | 0.622476i | \(-0.213873\pi\) | ||||
0.782639 | + | 0.622476i | \(0.213873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.7931 | 0.689546 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.21819 | 0.141140 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.0113 | −0.884385 | −0.442192 | − | 0.896920i | \(-0.645799\pi\) | ||||
−0.442192 | + | 0.896920i | \(0.645799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.56363 | 0.475521 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9204 | 0.681193 | 0.340596 | − | 0.940210i | \(-0.389371\pi\) | ||||
0.340596 | + | 0.940210i | \(0.389371\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.35673 | 0.581399 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.6658 | −0.657684 | −0.328842 | − | 0.944385i | \(-0.606658\pi\) | ||||
−0.328842 | + | 0.944385i | \(0.606658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.643274 | −0.0395160 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0113 | −0.976225 | −0.488113 | − | 0.872781i | \(-0.662314\pi\) | ||||
−0.488113 | + | 0.872781i | \(0.662314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.7360 | −1.86708 | −0.933540 | − | 0.358473i | \(-0.883298\pi\) | ||||
−0.933540 | + | 0.358473i | \(0.883298\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.57491 | −0.336180 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.2996 | 1.21969 | 0.609844 | − | 0.792522i | \(-0.291232\pi\) | ||||
0.609844 | + | 0.792522i | \(0.291232\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5844 | 1.10865 | 0.554326 | − | 0.832300i | \(-0.312976\pi\) | ||||
0.554326 | + | 0.832300i | \(0.312976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.0909 | −1.49150 | −0.745751 | − | 0.666225i | \(-0.767909\pi\) | ||||
−0.745751 | + | 0.666225i | \(0.767909\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.0796 | 0.890123 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5862 | −0.975659 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.7931 | −0.688960 | −0.344480 | − | 0.938794i | \(-0.611945\pi\) | ||||
−0.344480 | + | 0.938794i | \(0.611945\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.43637 | 0.258296 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00947 | 0.174042 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.920352 | 0.0530482 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.0796 | 0.748938 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.85018 | −0.505106 | −0.252553 | − | 0.967583i | \(-0.581270\pi\) | ||||
−0.252553 | + | 0.967583i | \(0.581270\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.8709 | 1.24019 | 0.620093 | − | 0.784528i | \(-0.287095\pi\) | ||||
0.620093 | + | 0.784528i | \(0.287095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.14982 | −0.0649919 | −0.0324960 | − | 0.999472i | \(-0.510346\pi\) | ||||
−0.0324960 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.1022 | −1.63454 | −0.817272 | − | 0.576252i | \(-0.804514\pi\) | ||||
−0.817272 | + | 0.576252i | \(0.804514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.1022 | 1.51743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.643274 | 0.0357927 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.21819 | −0.123043 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.72292 | −0.315515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.94292 | −0.491548 | −0.245774 | − | 0.969327i | \(-0.579042\pi\) | ||||
−0.245774 | + | 0.969327i | \(0.579042\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.28655 | 0.0702917 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3775 | 1.11003 | 0.555016 | − | 0.831840i | \(-0.312712\pi\) | ||||
0.555016 | + | 0.831840i | \(0.312712\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.7360 | −0.798000 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0000 | −0.863919 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.07965 | −0.380055 | −0.190028 | − | 0.981779i | \(-0.560858\pi\) | ||||
−0.190028 | + | 0.981779i | \(0.560858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.1593 | 1.93556 | 0.967781 | − | 0.251792i | \(-0.0810199\pi\) | ||||
0.967781 | + | 0.251792i | \(0.0810199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.1593 | −1.71167 | −0.855833 | − | 0.517252i | \(-0.826955\pi\) | ||||
−0.855833 | + | 0.517252i | \(0.826955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.1498 | −0.591771 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.86146 | 0.151022 | 0.0755111 | − | 0.997145i | \(-0.475941\pi\) | ||||
0.0755111 | + | 0.997145i | \(0.475941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.3585 | −0.645111 | −0.322555 | − | 0.946551i | \(-0.604542\pi\) | ||||
−0.322555 | + | 0.946551i | \(0.604542\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.71345 | 0.140875 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.495265 | 0.0256438 | 0.0128219 | − | 0.999918i | \(-0.495919\pi\) | ||||
0.0128219 | + | 0.999918i | \(0.495919\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.7836 | 0.555385 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.78363 | 0.142985 | 0.0714927 | − | 0.997441i | \(-0.477224\pi\) | ||||
0.0714927 | + | 0.997441i | \(0.477224\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.0131 | 1.68689 | 0.843445 | − | 0.537215i | \(-0.180524\pi\) | ||||
0.843445 | + | 0.537215i | \(0.180524\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.5160 | 1.19849 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.4589 | −1.54433 | −0.772165 | − | 0.635422i | \(-0.780826\pi\) | ||||
−0.772165 | + | 0.635422i | \(0.780826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.872747 | 0.0441367 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.28655 | −0.0647333 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.2865 | −0.767210 | −0.383605 | − | 0.923497i | \(-0.625318\pi\) | ||||
−0.383605 | + | 0.923497i | \(0.625318\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.0339 | 1.79944 | 0.899722 | − | 0.436462i | \(-0.143769\pi\) | ||||
0.899722 | + | 0.436462i | \(0.143769\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.86328 | −0.292071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.3662 | 0.612970 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.0226 | −1.68231 | −0.841154 | − | 0.540796i | \(-0.818123\pi\) | ||||
−0.841154 | + | 0.540796i | \(0.818123\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.7135 | −0.920829 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.3662 | −0.607033 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.72474 | 0.426231 | 0.213116 | − | 0.977027i | \(-0.431639\pi\) | ||||
0.213116 | + | 0.977027i | \(0.431639\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0131 | 1.70643 | 0.853217 | − | 0.521556i | \(-0.174648\pi\) | ||||
0.853217 | + | 0.521556i | \(0.174648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.643274 | −0.0312034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −55.1724 | −2.66998 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8633 | 0.667771 | 0.333885 | − | 0.942614i | \(-0.391640\pi\) | ||||
0.333885 | + | 0.942614i | \(0.391640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.2408 | −1.45328 | −0.726639 | − | 0.687019i | \(-0.758919\pi\) | ||||
−0.726639 | + | 0.687019i | \(0.758919\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.35673 | 0.0649010 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.5862 | 1.50753 | 0.753763 | − | 0.657146i | \(-0.228236\pi\) | ||||
0.753763 | + | 0.657146i | \(0.228236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.2295 | −0.866108 | −0.433054 | − | 0.901368i | \(-0.642564\pi\) | ||||
−0.433054 | + | 0.901368i | \(0.642564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0113 | −0.569390 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.71164 | 0.458320 | 0.229160 | − | 0.973389i | \(-0.426402\pi\) | ||||
0.229160 | + | 0.973389i | \(0.426402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.9298 | 0.938459 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.35673 | 0.438650 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.8633 | −0.929165 | −0.464582 | − | 0.885530i | \(-0.653796\pi\) | ||||
−0.464582 | + | 0.885530i | \(0.653796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.2996 | 0.945449 | 0.472724 | − | 0.881210i | \(-0.343271\pi\) | ||||
0.472724 | + | 0.881210i | \(0.343271\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.2408 | 1.49836 | 0.749178 | − | 0.662369i | \(-0.230449\pi\) | ||||
0.749178 | + | 0.662369i | \(0.230449\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.2295 | 1.21376 | 0.606878 | − | 0.794795i | \(-0.292422\pi\) | ||||
0.606878 | + | 0.794795i | \(0.292422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.42690 | −0.250591 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.21637 | 0.0559288 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.1611 | −1.51517 | −0.757585 | − | 0.652737i | \(-0.773621\pi\) | ||||
−0.757585 | + | 0.652737i | \(0.773621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.92035 | 0.224349 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.78181 | 0.262539 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.5636 | −0.886513 | −0.443256 | − | 0.896395i | \(-0.646177\pi\) | ||||
−0.443256 | + | 0.896395i | \(0.646177\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8615 | 1.21224 | 0.606120 | − | 0.795373i | \(-0.292725\pi\) | ||||
0.606120 | + | 0.795373i | \(0.292725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.12725 | 0.140844 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47.0320 | 2.10968 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.0226 | 1.79166 | 0.895828 | − | 0.444401i | \(-0.146583\pi\) | ||||
0.895828 | + | 0.444401i | \(0.146583\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.6527 | 0.787097 | 0.393549 | − | 0.919304i | \(-0.371247\pi\) | ||||
0.393549 | + | 0.919304i | \(0.371247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.43637 | 0.286415 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8615 | 0.747371 | 0.373686 | − | 0.927555i | \(-0.378094\pi\) | ||||
0.373686 | + | 0.927555i | \(0.378094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.1819 | −1.86602 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.28655 | −0.0566921 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.56363 | −0.332648 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.57491 | −0.156620 | −0.0783099 | − | 0.996929i | \(-0.524952\pi\) | ||||
−0.0783099 | + | 0.996929i | \(0.524952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.4364 | −1.24344 | −0.621718 | − | 0.783241i | \(-0.713565\pi\) | ||||
−0.621718 | + | 0.783241i | \(0.713565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.70035 | −0.0740684 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1593 | −0.919969 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.92982 | 0.343479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.28655 | 0.0556224 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −60.1706 | −2.59173 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.573097 | 0.0246394 | 0.0123197 | − | 0.999924i | \(-0.496078\pi\) | ||||
0.0123197 | + | 0.999924i | \(0.496078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.4364 | 0.789727 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.85018 | −0.378406 | −0.189203 | − | 0.981938i | \(-0.560590\pi\) | ||||
−0.189203 | + | 0.981938i | \(0.560590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.86146 | 0.207105 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.42690 | 0.230775 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.29965 | −0.351667 | −0.175834 | − | 0.984420i | \(-0.556262\pi\) | ||||
−0.175834 | + | 0.984420i | \(0.556262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.483979 | 0.0204701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.3793 | −0.732450 | −0.366225 | − | 0.930526i | \(-0.619350\pi\) | ||||
−0.366225 | + | 0.930526i | \(0.619350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.0796 | −0.550265 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.4346 | −0.814739 | −0.407370 | − | 0.913263i | \(-0.633554\pi\) | ||||
−0.407370 | + | 0.913263i | \(0.633554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.1629 | 1.34598 | 0.672988 | − | 0.739653i | \(-0.265010\pi\) | ||||
0.672988 | + | 0.739653i | \(0.265010\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.35673 | −0.0565794 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.1688 | −1.29757 | −0.648786 | − | 0.760971i | \(-0.724723\pi\) | ||||
−0.648786 | + | 0.760971i | \(0.724723\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.1629 | 2.16408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.58620 | 0.148525 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.5160 | −0.970610 | −0.485305 | − | 0.874345i | \(-0.661291\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.64327 | −0.108914 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.0131 | 1.27356 | 0.636778 | − | 0.771047i | \(-0.280267\pi\) | ||||
0.636778 | + | 0.771047i | \(0.280267\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.71345 | 0.111241 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.1724 | −1.60054 | −0.800270 | − | 0.599639i | \(-0.795311\pi\) | ||||
−0.800270 | + | 0.599639i | \(0.795311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.86328 | −0.157586 | −0.0787932 | − | 0.996891i | \(-0.525107\pi\) | ||||
−0.0787932 | + | 0.996891i | \(0.525107\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.0796 | 0.816354 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.02257 | 0.325626 | 0.162813 | − | 0.986657i | \(-0.447943\pi\) | ||||
0.162813 | + | 0.986657i | \(0.447943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00947 | −0.121750 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.8633 | 0.802270 | 0.401135 | − | 0.916019i | \(-0.368616\pi\) | ||||
0.401135 | + | 0.916019i | \(0.368616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.3888 | −0.740304 | −0.370152 | − | 0.928971i | \(-0.620694\pi\) | ||||
−0.370152 | + | 0.928971i | \(0.620694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.4364 | 0.499860 | 0.249930 | − | 0.968264i | \(-0.419592\pi\) | ||||
0.249930 | + | 0.968264i | \(0.419592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 50.6658 | 2.02988 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.42690 | 0.0568943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.6182 | 1.69661 | 0.848303 | − | 0.529512i | \(-0.177625\pi\) | ||||
0.848303 | + | 0.529512i | \(0.177625\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.28655 | −0.368525 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.9411 | −0.948581 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.16111 | 0.124856 | 0.0624282 | − | 0.998049i | \(-0.480116\pi\) | ||||
0.0624282 | + | 0.998049i | \(0.480116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.5368 | 1.44087 | 0.720435 | − | 0.693523i | \(-0.243942\pi\) | ||||
0.720435 | + | 0.693523i | \(0.243942\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.6527 | 0.694001 | 0.347001 | − | 0.937865i | \(-0.387200\pi\) | ||||
0.347001 | + | 0.937865i | \(0.387200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.7324 | −0.970831 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.51602 | 0.215859 | 0.107929 | − | 0.994159i | \(-0.465578\pi\) | ||||
0.107929 | + | 0.994159i | \(0.465578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.86146 | −0.111807 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2996 | −0.712853 | −0.356427 | − | 0.934323i | \(-0.616005\pi\) | ||||
−0.356427 | + | 0.934323i | \(0.616005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.72292 | 0.300387 | 0.150193 | − | 0.988657i | \(-0.452010\pi\) | ||||
0.150193 | + | 0.988657i | \(0.452010\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.21819 | 0.163574 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.59567 | 0.255385 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −72.9179 | −2.81496 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9637 | 1.54049 | 0.770243 | − | 0.637750i | \(-0.220135\pi\) | ||||
0.770243 | + | 0.637750i | \(0.220135\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.2295 | 1.85361 | 0.926805 | − | 0.375544i | \(-0.122544\pi\) | ||||
0.926805 | + | 0.375544i | \(0.122544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.3888 | −0.935955 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5862 | 0.596389 | 0.298195 | − | 0.954505i | \(-0.403616\pi\) | ||||
0.298195 | + | 0.954505i | \(0.403616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.8727 | 0.568258 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.42690 | 0.0543607 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.8633 | 1.28822 | 0.644110 | − | 0.764933i | \(-0.277228\pi\) | ||||
0.644110 | + | 0.764933i | \(0.277228\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.850175 | 0.0322490 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.29965 | 0.0871054 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.3317 | −1.18338 | −0.591691 | − | 0.806165i | \(-0.701539\pi\) | ||||
−0.591691 | + | 0.806165i | \(0.701539\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.21819 | 0.0836605 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.1498 | −1.02107 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.939294 | −0.0352759 | −0.0176380 | − | 0.999844i | \(-0.505615\pi\) | ||||
−0.0176380 | + | 0.999844i | \(0.505615\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.58620 | −0.134304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.3662 | 0.462470 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.1611 | 1.23670 | 0.618350 | − | 0.785903i | \(-0.287801\pi\) | ||||
0.618350 | + | 0.785903i | \(0.287801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.42690 | 0.202108 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.86146 | −0.180550 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.2408 | −1.19574 | −0.597872 | − | 0.801592i | \(-0.703987\pi\) | ||||
−0.597872 | + | 0.801592i | \(0.703987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.140354 | 0.00519118 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.5862 | 0.649561 | 0.324781 | − | 0.945789i | \(-0.394710\pi\) | ||||
0.324781 | + | 0.945789i | \(0.394710\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.17240 | −0.264199 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5731 | 0.536080 | 0.268040 | − | 0.963408i | \(-0.413624\pi\) | ||||
0.268040 | + | 0.963408i | \(0.413624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.5862 | 1.01204 | 0.506020 | − | 0.862522i | \(-0.331116\pi\) | ||||
0.506020 | + | 0.862522i | \(0.331116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.1593 | 0.738579 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.42690 | −0.198295 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5160 | −0.420226 | −0.210113 | − | 0.977677i | \(-0.567383\pi\) | ||||
−0.210113 | + | 0.977677i | \(0.567383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.5160 | 0.419111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.2902 | −0.483040 | −0.241520 | − | 0.970396i | \(-0.577646\pi\) | ||||
−0.241520 | + | 0.970396i | \(0.577646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.84070 | 0.284225 | 0.142113 | − | 0.989850i | \(-0.454610\pi\) | ||||
0.142113 | + | 0.989850i | \(0.454610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −77.7681 | −2.81539 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.84070 | −0.355327 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.2996 | −1.88597 | −0.942987 | − | 0.332830i | \(-0.891996\pi\) | ||||
−0.942987 | + | 0.332830i | \(0.891996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.2426 | 0.907912 | 0.453956 | − | 0.891024i | \(-0.350012\pi\) | ||||
0.453956 | + | 0.891024i | \(0.350012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.64327 | 0.0949492 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.57491 | 0.128085 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.1593 | 2.22423 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.14982 | 0.326571 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.8633 | −0.636757 | −0.318379 | − | 0.947964i | \(-0.603138\pi\) | ||||
−0.318379 | + | 0.947964i | \(0.603138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 55.1724 | 1.96170 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.0131 | −1.03029 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.50655 | −0.230474 | −0.115237 | − | 0.993338i | \(-0.536763\pi\) | ||||
−0.115237 | + | 0.993338i | \(0.536763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.872747 | −0.0308756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −55.7491 | −1.96734 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.72292 | 0.201707 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.84070 | −0.135032 | −0.0675160 | − | 0.997718i | \(-0.521507\pi\) | ||||
−0.0675160 | + | 0.997718i | \(0.521507\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.44584 | −0.261459 | −0.130729 | − | 0.991418i | \(-0.541732\pi\) | ||||
−0.130729 | + | 0.991418i | \(0.541732\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.50474 | −0.192822 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.218187 | 0.00763339 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2960 | 1.05734 | 0.528669 | − | 0.848828i | \(-0.322691\pi\) | ||||
0.528669 | + | 0.848828i | \(0.322691\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.3811 | 1.12873 | 0.564367 | − | 0.825524i | \(-0.309120\pi\) | ||||
0.564367 | + | 0.825524i | \(0.309120\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.9524 | 0.415625 | 0.207813 | − | 0.978169i | \(-0.433366\pi\) | ||||
0.207813 | + | 0.978169i | \(0.433366\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.5767 | −0.784122 | −0.392061 | − | 0.919939i | \(-0.628238\pi\) | ||||
−0.392061 | + | 0.919939i | \(0.628238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.94292 | −0.240558 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.920352 | 0.0318501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.14982 | 0.108744 | 0.0543720 | − | 0.998521i | \(-0.482684\pi\) | ||||
0.0543720 | + | 0.998521i | \(0.482684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.36620 | −0.185041 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.07965 | −0.277948 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −84.6997 | −2.91032 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.00947 | 0.103163 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.5826 | 0.396580 | 0.198290 | − | 0.980143i | \(-0.436461\pi\) | ||||
0.198290 | + | 0.980143i | \(0.436461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.91088 | −0.133593 | −0.0667966 | − | 0.997767i | \(-0.521278\pi\) | ||||
−0.0667966 | + | 0.997767i | \(0.521278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.01310 | −0.171045 | −0.0855224 | − | 0.996336i | \(-0.527256\pi\) | ||||
−0.0855224 | + | 0.996336i | \(0.527256\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.7324 | −1.38655 | −0.693273 | − | 0.720675i | \(-0.743832\pi\) | ||||
−0.693273 | + | 0.720675i | \(0.743832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6658 | 0.566656 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.17240 | 0.243307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.85381 | −0.0966975 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.21819 | −0.142601 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.2371 | 1.22364 | 0.611820 | − | 0.790997i | \(-0.290438\pi\) | ||||
0.611820 | + | 0.790997i | \(0.290438\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0226 | 0.607196 | 0.303598 | − | 0.952800i | \(-0.401812\pi\) | ||||
0.303598 | + | 0.952800i | \(0.401812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.6771 | −1.77273 | −0.886363 | − | 0.462990i | \(-0.846776\pi\) | ||||
−0.886363 | + | 0.462990i | \(0.846776\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.8727 | −1.10376 | −0.551879 | − | 0.833924i | \(-0.686089\pi\) | ||||
−0.551879 | + | 0.833924i | \(0.686089\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.1724 | 1.31380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.35673 | −0.0454011 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0226 | 0.802986 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.8502 | −0.428577 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.413802 | 0.0137857 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.14982 | −0.304150 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.5957 | −0.883095 | −0.441547 | − | 0.897238i | \(-0.645570\pi\) | ||||
−0.441547 | + | 0.897238i | \(0.645570\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.15930 | −0.204067 | −0.102033 | − | 0.994781i | \(-0.532535\pi\) | ||||
−0.102033 | + | 0.994781i | \(0.532535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68.9405 | 2.28160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0702 | 0.398592 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.8858 | −1.11779 | −0.558895 | − | 0.829238i | \(-0.688775\pi\) | ||||
−0.558895 | + | 0.829238i | \(0.688775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.7324 | 0.814077 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.21819 | −0.0729335 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.8953 | 1.14488 | 0.572439 | − | 0.819947i | \(-0.305997\pi\) | ||||
0.572439 | + | 0.819947i | \(0.305997\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.7931 | −0.353730 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.58620 | 0.117281 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.29602 | −0.205682 | −0.102841 | − | 0.994698i | \(-0.532793\pi\) | ||||
−0.102841 | + | 0.994698i | \(0.532793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.8651 | −0.354192 | −0.177096 | − | 0.984194i | \(-0.556670\pi\) | ||||
−0.177096 | + | 0.984194i | \(0.556670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.85018 | 0.157943 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.79310 | 0.318233 | 0.159116 | − | 0.987260i | \(-0.449135\pi\) | ||||
0.159116 | + | 0.987260i | \(0.449135\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.1819 | −0.720054 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.35310 | −0.0438311 | −0.0219155 | − | 0.999760i | \(-0.506976\pi\) | ||||
−0.0219155 | + | 0.999760i | \(0.506976\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.2884 | 0.527079 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −62.7360 | −2.02585 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0131 | −0.774616 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.5047 | 0.627880 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.9637 | 0.706304 | 0.353152 | − | 0.935566i | \(-0.385110\pi\) | ||||
0.353152 | + | 0.935566i | \(0.385110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.7455 | 0.441114 | 0.220557 | − | 0.975374i | \(-0.429213\pi\) | ||||
0.220557 | + | 0.975374i | \(0.429213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.58620 | −0.114968 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.3698 | −1.54749 | −0.773744 | − | 0.633498i | \(-0.781618\pi\) | ||||
−0.773744 | + | 0.633498i | \(0.781618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66.9619 | 2.14011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.0665 | −0.448653 | −0.224327 | − | 0.974514i | \(-0.572018\pi\) | ||||
−0.224327 | + | 0.974514i | \(0.572018\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.51602 | −0.303206 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.296019 | 0.00941287 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.2865 | −1.05738 | −0.528691 | − | 0.848814i | \(-0.677317\pi\) | ||||
−0.528691 | + | 0.848814i | \(0.677317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.27708 | −0.0721882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.5957 | −1.53904 | −0.769520 | − | 0.638623i | \(-0.779505\pi\) | ||||
−0.769520 | + | 0.638623i | \(0.779505\pi\) | |||||||
\(998\) | 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 | 6840.2.a.bn.1.1 | 3 | ||
3.2 | odd | 2 | 2280.2.a.t.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 4560.2.a.bq.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.t.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
4560.2.a.bq.1.3 | 3 | 12.11 | even | 2 | |||
6840.2.a.bn.1.1 | 3 | 1.1 | even | 1 | trivial |