Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.36538000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 13x^{4} - 4x^{3} + 41x^{2} + 16x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.479869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.479869 | 0.277052 | 0.138526 | − | 0.990359i | \(-0.455763\pi\) | ||||
0.138526 | + | 0.990359i | \(0.455763\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.85512 | −1.27685 | −0.638424 | − | 0.769685i | \(-0.720413\pi\) | ||||
−0.638424 | + | 0.769685i | \(0.720413\pi\) | |||||||
\(6\) | −0.479869 | −0.195906 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.76973 | −0.923242 | ||||||||
\(10\) | 2.85512 | 0.902867 | ||||||||
\(11\) | 5.13981 | 1.54971 | 0.774855 | − | 0.632139i | \(-0.217823\pi\) | ||||
0.774855 | + | 0.632139i | \(0.217823\pi\) | |||||||
\(12\) | 0.479869 | 0.138526 | ||||||||
\(13\) | −0.235441 | −0.0652995 | −0.0326498 | − | 0.999467i | \(-0.510395\pi\) | ||||
−0.0326498 | + | 0.999467i | \(0.510395\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.37008 | −0.353753 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.72430 | −1.14581 | −0.572905 | − | 0.819622i | \(-0.694184\pi\) | ||||
−0.572905 | + | 0.819622i | \(0.694184\pi\) | |||||||
\(18\) | 2.76973 | 0.652831 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.85512 | −0.638424 | ||||||||
\(21\) | 0.479869 | 0.104716 | ||||||||
\(22\) | −5.13981 | −1.09581 | ||||||||
\(23\) | 6.09954 | 1.27184 | 0.635922 | − | 0.771754i | \(-0.280620\pi\) | ||||
0.635922 | + | 0.771754i | \(0.280620\pi\) | |||||||
\(24\) | −0.479869 | −0.0979528 | ||||||||
\(25\) | 3.15169 | 0.630338 | ||||||||
\(26\) | 0.235441 | 0.0461737 | ||||||||
\(27\) | −2.76871 | −0.532839 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −5.85159 | −1.08661 | −0.543307 | − | 0.839534i | \(-0.682828\pi\) | ||||
−0.543307 | + | 0.839534i | \(0.682828\pi\) | |||||||
\(30\) | 1.37008 | 0.250141 | ||||||||
\(31\) | 5.68999 | 1.02195 | 0.510976 | − | 0.859595i | \(-0.329284\pi\) | ||||
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.46643 | 0.429351 | ||||||||
\(34\) | 4.72430 | 0.810210 | ||||||||
\(35\) | −2.85512 | −0.482603 | ||||||||
\(36\) | −2.76973 | −0.461621 | ||||||||
\(37\) | −2.94785 | −0.484624 | −0.242312 | − | 0.970198i | \(-0.577906\pi\) | ||||
−0.242312 | + | 0.970198i | \(0.577906\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.112981 | −0.0180914 | ||||||||
\(40\) | 2.85512 | 0.451434 | ||||||||
\(41\) | 3.33146 | 0.520287 | 0.260143 | − | 0.965570i | \(-0.416230\pi\) | ||||
0.260143 | + | 0.965570i | \(0.416230\pi\) | |||||||
\(42\) | −0.479869 | −0.0740454 | ||||||||
\(43\) | −6.50989 | −0.992749 | −0.496374 | − | 0.868109i | \(-0.665336\pi\) | ||||
−0.496374 | + | 0.868109i | \(0.665336\pi\) | |||||||
\(44\) | 5.13981 | 0.774855 | ||||||||
\(45\) | 7.90789 | 1.17884 | ||||||||
\(46\) | −6.09954 | −0.899329 | ||||||||
\(47\) | −0.589626 | −0.0860057 | −0.0430029 | − | 0.999075i | \(-0.513692\pi\) | ||||
−0.0430029 | + | 0.999075i | \(0.513692\pi\) | |||||||
\(48\) | 0.479869 | 0.0692631 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.15169 | −0.445717 | ||||||||
\(51\) | −2.26704 | −0.317449 | ||||||||
\(52\) | −0.235441 | −0.0326498 | ||||||||
\(53\) | 8.65809 | 1.18928 | 0.594640 | − | 0.803992i | \(-0.297295\pi\) | ||||
0.594640 | + | 0.803992i | \(0.297295\pi\) | |||||||
\(54\) | 2.76871 | 0.376774 | ||||||||
\(55\) | −14.6748 | −1.97874 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.85159 | 0.768352 | ||||||||
\(59\) | 8.79576 | 1.14511 | 0.572556 | − | 0.819866i | \(-0.305952\pi\) | ||||
0.572556 | + | 0.819866i | \(0.305952\pi\) | |||||||
\(60\) | −1.37008 | −0.176877 | ||||||||
\(61\) | −5.43170 | −0.695458 | −0.347729 | − | 0.937595i | \(-0.613047\pi\) | ||||
−0.347729 | + | 0.937595i | \(0.613047\pi\) | |||||||
\(62\) | −5.68999 | −0.722629 | ||||||||
\(63\) | −2.76973 | −0.348953 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.672211 | 0.0833775 | ||||||||
\(66\) | −2.46643 | −0.303597 | ||||||||
\(67\) | −11.1291 | −1.35964 | −0.679818 | − | 0.733380i | \(-0.737941\pi\) | ||||
−0.679818 | + | 0.733380i | \(0.737941\pi\) | |||||||
\(68\) | −4.72430 | −0.572905 | ||||||||
\(69\) | 2.92698 | 0.352367 | ||||||||
\(70\) | 2.85512 | 0.341252 | ||||||||
\(71\) | −3.04026 | −0.360813 | −0.180406 | − | 0.983592i | \(-0.557741\pi\) | ||||
−0.180406 | + | 0.983592i | \(0.557741\pi\) | |||||||
\(72\) | 2.76973 | 0.326415 | ||||||||
\(73\) | 10.8507 | 1.26997 | 0.634987 | − | 0.772523i | \(-0.281005\pi\) | ||||
0.634987 | + | 0.772523i | \(0.281005\pi\) | |||||||
\(74\) | 2.94785 | 0.342681 | ||||||||
\(75\) | 1.51240 | 0.174637 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.13981 | 0.585735 | ||||||||
\(78\) | 0.112981 | 0.0127925 | ||||||||
\(79\) | −10.2573 | −1.15404 | −0.577020 | − | 0.816730i | \(-0.695784\pi\) | ||||
−0.577020 | + | 0.816730i | \(0.695784\pi\) | |||||||
\(80\) | −2.85512 | −0.319212 | ||||||||
\(81\) | 6.98056 | 0.775618 | ||||||||
\(82\) | −3.33146 | −0.367898 | ||||||||
\(83\) | 12.1326 | 1.33173 | 0.665863 | − | 0.746074i | \(-0.268063\pi\) | ||||
0.665863 | + | 0.746074i | \(0.268063\pi\) | |||||||
\(84\) | 0.479869 | 0.0523580 | ||||||||
\(85\) | 13.4884 | 1.46302 | ||||||||
\(86\) | 6.50989 | 0.701979 | ||||||||
\(87\) | −2.80800 | −0.301049 | ||||||||
\(88\) | −5.13981 | −0.547905 | ||||||||
\(89\) | −15.2958 | −1.62135 | −0.810673 | − | 0.585499i | \(-0.800899\pi\) | ||||
−0.810673 | + | 0.585499i | \(0.800899\pi\) | |||||||
\(90\) | −7.90789 | −0.833565 | ||||||||
\(91\) | −0.235441 | −0.0246809 | ||||||||
\(92\) | 6.09954 | 0.635922 | ||||||||
\(93\) | 2.73045 | 0.283134 | ||||||||
\(94\) | 0.589626 | 0.0608152 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.479869 | −0.0489764 | ||||||||
\(97\) | −10.2497 | −1.04070 | −0.520352 | − | 0.853952i | \(-0.674199\pi\) | ||||
−0.520352 | + | 0.853952i | \(0.674199\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −14.2359 | −1.43076 | ||||||||
\(100\) | 3.15169 | 0.315169 | ||||||||
\(101\) | 13.6679 | 1.36001 | 0.680003 | − | 0.733209i | \(-0.261978\pi\) | ||||
0.680003 | + | 0.733209i | \(0.261978\pi\) | |||||||
\(102\) | 2.26704 | 0.224471 | ||||||||
\(103\) | −6.38388 | −0.629022 | −0.314511 | − | 0.949254i | \(-0.601841\pi\) | ||||
−0.314511 | + | 0.949254i | \(0.601841\pi\) | |||||||
\(104\) | 0.235441 | 0.0230869 | ||||||||
\(105\) | −1.37008 | −0.133706 | ||||||||
\(106\) | −8.65809 | −0.840948 | ||||||||
\(107\) | 8.23814 | 0.796411 | 0.398206 | − | 0.917296i | \(-0.369633\pi\) | ||||
0.398206 | + | 0.917296i | \(0.369633\pi\) | |||||||
\(108\) | −2.76871 | −0.266419 | ||||||||
\(109\) | −12.8636 | −1.23211 | −0.616056 | − | 0.787703i | \(-0.711270\pi\) | ||||
−0.616056 | + | 0.787703i | \(0.711270\pi\) | |||||||
\(110\) | 14.6748 | 1.39918 | ||||||||
\(111\) | −1.41458 | −0.134266 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −1.48774 | −0.139955 | −0.0699775 | − | 0.997549i | \(-0.522293\pi\) | ||||
−0.0699775 | + | 0.997549i | \(0.522293\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.4149 | −1.62395 | ||||||||
\(116\) | −5.85159 | −0.543307 | ||||||||
\(117\) | 0.652106 | 0.0602873 | ||||||||
\(118\) | −8.79576 | −0.809716 | ||||||||
\(119\) | −4.72430 | −0.433076 | ||||||||
\(120\) | 1.37008 | 0.125071 | ||||||||
\(121\) | 15.4176 | 1.40160 | ||||||||
\(122\) | 5.43170 | 0.491763 | ||||||||
\(123\) | 1.59866 | 0.144147 | ||||||||
\(124\) | 5.68999 | 0.510976 | ||||||||
\(125\) | 5.27714 | 0.472001 | ||||||||
\(126\) | 2.76973 | 0.246747 | ||||||||
\(127\) | −0.603911 | −0.0535884 | −0.0267942 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267942 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.12389 | −0.275043 | ||||||||
\(130\) | −0.672211 | −0.0589568 | ||||||||
\(131\) | 14.9371 | 1.30506 | 0.652529 | − | 0.757764i | \(-0.273708\pi\) | ||||
0.652529 | + | 0.757764i | \(0.273708\pi\) | |||||||
\(132\) | 2.46643 | 0.214675 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.1291 | 0.961409 | ||||||||
\(135\) | 7.90499 | 0.680354 | ||||||||
\(136\) | 4.72430 | 0.405105 | ||||||||
\(137\) | 16.1532 | 1.38006 | 0.690029 | − | 0.723781i | \(-0.257598\pi\) | ||||
0.690029 | + | 0.723781i | \(0.257598\pi\) | |||||||
\(138\) | −2.92698 | −0.249161 | ||||||||
\(139\) | −20.8094 | −1.76503 | −0.882514 | − | 0.470285i | \(-0.844151\pi\) | ||||
−0.882514 | + | 0.470285i | \(0.844151\pi\) | |||||||
\(140\) | −2.85512 | −0.241301 | ||||||||
\(141\) | −0.282943 | −0.0238281 | ||||||||
\(142\) | 3.04026 | 0.255133 | ||||||||
\(143\) | −1.21012 | −0.101195 | ||||||||
\(144\) | −2.76973 | −0.230810 | ||||||||
\(145\) | 16.7070 | 1.38744 | ||||||||
\(146\) | −10.8507 | −0.898008 | ||||||||
\(147\) | 0.479869 | 0.0395789 | ||||||||
\(148\) | −2.94785 | −0.242312 | ||||||||
\(149\) | −17.3680 | −1.42284 | −0.711420 | − | 0.702767i | \(-0.751948\pi\) | ||||
−0.711420 | + | 0.702767i | \(0.751948\pi\) | |||||||
\(150\) | −1.51240 | −0.123487 | ||||||||
\(151\) | −15.6190 | −1.27106 | −0.635528 | − | 0.772078i | \(-0.719217\pi\) | ||||
−0.635528 | + | 0.772078i | \(0.719217\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.0850 | 1.05786 | ||||||||
\(154\) | −5.13981 | −0.414177 | ||||||||
\(155\) | −16.2456 | −1.30488 | ||||||||
\(156\) | −0.112981 | −0.00904569 | ||||||||
\(157\) | 13.7329 | 1.09601 | 0.548003 | − | 0.836477i | \(-0.315388\pi\) | ||||
0.548003 | + | 0.836477i | \(0.315388\pi\) | |||||||
\(158\) | 10.2573 | 0.816029 | ||||||||
\(159\) | 4.15475 | 0.329493 | ||||||||
\(160\) | 2.85512 | 0.225717 | ||||||||
\(161\) | 6.09954 | 0.480711 | ||||||||
\(162\) | −6.98056 | −0.548445 | ||||||||
\(163\) | −2.13899 | −0.167539 | −0.0837693 | − | 0.996485i | \(-0.526696\pi\) | ||||
−0.0837693 | + | 0.996485i | \(0.526696\pi\) | |||||||
\(164\) | 3.33146 | 0.260143 | ||||||||
\(165\) | −7.04195 | −0.548215 | ||||||||
\(166\) | −12.1326 | −0.941673 | ||||||||
\(167\) | 6.26600 | 0.484877 | 0.242439 | − | 0.970167i | \(-0.422053\pi\) | ||||
0.242439 | + | 0.970167i | \(0.422053\pi\) | |||||||
\(168\) | −0.479869 | −0.0370227 | ||||||||
\(169\) | −12.9446 | −0.995736 | ||||||||
\(170\) | −13.4884 | −1.03451 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.50989 | −0.496374 | ||||||||
\(173\) | 6.18843 | 0.470498 | 0.235249 | − | 0.971935i | \(-0.424410\pi\) | ||||
0.235249 | + | 0.971935i | \(0.424410\pi\) | |||||||
\(174\) | 2.80800 | 0.212874 | ||||||||
\(175\) | 3.15169 | 0.238246 | ||||||||
\(176\) | 5.13981 | 0.387428 | ||||||||
\(177\) | 4.22081 | 0.317256 | ||||||||
\(178\) | 15.2958 | 1.14646 | ||||||||
\(179\) | −25.3882 | −1.89761 | −0.948803 | − | 0.315870i | \(-0.897704\pi\) | ||||
−0.948803 | + | 0.315870i | \(0.897704\pi\) | |||||||
\(180\) | 7.90789 | 0.589419 | ||||||||
\(181\) | 7.26993 | 0.540370 | 0.270185 | − | 0.962808i | \(-0.412915\pi\) | ||||
0.270185 | + | 0.962808i | \(0.412915\pi\) | |||||||
\(182\) | 0.235441 | 0.0174520 | ||||||||
\(183\) | −2.60650 | −0.192678 | ||||||||
\(184\) | −6.09954 | −0.449664 | ||||||||
\(185\) | 8.41646 | 0.618791 | ||||||||
\(186\) | −2.73045 | −0.200206 | ||||||||
\(187\) | −24.2820 | −1.77567 | ||||||||
\(188\) | −0.589626 | −0.0430029 | ||||||||
\(189\) | −2.76871 | −0.201394 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.6408 | −1.34880 | −0.674400 | − | 0.738366i | \(-0.735598\pi\) | ||||
−0.674400 | + | 0.738366i | \(0.735598\pi\) | |||||||
\(192\) | 0.479869 | 0.0346315 | ||||||||
\(193\) | −21.7466 | −1.56535 | −0.782676 | − | 0.622429i | \(-0.786146\pi\) | ||||
−0.782676 | + | 0.622429i | \(0.786146\pi\) | |||||||
\(194\) | 10.2497 | 0.735889 | ||||||||
\(195\) | 0.322573 | 0.0230999 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −21.8153 | −1.55427 | −0.777137 | − | 0.629331i | \(-0.783329\pi\) | ||||
−0.777137 | + | 0.629331i | \(0.783329\pi\) | |||||||
\(198\) | 14.2359 | 1.01170 | ||||||||
\(199\) | −3.08558 | −0.218731 | −0.109366 | − | 0.994002i | \(-0.534882\pi\) | ||||
−0.109366 | + | 0.994002i | \(0.534882\pi\) | |||||||
\(200\) | −3.15169 | −0.222858 | ||||||||
\(201\) | −5.34051 | −0.376691 | ||||||||
\(202\) | −13.6679 | −0.961670 | ||||||||
\(203\) | −5.85159 | −0.410701 | ||||||||
\(204\) | −2.26704 | −0.158725 | ||||||||
\(205\) | −9.51171 | −0.664327 | ||||||||
\(206\) | 6.38388 | 0.444786 | ||||||||
\(207\) | −16.8941 | −1.17422 | ||||||||
\(208\) | −0.235441 | −0.0163249 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.37008 | 0.0945446 | ||||||||
\(211\) | 10.5582 | 0.726860 | 0.363430 | − | 0.931622i | \(-0.381606\pi\) | ||||
0.363430 | + | 0.931622i | \(0.381606\pi\) | |||||||
\(212\) | 8.65809 | 0.594640 | ||||||||
\(213\) | −1.45893 | −0.0999640 | ||||||||
\(214\) | −8.23814 | −0.563148 | ||||||||
\(215\) | 18.5865 | 1.26759 | ||||||||
\(216\) | 2.76871 | 0.188387 | ||||||||
\(217\) | 5.68999 | 0.386262 | ||||||||
\(218\) | 12.8636 | 0.871234 | ||||||||
\(219\) | 5.20690 | 0.351849 | ||||||||
\(220\) | −14.6748 | −0.989371 | ||||||||
\(221\) | 1.11229 | 0.0748209 | ||||||||
\(222\) | 1.41458 | 0.0949406 | ||||||||
\(223\) | −12.5217 | −0.838513 | −0.419256 | − | 0.907868i | \(-0.637709\pi\) | ||||
−0.419256 | + | 0.907868i | \(0.637709\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −8.72932 | −0.581955 | ||||||||
\(226\) | 1.48774 | 0.0989631 | ||||||||
\(227\) | −26.7753 | −1.77714 | −0.888569 | − | 0.458743i | \(-0.848300\pi\) | ||||
−0.888569 | + | 0.458743i | \(0.848300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.8086 | 1.24291 | 0.621454 | − | 0.783451i | \(-0.286542\pi\) | ||||
0.621454 | + | 0.783451i | \(0.286542\pi\) | |||||||
\(230\) | 17.4149 | 1.14831 | ||||||||
\(231\) | 2.46643 | 0.162279 | ||||||||
\(232\) | 5.85159 | 0.384176 | ||||||||
\(233\) | −10.2268 | −0.669981 | −0.334991 | − | 0.942221i | \(-0.608733\pi\) | ||||
−0.334991 | + | 0.942221i | \(0.608733\pi\) | |||||||
\(234\) | −0.652106 | −0.0426295 | ||||||||
\(235\) | 1.68345 | 0.109816 | ||||||||
\(236\) | 8.79576 | 0.572556 | ||||||||
\(237\) | −4.92217 | −0.319729 | ||||||||
\(238\) | 4.72430 | 0.306231 | ||||||||
\(239\) | −16.8837 | −1.09212 | −0.546058 | − | 0.837747i | \(-0.683872\pi\) | ||||
−0.546058 | + | 0.837747i | \(0.683872\pi\) | |||||||
\(240\) | −1.37008 | −0.0884384 | ||||||||
\(241\) | −21.5302 | −1.38688 | −0.693442 | − | 0.720513i | \(-0.743907\pi\) | ||||
−0.693442 | + | 0.720513i | \(0.743907\pi\) | |||||||
\(242\) | −15.4176 | −0.991082 | ||||||||
\(243\) | 11.6559 | 0.747725 | ||||||||
\(244\) | −5.43170 | −0.347729 | ||||||||
\(245\) | −2.85512 | −0.182407 | ||||||||
\(246\) | −1.59866 | −0.101927 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.68999 | −0.361315 | ||||||||
\(249\) | 5.82206 | 0.368958 | ||||||||
\(250\) | −5.27714 | −0.333755 | ||||||||
\(251\) | 4.88717 | 0.308476 | 0.154238 | − | 0.988034i | \(-0.450708\pi\) | ||||
0.154238 | + | 0.988034i | \(0.450708\pi\) | |||||||
\(252\) | −2.76973 | −0.174476 | ||||||||
\(253\) | 31.3505 | 1.97099 | ||||||||
\(254\) | 0.603911 | 0.0378927 | ||||||||
\(255\) | 6.47267 | 0.405334 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.1725 | 1.75736 | 0.878678 | − | 0.477416i | \(-0.158426\pi\) | ||||
0.878678 | + | 0.477416i | \(0.158426\pi\) | |||||||
\(258\) | 3.12389 | 0.194485 | ||||||||
\(259\) | −2.94785 | −0.183171 | ||||||||
\(260\) | 0.672211 | 0.0416888 | ||||||||
\(261\) | 16.2073 | 1.00321 | ||||||||
\(262\) | −14.9371 | −0.922816 | ||||||||
\(263\) | −2.20491 | −0.135961 | −0.0679803 | − | 0.997687i | \(-0.521656\pi\) | ||||
−0.0679803 | + | 0.997687i | \(0.521656\pi\) | |||||||
\(264\) | −2.46643 | −0.151798 | ||||||||
\(265\) | −24.7198 | −1.51853 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.33995 | −0.449198 | ||||||||
\(268\) | −11.1291 | −0.679818 | ||||||||
\(269\) | −9.96810 | −0.607766 | −0.303883 | − | 0.952709i | \(-0.598283\pi\) | ||||
−0.303883 | + | 0.952709i | \(0.598283\pi\) | |||||||
\(270\) | −7.90499 | −0.481083 | ||||||||
\(271\) | 19.2204 | 1.16755 | 0.583777 | − | 0.811914i | \(-0.301574\pi\) | ||||
0.583777 | + | 0.811914i | \(0.301574\pi\) | |||||||
\(272\) | −4.72430 | −0.286453 | ||||||||
\(273\) | −0.112981 | −0.00683790 | ||||||||
\(274\) | −16.1532 | −0.975849 | ||||||||
\(275\) | 16.1991 | 0.976842 | ||||||||
\(276\) | 2.92698 | 0.176184 | ||||||||
\(277\) | 8.70088 | 0.522785 | 0.261392 | − | 0.965233i | \(-0.415818\pi\) | ||||
0.261392 | + | 0.965233i | \(0.415818\pi\) | |||||||
\(278\) | 20.8094 | 1.24806 | ||||||||
\(279\) | −15.7597 | −0.943509 | ||||||||
\(280\) | 2.85512 | 0.170626 | ||||||||
\(281\) | −26.5023 | −1.58100 | −0.790498 | − | 0.612464i | \(-0.790178\pi\) | ||||
−0.790498 | + | 0.612464i | \(0.790178\pi\) | |||||||
\(282\) | 0.282943 | 0.0168490 | ||||||||
\(283\) | −32.3219 | −1.92134 | −0.960670 | − | 0.277694i | \(-0.910430\pi\) | ||||
−0.960670 | + | 0.277694i | \(0.910430\pi\) | |||||||
\(284\) | −3.04026 | −0.180406 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.21012 | 0.0715559 | ||||||||
\(287\) | 3.33146 | 0.196650 | ||||||||
\(288\) | 2.76973 | 0.163208 | ||||||||
\(289\) | 5.31898 | 0.312881 | ||||||||
\(290\) | −16.7070 | −0.981068 | ||||||||
\(291\) | −4.91853 | −0.288329 | ||||||||
\(292\) | 10.8507 | 0.634987 | ||||||||
\(293\) | −32.3512 | −1.88998 | −0.944988 | − | 0.327106i | \(-0.893926\pi\) | ||||
−0.944988 | + | 0.327106i | \(0.893926\pi\) | |||||||
\(294\) | −0.479869 | −0.0279865 | ||||||||
\(295\) | −25.1129 | −1.46213 | ||||||||
\(296\) | 2.94785 | 0.171340 | ||||||||
\(297\) | −14.2306 | −0.825746 | ||||||||
\(298\) | 17.3680 | 1.00610 | ||||||||
\(299\) | −1.43608 | −0.0830507 | ||||||||
\(300\) | 1.51240 | 0.0873184 | ||||||||
\(301\) | −6.50989 | −0.375224 | ||||||||
\(302\) | 15.6190 | 0.898772 | ||||||||
\(303\) | 6.55879 | 0.376793 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.5081 | 0.887994 | ||||||||
\(306\) | −13.0850 | −0.748020 | ||||||||
\(307\) | 5.06829 | 0.289263 | 0.144631 | − | 0.989486i | \(-0.453800\pi\) | ||||
0.144631 | + | 0.989486i | \(0.453800\pi\) | |||||||
\(308\) | 5.13981 | 0.292868 | ||||||||
\(309\) | −3.06342 | −0.174272 | ||||||||
\(310\) | 16.2456 | 0.922687 | ||||||||
\(311\) | −15.9316 | −0.903398 | −0.451699 | − | 0.892170i | \(-0.649182\pi\) | ||||
−0.451699 | + | 0.892170i | \(0.649182\pi\) | |||||||
\(312\) | 0.112981 | 0.00639627 | ||||||||
\(313\) | 2.20536 | 0.124654 | 0.0623271 | − | 0.998056i | \(-0.480148\pi\) | ||||
0.0623271 | + | 0.998056i | \(0.480148\pi\) | |||||||
\(314\) | −13.7329 | −0.774993 | ||||||||
\(315\) | 7.90789 | 0.445559 | ||||||||
\(316\) | −10.2573 | −0.577020 | ||||||||
\(317\) | −18.1717 | −1.02063 | −0.510313 | − | 0.859989i | \(-0.670471\pi\) | ||||
−0.510313 | + | 0.859989i | \(0.670471\pi\) | |||||||
\(318\) | −4.15475 | −0.232987 | ||||||||
\(319\) | −30.0761 | −1.68394 | ||||||||
\(320\) | −2.85512 | −0.159606 | ||||||||
\(321\) | 3.95323 | 0.220648 | ||||||||
\(322\) | −6.09954 | −0.339914 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 6.98056 | 0.387809 | ||||||||
\(325\) | −0.742037 | −0.0411608 | ||||||||
\(326\) | 2.13899 | 0.118468 | ||||||||
\(327\) | −6.17285 | −0.341359 | ||||||||
\(328\) | −3.33146 | −0.183949 | ||||||||
\(329\) | −0.589626 | −0.0325071 | ||||||||
\(330\) | 7.04195 | 0.387647 | ||||||||
\(331\) | −1.92750 | −0.105945 | −0.0529724 | − | 0.998596i | \(-0.516870\pi\) | ||||
−0.0529724 | + | 0.998596i | \(0.516870\pi\) | |||||||
\(332\) | 12.1326 | 0.665863 | ||||||||
\(333\) | 8.16474 | 0.447425 | ||||||||
\(334\) | −6.26600 | −0.342860 | ||||||||
\(335\) | 31.7749 | 1.73605 | ||||||||
\(336\) | 0.479869 | 0.0261790 | ||||||||
\(337\) | 4.91677 | 0.267833 | 0.133917 | − | 0.990993i | \(-0.457245\pi\) | ||||
0.133917 | + | 0.990993i | \(0.457245\pi\) | |||||||
\(338\) | 12.9446 | 0.704092 | ||||||||
\(339\) | −0.713921 | −0.0387749 | ||||||||
\(340\) | 13.4884 | 0.731512 | ||||||||
\(341\) | 29.2454 | 1.58373 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.50989 | 0.350990 | ||||||||
\(345\) | −8.35687 | −0.449919 | ||||||||
\(346\) | −6.18843 | −0.332692 | ||||||||
\(347\) | −11.1668 | −0.599465 | −0.299732 | − | 0.954023i | \(-0.596897\pi\) | ||||
−0.299732 | + | 0.954023i | \(0.596897\pi\) | |||||||
\(348\) | −2.80800 | −0.150524 | ||||||||
\(349\) | −17.6629 | −0.945472 | −0.472736 | − | 0.881204i | \(-0.656733\pi\) | ||||
−0.472736 | + | 0.881204i | \(0.656733\pi\) | |||||||
\(350\) | −3.15169 | −0.168465 | ||||||||
\(351\) | 0.651867 | 0.0347941 | ||||||||
\(352\) | −5.13981 | −0.273953 | ||||||||
\(353\) | 7.02213 | 0.373750 | 0.186875 | − | 0.982384i | \(-0.440164\pi\) | ||||
0.186875 | + | 0.982384i | \(0.440164\pi\) | |||||||
\(354\) | −4.22081 | −0.224334 | ||||||||
\(355\) | 8.68030 | 0.460703 | ||||||||
\(356\) | −15.2958 | −0.810673 | ||||||||
\(357\) | −2.26704 | −0.119985 | ||||||||
\(358\) | 25.3882 | 1.34181 | ||||||||
\(359\) | 1.31686 | 0.0695014 | 0.0347507 | − | 0.999396i | \(-0.488936\pi\) | ||||
0.0347507 | + | 0.999396i | \(0.488936\pi\) | |||||||
\(360\) | −7.90789 | −0.416782 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −7.26993 | −0.382099 | ||||||||
\(363\) | 7.39843 | 0.388317 | ||||||||
\(364\) | −0.235441 | −0.0123404 | ||||||||
\(365\) | −30.9799 | −1.62156 | ||||||||
\(366\) | 2.60650 | 0.136244 | ||||||||
\(367\) | 17.2226 | 0.899012 | 0.449506 | − | 0.893277i | \(-0.351600\pi\) | ||||
0.449506 | + | 0.893277i | \(0.351600\pi\) | |||||||
\(368\) | 6.09954 | 0.317961 | ||||||||
\(369\) | −9.22723 | −0.480351 | ||||||||
\(370\) | −8.41646 | −0.437551 | ||||||||
\(371\) | 8.65809 | 0.449505 | ||||||||
\(372\) | 2.73045 | 0.141567 | ||||||||
\(373\) | 11.1310 | 0.576341 | 0.288171 | − | 0.957579i | \(-0.406953\pi\) | ||||
0.288171 | + | 0.957579i | \(0.406953\pi\) | |||||||
\(374\) | 24.2820 | 1.25559 | ||||||||
\(375\) | 2.53233 | 0.130769 | ||||||||
\(376\) | 0.589626 | 0.0304076 | ||||||||
\(377\) | 1.37770 | 0.0709553 | ||||||||
\(378\) | 2.76871 | 0.142407 | ||||||||
\(379\) | 13.0836 | 0.672059 | 0.336030 | − | 0.941851i | \(-0.390916\pi\) | ||||
0.336030 | + | 0.941851i | \(0.390916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.289798 | −0.0148468 | ||||||||
\(382\) | 18.6408 | 0.953746 | ||||||||
\(383\) | 34.8408 | 1.78028 | 0.890141 | − | 0.455686i | \(-0.150606\pi\) | ||||
0.890141 | + | 0.455686i | \(0.150606\pi\) | |||||||
\(384\) | −0.479869 | −0.0244882 | ||||||||
\(385\) | −14.6748 | −0.747895 | ||||||||
\(386\) | 21.7466 | 1.10687 | ||||||||
\(387\) | 18.0306 | 0.916547 | ||||||||
\(388\) | −10.2497 | −0.520352 | ||||||||
\(389\) | −9.69653 | −0.491634 | −0.245817 | − | 0.969316i | \(-0.579056\pi\) | ||||
−0.245817 | + | 0.969316i | \(0.579056\pi\) | |||||||
\(390\) | −0.322573 | −0.0163341 | ||||||||
\(391\) | −28.8161 | −1.45729 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 7.16783 | 0.361569 | ||||||||
\(394\) | 21.8153 | 1.09904 | ||||||||
\(395\) | 29.2859 | 1.47353 | ||||||||
\(396\) | −14.2359 | −0.715379 | ||||||||
\(397\) | −6.18850 | −0.310592 | −0.155296 | − | 0.987868i | \(-0.549633\pi\) | ||||
−0.155296 | + | 0.987868i | \(0.549633\pi\) | |||||||
\(398\) | 3.08558 | 0.154666 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.15169 | 0.157585 | ||||||||
\(401\) | −31.9390 | −1.59496 | −0.797478 | − | 0.603348i | \(-0.793833\pi\) | ||||
−0.797478 | + | 0.603348i | \(0.793833\pi\) | |||||||
\(402\) | 5.34051 | 0.266360 | ||||||||
\(403\) | −1.33966 | −0.0667330 | ||||||||
\(404\) | 13.6679 | 0.680003 | ||||||||
\(405\) | −19.9303 | −0.990345 | ||||||||
\(406\) | 5.85159 | 0.290410 | ||||||||
\(407\) | −15.1514 | −0.751027 | ||||||||
\(408\) | 2.26704 | 0.112235 | ||||||||
\(409\) | −1.74937 | −0.0865009 | −0.0432504 | − | 0.999064i | \(-0.513771\pi\) | ||||
−0.0432504 | + | 0.999064i | \(0.513771\pi\) | |||||||
\(410\) | 9.51171 | 0.469750 | ||||||||
\(411\) | 7.75140 | 0.382349 | ||||||||
\(412\) | −6.38388 | −0.314511 | ||||||||
\(413\) | 8.79576 | 0.432811 | ||||||||
\(414\) | 16.8941 | 0.830298 | ||||||||
\(415\) | −34.6400 | −1.70041 | ||||||||
\(416\) | 0.235441 | 0.0115434 | ||||||||
\(417\) | −9.98577 | −0.489005 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.7702 | 0.770427 | 0.385213 | − | 0.922828i | \(-0.374128\pi\) | ||||
0.385213 | + | 0.922828i | \(0.374128\pi\) | |||||||
\(420\) | −1.37008 | −0.0668531 | ||||||||
\(421\) | −12.0823 | −0.588853 | −0.294427 | − | 0.955674i | \(-0.595129\pi\) | ||||
−0.294427 | + | 0.955674i | \(0.595129\pi\) | |||||||
\(422\) | −10.5582 | −0.513967 | ||||||||
\(423\) | 1.63310 | 0.0794041 | ||||||||
\(424\) | −8.65809 | −0.420474 | ||||||||
\(425\) | −14.8895 | −0.722248 | ||||||||
\(426\) | 1.45893 | 0.0706852 | ||||||||
\(427\) | −5.43170 | −0.262859 | ||||||||
\(428\) | 8.23814 | 0.398206 | ||||||||
\(429\) | −0.580699 | −0.0280364 | ||||||||
\(430\) | −18.5865 | −0.896320 | ||||||||
\(431\) | 10.5216 | 0.506807 | 0.253403 | − | 0.967361i | \(-0.418450\pi\) | ||||
0.253403 | + | 0.967361i | \(0.418450\pi\) | |||||||
\(432\) | −2.76871 | −0.133210 | ||||||||
\(433\) | 24.6468 | 1.18445 | 0.592226 | − | 0.805772i | \(-0.298249\pi\) | ||||
0.592226 | + | 0.805772i | \(0.298249\pi\) | |||||||
\(434\) | −5.68999 | −0.273128 | ||||||||
\(435\) | 8.01716 | 0.384393 | ||||||||
\(436\) | −12.8636 | −0.616056 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −5.20690 | −0.248795 | ||||||||
\(439\) | −8.56215 | −0.408649 | −0.204325 | − | 0.978903i | \(-0.565500\pi\) | ||||
−0.204325 | + | 0.978903i | \(0.565500\pi\) | |||||||
\(440\) | 14.6748 | 0.699591 | ||||||||
\(441\) | −2.76973 | −0.131892 | ||||||||
\(442\) | −1.11229 | −0.0529063 | ||||||||
\(443\) | 0.396798 | 0.0188524 | 0.00942621 | − | 0.999956i | \(-0.496999\pi\) | ||||
0.00942621 | + | 0.999956i | \(0.496999\pi\) | |||||||
\(444\) | −1.41458 | −0.0671331 | ||||||||
\(445\) | 43.6712 | 2.07021 | ||||||||
\(446\) | 12.5217 | 0.592918 | ||||||||
\(447\) | −8.33435 | −0.394201 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 39.6700 | 1.87214 | 0.936070 | − | 0.351813i | \(-0.114435\pi\) | ||||
0.936070 | + | 0.351813i | \(0.114435\pi\) | |||||||
\(450\) | 8.72932 | 0.411504 | ||||||||
\(451\) | 17.1231 | 0.806294 | ||||||||
\(452\) | −1.48774 | −0.0699775 | ||||||||
\(453\) | −7.49507 | −0.352149 | ||||||||
\(454\) | 26.7753 | 1.25663 | ||||||||
\(455\) | 0.672211 | 0.0315137 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.26900 | 0.246474 | 0.123237 | − | 0.992377i | \(-0.460673\pi\) | ||||
0.123237 | + | 0.992377i | \(0.460673\pi\) | |||||||
\(458\) | −18.8086 | −0.878868 | ||||||||
\(459\) | 13.0802 | 0.610532 | ||||||||
\(460\) | −17.4149 | −0.811974 | ||||||||
\(461\) | −7.92353 | −0.369036 | −0.184518 | − | 0.982829i | \(-0.559072\pi\) | ||||
−0.184518 | + | 0.982829i | \(0.559072\pi\) | |||||||
\(462\) | −2.46643 | −0.114749 | ||||||||
\(463\) | 16.7306 | 0.777538 | 0.388769 | − | 0.921335i | \(-0.372900\pi\) | ||||
0.388769 | + | 0.921335i | \(0.372900\pi\) | |||||||
\(464\) | −5.85159 | −0.271653 | ||||||||
\(465\) | −7.79575 | −0.361519 | ||||||||
\(466\) | 10.2268 | 0.473748 | ||||||||
\(467\) | −9.87110 | −0.456780 | −0.228390 | − | 0.973570i | \(-0.573346\pi\) | ||||
−0.228390 | + | 0.973570i | \(0.573346\pi\) | |||||||
\(468\) | 0.652106 | 0.0301436 | ||||||||
\(469\) | −11.1291 | −0.513894 | ||||||||
\(470\) | −1.68345 | −0.0776518 | ||||||||
\(471\) | 6.58999 | 0.303651 | ||||||||
\(472\) | −8.79576 | −0.404858 | ||||||||
\(473\) | −33.4596 | −1.53847 | ||||||||
\(474\) | 4.92217 | 0.226083 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.72430 | −0.216538 | ||||||||
\(477\) | −23.9805 | −1.09799 | ||||||||
\(478\) | 16.8837 | 0.772243 | ||||||||
\(479\) | 3.43432 | 0.156918 | 0.0784591 | − | 0.996917i | \(-0.475000\pi\) | ||||
0.0784591 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(480\) | 1.37008 | 0.0625354 | ||||||||
\(481\) | 0.694045 | 0.0316457 | ||||||||
\(482\) | 21.5302 | 0.980675 | ||||||||
\(483\) | 2.92698 | 0.133182 | ||||||||
\(484\) | 15.4176 | 0.700801 | ||||||||
\(485\) | 29.2642 | 1.32882 | ||||||||
\(486\) | −11.6559 | −0.528722 | ||||||||
\(487\) | −18.6872 | −0.846799 | −0.423399 | − | 0.905943i | \(-0.639163\pi\) | ||||
−0.423399 | + | 0.905943i | \(0.639163\pi\) | |||||||
\(488\) | 5.43170 | 0.245882 | ||||||||
\(489\) | −1.02643 | −0.0464169 | ||||||||
\(490\) | 2.85512 | 0.128981 | ||||||||
\(491\) | 31.2379 | 1.40975 | 0.704873 | − | 0.709333i | \(-0.251004\pi\) | ||||
0.704873 | + | 0.709333i | \(0.251004\pi\) | |||||||
\(492\) | 1.59866 | 0.0720733 | ||||||||
\(493\) | 27.6447 | 1.24505 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 40.6450 | 1.82686 | ||||||||
\(496\) | 5.68999 | 0.255488 | ||||||||
\(497\) | −3.04026 | −0.136374 | ||||||||
\(498\) | −5.82206 | −0.260893 | ||||||||
\(499\) | −11.4120 | −0.510870 | −0.255435 | − | 0.966826i | \(-0.582219\pi\) | ||||
−0.255435 | + | 0.966826i | \(0.582219\pi\) | |||||||
\(500\) | 5.27714 | 0.236001 | ||||||||
\(501\) | 3.00686 | 0.134336 | ||||||||
\(502\) | −4.88717 | −0.218125 | ||||||||
\(503\) | −36.2498 | −1.61630 | −0.808150 | − | 0.588976i | \(-0.799531\pi\) | ||||
−0.808150 | + | 0.588976i | \(0.799531\pi\) | |||||||
\(504\) | 2.76973 | 0.123373 | ||||||||
\(505\) | −39.0234 | −1.73652 | ||||||||
\(506\) | −31.3505 | −1.39370 | ||||||||
\(507\) | −6.21169 | −0.275871 | ||||||||
\(508\) | −0.603911 | −0.0267942 | ||||||||
\(509\) | 20.7401 | 0.919288 | 0.459644 | − | 0.888103i | \(-0.347977\pi\) | ||||
0.459644 | + | 0.888103i | \(0.347977\pi\) | |||||||
\(510\) | −6.47267 | −0.286615 | ||||||||
\(511\) | 10.8507 | 0.480005 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.1725 | −1.24264 | ||||||||
\(515\) | 18.2267 | 0.803165 | ||||||||
\(516\) | −3.12389 | −0.137522 | ||||||||
\(517\) | −3.03056 | −0.133284 | ||||||||
\(518\) | 2.94785 | 0.129521 | ||||||||
\(519\) | 2.96963 | 0.130352 | ||||||||
\(520\) | −0.672211 | −0.0294784 | ||||||||
\(521\) | −39.0045 | −1.70882 | −0.854409 | − | 0.519602i | \(-0.826080\pi\) | ||||
−0.854409 | + | 0.519602i | \(0.826080\pi\) | |||||||
\(522\) | −16.2073 | −0.709375 | ||||||||
\(523\) | −42.6216 | −1.86371 | −0.931856 | − | 0.362827i | \(-0.881812\pi\) | ||||
−0.931856 | + | 0.362827i | \(0.881812\pi\) | |||||||
\(524\) | 14.9371 | 0.652529 | ||||||||
\(525\) | 1.51240 | 0.0660065 | ||||||||
\(526\) | 2.20491 | 0.0961387 | ||||||||
\(527\) | −26.8812 | −1.17096 | ||||||||
\(528\) | 2.46643 | 0.107338 | ||||||||
\(529\) | 14.2044 | 0.617585 | ||||||||
\(530\) | 24.7198 | 1.07376 | ||||||||
\(531\) | −24.3619 | −1.05721 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.784362 | −0.0339745 | ||||||||
\(534\) | 7.33995 | 0.317631 | ||||||||
\(535\) | −23.5209 | −1.01690 | ||||||||
\(536\) | 11.1291 | 0.480704 | ||||||||
\(537\) | −12.1830 | −0.525736 | ||||||||
\(538\) | 9.96810 | 0.429755 | ||||||||
\(539\) | 5.13981 | 0.221387 | ||||||||
\(540\) | 7.90499 | 0.340177 | ||||||||
\(541\) | −12.4210 | −0.534019 | −0.267010 | − | 0.963694i | \(-0.586036\pi\) | ||||
−0.267010 | + | 0.963694i | \(0.586036\pi\) | |||||||
\(542\) | −19.2204 | −0.825585 | ||||||||
\(543\) | 3.48861 | 0.149711 | ||||||||
\(544\) | 4.72430 | 0.202553 | ||||||||
\(545\) | 36.7271 | 1.57322 | ||||||||
\(546\) | 0.112981 | 0.00483513 | ||||||||
\(547\) | −21.6915 | −0.927461 | −0.463731 | − | 0.885976i | \(-0.653489\pi\) | ||||
−0.463731 | + | 0.885976i | \(0.653489\pi\) | |||||||
\(548\) | 16.1532 | 0.690029 | ||||||||
\(549\) | 15.0443 | 0.642076 | ||||||||
\(550\) | −16.1991 | −0.690731 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.92698 | −0.124581 | ||||||||
\(553\) | −10.2573 | −0.436186 | ||||||||
\(554\) | −8.70088 | −0.369665 | ||||||||
\(555\) | 4.03880 | 0.171437 | ||||||||
\(556\) | −20.8094 | −0.882514 | ||||||||
\(557\) | 18.1866 | 0.770593 | 0.385296 | − | 0.922793i | \(-0.374099\pi\) | ||||
0.385296 | + | 0.922793i | \(0.374099\pi\) | |||||||
\(558\) | 15.7597 | 0.667162 | ||||||||
\(559\) | 1.53269 | 0.0648260 | ||||||||
\(560\) | −2.85512 | −0.120651 | ||||||||
\(561\) | −11.6522 | −0.491955 | ||||||||
\(562\) | 26.5023 | 1.11793 | ||||||||
\(563\) | −24.5873 | −1.03623 | −0.518116 | − | 0.855310i | \(-0.673366\pi\) | ||||
−0.518116 | + | 0.855310i | \(0.673366\pi\) | |||||||
\(564\) | −0.282943 | −0.0119140 | ||||||||
\(565\) | 4.24768 | 0.178701 | ||||||||
\(566\) | 32.3219 | 1.35859 | ||||||||
\(567\) | 6.98056 | 0.293156 | ||||||||
\(568\) | 3.04026 | 0.127567 | ||||||||
\(569\) | 33.1071 | 1.38792 | 0.693960 | − | 0.720013i | \(-0.255864\pi\) | ||||
0.693960 | + | 0.720013i | \(0.255864\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.83997 | −0.411790 | −0.205895 | − | 0.978574i | \(-0.566011\pi\) | ||||
−0.205895 | + | 0.978574i | \(0.566011\pi\) | |||||||
\(572\) | −1.21012 | −0.0505977 | ||||||||
\(573\) | −8.94514 | −0.373688 | ||||||||
\(574\) | −3.33146 | −0.139052 | ||||||||
\(575\) | 19.2239 | 0.801691 | ||||||||
\(576\) | −2.76973 | −0.115405 | ||||||||
\(577\) | −4.66787 | −0.194326 | −0.0971630 | − | 0.995268i | \(-0.530977\pi\) | ||||
−0.0971630 | + | 0.995268i | \(0.530977\pi\) | |||||||
\(578\) | −5.31898 | −0.221240 | ||||||||
\(579\) | −10.4355 | −0.433684 | ||||||||
\(580\) | 16.7070 | 0.693720 | ||||||||
\(581\) | 12.1326 | 0.503345 | ||||||||
\(582\) | 4.91853 | 0.203880 | ||||||||
\(583\) | 44.5009 | 1.84304 | ||||||||
\(584\) | −10.8507 | −0.449004 | ||||||||
\(585\) | −1.86184 | −0.0769776 | ||||||||
\(586\) | 32.3512 | 1.33641 | ||||||||
\(587\) | −22.0622 | −0.910603 | −0.455302 | − | 0.890337i | \(-0.650469\pi\) | ||||
−0.455302 | + | 0.890337i | \(0.650469\pi\) | |||||||
\(588\) | 0.479869 | 0.0197895 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 25.1129 | 1.03388 | ||||||||
\(591\) | −10.4685 | −0.430615 | ||||||||
\(592\) | −2.94785 | −0.121156 | ||||||||
\(593\) | −37.7846 | −1.55163 | −0.775814 | − | 0.630962i | \(-0.782660\pi\) | ||||
−0.775814 | + | 0.630962i | \(0.782660\pi\) | |||||||
\(594\) | 14.2306 | 0.583890 | ||||||||
\(595\) | 13.4884 | 0.552971 | ||||||||
\(596\) | −17.3680 | −0.711420 | ||||||||
\(597\) | −1.48067 | −0.0605999 | ||||||||
\(598\) | 1.43608 | 0.0587257 | ||||||||
\(599\) | −17.0576 | −0.696956 | −0.348478 | − | 0.937317i | \(-0.613301\pi\) | ||||
−0.348478 | + | 0.937317i | \(0.613301\pi\) | |||||||
\(600\) | −1.51240 | −0.0617434 | ||||||||
\(601\) | −20.7601 | −0.846822 | −0.423411 | − | 0.905938i | \(-0.639167\pi\) | ||||
−0.423411 | + | 0.905938i | \(0.639167\pi\) | |||||||
\(602\) | 6.50989 | 0.265323 | ||||||||
\(603\) | 30.8246 | 1.25527 | ||||||||
\(604\) | −15.6190 | −0.635528 | ||||||||
\(605\) | −44.0191 | −1.78963 | ||||||||
\(606\) | −6.55879 | −0.266433 | ||||||||
\(607\) | −1.83551 | −0.0745009 | −0.0372504 | − | 0.999306i | \(-0.511860\pi\) | ||||
−0.0372504 | + | 0.999306i | \(0.511860\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.80800 | −0.113786 | ||||||||
\(610\) | −15.5081 | −0.627906 | ||||||||
\(611\) | 0.138822 | 0.00561613 | ||||||||
\(612\) | 13.0850 | 0.528930 | ||||||||
\(613\) | 17.4650 | 0.705406 | 0.352703 | − | 0.935735i | \(-0.385263\pi\) | ||||
0.352703 | + | 0.935735i | \(0.385263\pi\) | |||||||
\(614\) | −5.06829 | −0.204540 | ||||||||
\(615\) | −4.56437 | −0.184053 | ||||||||
\(616\) | −5.13981 | −0.207089 | ||||||||
\(617\) | −42.3214 | −1.70379 | −0.851897 | − | 0.523709i | \(-0.824548\pi\) | ||||
−0.851897 | + | 0.523709i | \(0.824548\pi\) | |||||||
\(618\) | 3.06342 | 0.123229 | ||||||||
\(619\) | 45.8999 | 1.84487 | 0.922437 | − | 0.386147i | \(-0.126194\pi\) | ||||
0.922437 | + | 0.386147i | \(0.126194\pi\) | |||||||
\(620\) | −16.2456 | −0.652438 | ||||||||
\(621\) | −16.8879 | −0.677687 | ||||||||
\(622\) | 15.9316 | 0.638799 | ||||||||
\(623\) | −15.2958 | −0.612811 | ||||||||
\(624\) | −0.112981 | −0.00452285 | ||||||||
\(625\) | −30.8253 | −1.23301 | ||||||||
\(626\) | −2.20536 | −0.0881439 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.7329 | 0.548003 | ||||||||
\(629\) | 13.9265 | 0.555287 | ||||||||
\(630\) | −7.90789 | −0.315058 | ||||||||
\(631\) | −24.0296 | −0.956604 | −0.478302 | − | 0.878195i | \(-0.658748\pi\) | ||||
−0.478302 | + | 0.878195i | \(0.658748\pi\) | |||||||
\(632\) | 10.2573 | 0.408015 | ||||||||
\(633\) | 5.06657 | 0.201378 | ||||||||
\(634\) | 18.1717 | 0.721692 | ||||||||
\(635\) | 1.72424 | 0.0684242 | ||||||||
\(636\) | 4.15475 | 0.164746 | ||||||||
\(637\) | −0.235441 | −0.00932850 | ||||||||
\(638\) | 30.0761 | 1.19072 | ||||||||
\(639\) | 8.42069 | 0.333118 | ||||||||
\(640\) | 2.85512 | 0.112858 | ||||||||
\(641\) | 6.16026 | 0.243316 | 0.121658 | − | 0.992572i | \(-0.461179\pi\) | ||||
0.121658 | + | 0.992572i | \(0.461179\pi\) | |||||||
\(642\) | −3.95323 | −0.156021 | ||||||||
\(643\) | 0.690101 | 0.0272149 | 0.0136075 | − | 0.999907i | \(-0.495668\pi\) | ||||
0.0136075 | + | 0.999907i | \(0.495668\pi\) | |||||||
\(644\) | 6.09954 | 0.240356 | ||||||||
\(645\) | 8.91908 | 0.351188 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.2484 | −0.638791 | −0.319396 | − | 0.947621i | \(-0.603480\pi\) | ||||
−0.319396 | + | 0.947621i | \(0.603480\pi\) | |||||||
\(648\) | −6.98056 | −0.274222 | ||||||||
\(649\) | 45.2085 | 1.77459 | ||||||||
\(650\) | 0.742037 | 0.0291051 | ||||||||
\(651\) | 2.73045 | 0.107015 | ||||||||
\(652\) | −2.13899 | −0.0837693 | ||||||||
\(653\) | −16.6598 | −0.651947 | −0.325974 | − | 0.945379i | \(-0.605692\pi\) | ||||
−0.325974 | + | 0.945379i | \(0.605692\pi\) | |||||||
\(654\) | 6.17285 | 0.241377 | ||||||||
\(655\) | −42.6471 | −1.66636 | ||||||||
\(656\) | 3.33146 | 0.130072 | ||||||||
\(657\) | −30.0534 | −1.17249 | ||||||||
\(658\) | 0.589626 | 0.0229860 | ||||||||
\(659\) | −10.9663 | −0.427186 | −0.213593 | − | 0.976923i | \(-0.568517\pi\) | ||||
−0.213593 | + | 0.976923i | \(0.568517\pi\) | |||||||
\(660\) | −7.04195 | −0.274108 | ||||||||
\(661\) | −30.6314 | −1.19142 | −0.595711 | − | 0.803199i | \(-0.703130\pi\) | ||||
−0.595711 | + | 0.803199i | \(0.703130\pi\) | |||||||
\(662\) | 1.92750 | 0.0749144 | ||||||||
\(663\) | 0.533754 | 0.0207293 | ||||||||
\(664\) | −12.1326 | −0.470836 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.16474 | −0.316377 | ||||||||
\(667\) | −35.6920 | −1.38200 | ||||||||
\(668\) | 6.26600 | 0.242439 | ||||||||
\(669\) | −6.00875 | −0.232312 | ||||||||
\(670\) | −31.7749 | −1.22757 | ||||||||
\(671\) | −27.9179 | −1.07776 | ||||||||
\(672\) | −0.479869 | −0.0185113 | ||||||||
\(673\) | 7.30454 | 0.281569 | 0.140785 | − | 0.990040i | \(-0.455037\pi\) | ||||
0.140785 | + | 0.990040i | \(0.455037\pi\) | |||||||
\(674\) | −4.91677 | −0.189387 | ||||||||
\(675\) | −8.72612 | −0.335869 | ||||||||
\(676\) | −12.9446 | −0.497868 | ||||||||
\(677\) | 40.0820 | 1.54048 | 0.770238 | − | 0.637757i | \(-0.220138\pi\) | ||||
0.770238 | + | 0.637757i | \(0.220138\pi\) | |||||||
\(678\) | 0.713921 | 0.0274180 | ||||||||
\(679\) | −10.2497 | −0.393349 | ||||||||
\(680\) | −13.4884 | −0.517257 | ||||||||
\(681\) | −12.8486 | −0.492360 | ||||||||
\(682\) | −29.2454 | −1.11987 | ||||||||
\(683\) | −22.6845 | −0.867998 | −0.433999 | − | 0.900913i | \(-0.642898\pi\) | ||||
−0.433999 | + | 0.900913i | \(0.642898\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.1192 | −1.76212 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 9.02566 | 0.344350 | ||||||||
\(688\) | −6.50989 | −0.248187 | ||||||||
\(689\) | −2.03847 | −0.0776594 | ||||||||
\(690\) | 8.35687 | 0.318141 | ||||||||
\(691\) | −35.5384 | −1.35195 | −0.675973 | − | 0.736926i | \(-0.736276\pi\) | ||||
−0.675973 | + | 0.736926i | \(0.736276\pi\) | |||||||
\(692\) | 6.18843 | 0.235249 | ||||||||
\(693\) | −14.2359 | −0.540776 | ||||||||
\(694\) | 11.1668 | 0.423886 | ||||||||
\(695\) | 59.4132 | 2.25367 | ||||||||
\(696\) | 2.80800 | 0.106437 | ||||||||
\(697\) | −15.7388 | −0.596150 | ||||||||
\(698\) | 17.6629 | 0.668549 | ||||||||
\(699\) | −4.90753 | −0.185620 | ||||||||
\(700\) | 3.15169 | 0.119123 | ||||||||
\(701\) | 25.0390 | 0.945711 | 0.472855 | − | 0.881140i | \(-0.343223\pi\) | ||||
0.472855 | + | 0.881140i | \(0.343223\pi\) | |||||||
\(702\) | −0.651867 | −0.0246032 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.13981 | 0.193714 | ||||||||
\(705\) | 0.807835 | 0.0304248 | ||||||||
\(706\) | −7.02213 | −0.264281 | ||||||||
\(707\) | 13.6679 | 0.514034 | ||||||||
\(708\) | 4.22081 | 0.158628 | ||||||||
\(709\) | 13.5044 | 0.507170 | 0.253585 | − | 0.967313i | \(-0.418390\pi\) | ||||
0.253585 | + | 0.967313i | \(0.418390\pi\) | |||||||
\(710\) | −8.68030 | −0.325766 | ||||||||
\(711\) | 28.4100 | 1.06546 | ||||||||
\(712\) | 15.2958 | 0.573232 | ||||||||
\(713\) | 34.7063 | 1.29976 | ||||||||
\(714\) | 2.26704 | 0.0848419 | ||||||||
\(715\) | 3.45503 | 0.129211 | ||||||||
\(716\) | −25.3882 | −0.948803 | ||||||||
\(717\) | −8.10196 | −0.302573 | ||||||||
\(718\) | −1.31686 | −0.0491449 | ||||||||
\(719\) | 0.0885629 | 0.00330284 | 0.00165142 | − | 0.999999i | \(-0.499474\pi\) | ||||
0.00165142 | + | 0.999999i | \(0.499474\pi\) | |||||||
\(720\) | 7.90789 | 0.294710 | ||||||||
\(721\) | −6.38388 | −0.237748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.3317 | −0.384239 | ||||||||
\(724\) | 7.26993 | 0.270185 | ||||||||
\(725\) | −18.4424 | −0.684934 | ||||||||
\(726\) | −7.39843 | −0.274582 | ||||||||
\(727\) | 33.2385 | 1.23275 | 0.616373 | − | 0.787454i | \(-0.288601\pi\) | ||||
0.616373 | + | 0.787454i | \(0.288601\pi\) | |||||||
\(728\) | 0.235441 | 0.00872602 | ||||||||
\(729\) | −15.3484 | −0.568459 | ||||||||
\(730\) | 30.9799 | 1.14662 | ||||||||
\(731\) | 30.7546 | 1.13750 | ||||||||
\(732\) | −2.60650 | −0.0963392 | ||||||||
\(733\) | 4.68980 | 0.173222 | 0.0866109 | − | 0.996242i | \(-0.472396\pi\) | ||||
0.0866109 | + | 0.996242i | \(0.472396\pi\) | |||||||
\(734\) | −17.2226 | −0.635698 | ||||||||
\(735\) | −1.37008 | −0.0505362 | ||||||||
\(736\) | −6.09954 | −0.224832 | ||||||||
\(737\) | −57.2015 | −2.10704 | ||||||||
\(738\) | 9.22723 | 0.339659 | ||||||||
\(739\) | −19.1478 | −0.704365 | −0.352182 | − | 0.935931i | \(-0.614560\pi\) | ||||
−0.352182 | + | 0.935931i | \(0.614560\pi\) | |||||||
\(740\) | 8.41646 | 0.309395 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.65809 | −0.317848 | ||||||||
\(743\) | 31.3894 | 1.15156 | 0.575782 | − | 0.817603i | \(-0.304698\pi\) | ||||
0.575782 | + | 0.817603i | \(0.304698\pi\) | |||||||
\(744\) | −2.73045 | −0.100103 | ||||||||
\(745\) | 49.5876 | 1.81675 | ||||||||
\(746\) | −11.1310 | −0.407535 | ||||||||
\(747\) | −33.6040 | −1.22951 | ||||||||
\(748\) | −24.2820 | −0.887837 | ||||||||
\(749\) | 8.23814 | 0.301015 | ||||||||
\(750\) | −2.53233 | −0.0924677 | ||||||||
\(751\) | −15.7249 | −0.573811 | −0.286905 | − | 0.957959i | \(-0.592627\pi\) | ||||
−0.286905 | + | 0.957959i | \(0.592627\pi\) | |||||||
\(752\) | −0.589626 | −0.0215014 | ||||||||
\(753\) | 2.34520 | 0.0854639 | ||||||||
\(754\) | −1.37770 | −0.0501730 | ||||||||
\(755\) | 44.5940 | 1.62294 | ||||||||
\(756\) | −2.76871 | −0.100697 | ||||||||
\(757\) | 31.8058 | 1.15600 | 0.578000 | − | 0.816037i | \(-0.303833\pi\) | ||||
0.578000 | + | 0.816037i | \(0.303833\pi\) | |||||||
\(758\) | −13.0836 | −0.475218 | ||||||||
\(759\) | 15.0441 | 0.546067 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.99189 | −0.325956 | −0.162978 | − | 0.986630i | \(-0.552110\pi\) | ||||
−0.162978 | + | 0.986630i | \(0.552110\pi\) | |||||||
\(762\) | 0.289798 | 0.0104983 | ||||||||
\(763\) | −12.8636 | −0.465694 | ||||||||
\(764\) | −18.6408 | −0.674400 | ||||||||
\(765\) | −37.3592 | −1.35073 | ||||||||
\(766\) | −34.8408 | −1.25885 | ||||||||
\(767\) | −2.07088 | −0.0747752 | ||||||||
\(768\) | 0.479869 | 0.0173158 | ||||||||
\(769\) | −3.50825 | −0.126511 | −0.0632554 | − | 0.997997i | \(-0.520148\pi\) | ||||
−0.0632554 | + | 0.997997i | \(0.520148\pi\) | |||||||
\(770\) | 14.6748 | 0.528841 | ||||||||
\(771\) | 13.5191 | 0.486879 | ||||||||
\(772\) | −21.7466 | −0.782676 | ||||||||
\(773\) | 41.4008 | 1.48908 | 0.744542 | − | 0.667576i | \(-0.232668\pi\) | ||||
0.744542 | + | 0.667576i | \(0.232668\pi\) | |||||||
\(774\) | −18.0306 | −0.648097 | ||||||||
\(775\) | 17.9331 | 0.644176 | ||||||||
\(776\) | 10.2497 | 0.367944 | ||||||||
\(777\) | −1.41458 | −0.0507479 | ||||||||
\(778\) | 9.69653 | 0.347637 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.322573 | 0.0115500 | ||||||||
\(781\) | −15.6264 | −0.559155 | ||||||||
\(782\) | 28.8161 | 1.03046 | ||||||||
\(783\) | 16.2014 | 0.578990 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −39.2091 | −1.39943 | ||||||||
\(786\) | −7.16783 | −0.255668 | ||||||||
\(787\) | −24.0635 | −0.857770 | −0.428885 | − | 0.903359i | \(-0.641093\pi\) | ||||
−0.428885 | + | 0.903359i | \(0.641093\pi\) | |||||||
\(788\) | −21.8153 | −0.777137 | ||||||||
\(789\) | −1.05807 | −0.0376682 | ||||||||
\(790\) | −29.2859 | −1.04194 | ||||||||
\(791\) | −1.48774 | −0.0528980 | ||||||||
\(792\) | 14.2359 | 0.505849 | ||||||||
\(793\) | 1.27884 | 0.0454131 | ||||||||
\(794\) | 6.18850 | 0.219621 | ||||||||
\(795\) | −11.8623 | −0.420712 | ||||||||
\(796\) | −3.08558 | −0.109366 | ||||||||
\(797\) | 37.4880 | 1.32789 | 0.663947 | − | 0.747780i | \(-0.268880\pi\) | ||||
0.663947 | + | 0.747780i | \(0.268880\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.78557 | 0.0985463 | ||||||||
\(800\) | −3.15169 | −0.111429 | ||||||||
\(801\) | 42.3650 | 1.49690 | ||||||||
\(802\) | 31.9390 | 1.12780 | ||||||||
\(803\) | 55.7703 | 1.96809 | ||||||||
\(804\) | −5.34051 | −0.188345 | ||||||||
\(805\) | −17.4149 | −0.613795 | ||||||||
\(806\) | 1.33966 | 0.0471873 | ||||||||
\(807\) | −4.78338 | −0.168383 | ||||||||
\(808\) | −13.6679 | −0.480835 | ||||||||
\(809\) | −12.7505 | −0.448285 | −0.224143 | − | 0.974556i | \(-0.571958\pi\) | ||||
−0.224143 | + | 0.974556i | \(0.571958\pi\) | |||||||
\(810\) | 19.9303 | 0.700280 | ||||||||
\(811\) | 2.56267 | 0.0899876 | 0.0449938 | − | 0.998987i | \(-0.485673\pi\) | ||||
0.0449938 | + | 0.998987i | \(0.485673\pi\) | |||||||
\(812\) | −5.85159 | −0.205351 | ||||||||
\(813\) | 9.22325 | 0.323474 | ||||||||
\(814\) | 15.1514 | 0.531056 | ||||||||
\(815\) | 6.10706 | 0.213921 | ||||||||
\(816\) | −2.26704 | −0.0793624 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.74937 | 0.0611654 | ||||||||
\(819\) | 0.652106 | 0.0227864 | ||||||||
\(820\) | −9.51171 | −0.332163 | ||||||||
\(821\) | 42.7932 | 1.49349 | 0.746746 | − | 0.665109i | \(-0.231615\pi\) | ||||
0.746746 | + | 0.665109i | \(0.231615\pi\) | |||||||
\(822\) | −7.75140 | −0.270361 | ||||||||
\(823\) | 3.98657 | 0.138963 | 0.0694816 | − | 0.997583i | \(-0.477865\pi\) | ||||
0.0694816 | + | 0.997583i | \(0.477865\pi\) | |||||||
\(824\) | 6.38388 | 0.222393 | ||||||||
\(825\) | 7.77344 | 0.270636 | ||||||||
\(826\) | −8.79576 | −0.306044 | ||||||||
\(827\) | 50.3618 | 1.75125 | 0.875625 | − | 0.482991i | \(-0.160450\pi\) | ||||
0.875625 | + | 0.482991i | \(0.160450\pi\) | |||||||
\(828\) | −16.8941 | −0.587109 | ||||||||
\(829\) | −45.1081 | −1.56667 | −0.783335 | − | 0.621600i | \(-0.786483\pi\) | ||||
−0.783335 | + | 0.621600i | \(0.786483\pi\) | |||||||
\(830\) | 34.6400 | 1.20237 | ||||||||
\(831\) | 4.17528 | 0.144839 | ||||||||
\(832\) | −0.235441 | −0.00816244 | ||||||||
\(833\) | −4.72430 | −0.163687 | ||||||||
\(834\) | 9.98577 | 0.345779 | ||||||||
\(835\) | −17.8902 | −0.619114 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.7539 | −0.544536 | ||||||||
\(838\) | −15.7702 | −0.544774 | ||||||||
\(839\) | 20.3105 | 0.701196 | 0.350598 | − | 0.936526i | \(-0.385978\pi\) | ||||
0.350598 | + | 0.936526i | \(0.385978\pi\) | |||||||
\(840\) | 1.37008 | 0.0472723 | ||||||||
\(841\) | 5.24113 | 0.180729 | ||||||||
\(842\) | 12.0823 | 0.416382 | ||||||||
\(843\) | −12.7176 | −0.438019 | ||||||||
\(844\) | 10.5582 | 0.363430 | ||||||||
\(845\) | 36.9583 | 1.27140 | ||||||||
\(846\) | −1.63310 | −0.0561472 | ||||||||
\(847\) | 15.4176 | 0.529756 | ||||||||
\(848\) | 8.65809 | 0.297320 | ||||||||
\(849\) | −15.5103 | −0.532312 | ||||||||
\(850\) | 14.8895 | 0.510707 | ||||||||
\(851\) | −17.9806 | −0.616366 | ||||||||
\(852\) | −1.45893 | −0.0499820 | ||||||||
\(853\) | 13.1846 | 0.451433 | 0.225717 | − | 0.974193i | \(-0.427528\pi\) | ||||
0.225717 | + | 0.974193i | \(0.427528\pi\) | |||||||
\(854\) | 5.43170 | 0.185869 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.23814 | −0.281574 | ||||||||
\(857\) | 40.8695 | 1.39608 | 0.698038 | − | 0.716061i | \(-0.254057\pi\) | ||||
0.698038 | + | 0.716061i | \(0.254057\pi\) | |||||||
\(858\) | 0.580699 | 0.0198247 | ||||||||
\(859\) | −53.6037 | −1.82894 | −0.914468 | − | 0.404658i | \(-0.867390\pi\) | ||||
−0.914468 | + | 0.404658i | \(0.867390\pi\) | |||||||
\(860\) | 18.5865 | 0.633794 | ||||||||
\(861\) | 1.59866 | 0.0544823 | ||||||||
\(862\) | −10.5216 | −0.358366 | ||||||||
\(863\) | −24.0938 | −0.820162 | −0.410081 | − | 0.912049i | \(-0.634500\pi\) | ||||
−0.410081 | + | 0.912049i | \(0.634500\pi\) | |||||||
\(864\) | 2.76871 | 0.0941935 | ||||||||
\(865\) | −17.6687 | −0.600753 | ||||||||
\(866\) | −24.6468 | −0.837534 | ||||||||
\(867\) | 2.55241 | 0.0866845 | ||||||||
\(868\) | 5.68999 | 0.193131 | ||||||||
\(869\) | −52.7207 | −1.78843 | ||||||||
\(870\) | −8.01716 | −0.271807 | ||||||||
\(871\) | 2.62025 | 0.0887836 | ||||||||
\(872\) | 12.8636 | 0.435617 | ||||||||
\(873\) | 28.3890 | 0.960821 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.27714 | 0.178400 | ||||||||
\(876\) | 5.20690 | 0.175925 | ||||||||
\(877\) | −51.6182 | −1.74302 | −0.871512 | − | 0.490375i | \(-0.836860\pi\) | ||||
−0.871512 | + | 0.490375i | \(0.836860\pi\) | |||||||
\(878\) | 8.56215 | 0.288959 | ||||||||
\(879\) | −15.5243 | −0.523622 | ||||||||
\(880\) | −14.6748 | −0.494686 | ||||||||
\(881\) | 3.82731 | 0.128945 | 0.0644726 | − | 0.997919i | \(-0.479463\pi\) | ||||
0.0644726 | + | 0.997919i | \(0.479463\pi\) | |||||||
\(882\) | 2.76973 | 0.0932615 | ||||||||
\(883\) | 18.1829 | 0.611903 | 0.305952 | − | 0.952047i | \(-0.401025\pi\) | ||||
0.305952 | + | 0.952047i | \(0.401025\pi\) | |||||||
\(884\) | 1.11229 | 0.0374104 | ||||||||
\(885\) | −12.0509 | −0.405087 | ||||||||
\(886\) | −0.396798 | −0.0133307 | ||||||||
\(887\) | −8.09769 | −0.271894 | −0.135947 | − | 0.990716i | \(-0.543408\pi\) | ||||
−0.135947 | + | 0.990716i | \(0.543408\pi\) | |||||||
\(888\) | 1.41458 | 0.0474703 | ||||||||
\(889\) | −0.603911 | −0.0202545 | ||||||||
\(890\) | −43.6712 | −1.46386 | ||||||||
\(891\) | 35.8787 | 1.20198 | ||||||||
\(892\) | −12.5217 | −0.419256 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 8.33435 | 0.278742 | ||||||||
\(895\) | 72.4864 | 2.42295 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −0.689131 | −0.0230094 | ||||||||
\(898\) | −39.6700 | −1.32380 | ||||||||
\(899\) | −33.2955 | −1.11047 | ||||||||
\(900\) | −8.72932 | −0.290977 | ||||||||
\(901\) | −40.9034 | −1.36269 | ||||||||
\(902\) | −17.1231 | −0.570136 | ||||||||
\(903\) | −3.12389 | −0.103957 | ||||||||
\(904\) | 1.48774 | 0.0494816 | ||||||||
\(905\) | −20.7565 | −0.689969 | ||||||||
\(906\) | 7.49507 | 0.249007 | ||||||||
\(907\) | 32.6030 | 1.08256 | 0.541282 | − | 0.840841i | \(-0.317939\pi\) | ||||
0.541282 | + | 0.840841i | \(0.317939\pi\) | |||||||
\(908\) | −26.7753 | −0.888569 | ||||||||
\(909\) | −37.8563 | −1.25561 | ||||||||
\(910\) | −0.672211 | −0.0222836 | ||||||||
\(911\) | −6.09389 | −0.201900 | −0.100950 | − | 0.994892i | \(-0.532188\pi\) | ||||
−0.100950 | + | 0.994892i | \(0.532188\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 62.3592 | 2.06379 | ||||||||
\(914\) | −5.26900 | −0.174283 | ||||||||
\(915\) | 7.44187 | 0.246021 | ||||||||
\(916\) | 18.8086 | 0.621454 | ||||||||
\(917\) | 14.9371 | 0.493266 | ||||||||
\(918\) | −13.0802 | −0.431711 | ||||||||
\(919\) | −30.8160 | −1.01653 | −0.508263 | − | 0.861202i | \(-0.669712\pi\) | ||||
−0.508263 | + | 0.861202i | \(0.669712\pi\) | |||||||
\(920\) | 17.4149 | 0.574153 | ||||||||
\(921\) | 2.43211 | 0.0801409 | ||||||||
\(922\) | 7.92353 | 0.260948 | ||||||||
\(923\) | 0.715802 | 0.0235609 | ||||||||
\(924\) | 2.46643 | 0.0811397 | ||||||||
\(925\) | −9.29072 | −0.305477 | ||||||||
\(926\) | −16.7306 | −0.549803 | ||||||||
\(927\) | 17.6816 | 0.580740 | ||||||||
\(928\) | 5.85159 | 0.192088 | ||||||||
\(929\) | 43.0248 | 1.41160 | 0.705798 | − | 0.708413i | \(-0.250589\pi\) | ||||
0.705798 | + | 0.708413i | \(0.250589\pi\) | |||||||
\(930\) | 7.79575 | 0.255633 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.2268 | −0.334991 | ||||||||
\(933\) | −7.64508 | −0.250289 | ||||||||
\(934\) | 9.87110 | 0.322992 | ||||||||
\(935\) | 69.3279 | 2.26726 | ||||||||
\(936\) | −0.652106 | −0.0213148 | ||||||||
\(937\) | −27.1469 | −0.886852 | −0.443426 | − | 0.896311i | \(-0.646237\pi\) | ||||
−0.443426 | + | 0.896311i | \(0.646237\pi\) | |||||||
\(938\) | 11.1291 | 0.363378 | ||||||||
\(939\) | 1.05828 | 0.0345358 | ||||||||
\(940\) | 1.68345 | 0.0549081 | ||||||||
\(941\) | 45.0495 | 1.46857 | 0.734287 | − | 0.678840i | \(-0.237517\pi\) | ||||
0.734287 | + | 0.678840i | \(0.237517\pi\) | |||||||
\(942\) | −6.58999 | −0.214714 | ||||||||
\(943\) | 20.3204 | 0.661723 | ||||||||
\(944\) | 8.79576 | 0.286278 | ||||||||
\(945\) | 7.90499 | 0.257149 | ||||||||
\(946\) | 33.4596 | 1.08786 | ||||||||
\(947\) | 22.0222 | 0.715626 | 0.357813 | − | 0.933793i | \(-0.383523\pi\) | ||||
0.357813 | + | 0.933793i | \(0.383523\pi\) | |||||||
\(948\) | −4.92217 | −0.159865 | ||||||||
\(949\) | −2.55469 | −0.0829287 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.72005 | −0.282767 | ||||||||
\(952\) | 4.72430 | 0.153115 | ||||||||
\(953\) | 31.3488 | 1.01549 | 0.507744 | − | 0.861508i | \(-0.330480\pi\) | ||||
0.507744 | + | 0.861508i | \(0.330480\pi\) | |||||||
\(954\) | 23.9805 | 0.776398 | ||||||||
\(955\) | 53.2217 | 1.72221 | ||||||||
\(956\) | −16.8837 | −0.546058 | ||||||||
\(957\) | −14.4326 | −0.466538 | ||||||||
\(958\) | −3.43432 | −0.110958 | ||||||||
\(959\) | 16.1532 | 0.521613 | ||||||||
\(960\) | −1.37008 | −0.0442192 | ||||||||
\(961\) | 1.37597 | 0.0443863 | ||||||||
\(962\) | −0.694045 | −0.0223769 | ||||||||
\(963\) | −22.8174 | −0.735280 | ||||||||
\(964\) | −21.5302 | −0.693442 | ||||||||
\(965\) | 62.0890 | 1.99872 | ||||||||
\(966\) | −2.92698 | −0.0941741 | ||||||||
\(967\) | 48.3616 | 1.55521 | 0.777603 | − | 0.628756i | \(-0.216436\pi\) | ||||
0.777603 | + | 0.628756i | \(0.216436\pi\) | |||||||
\(968\) | −15.4176 | −0.495541 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29.2642 | −0.939617 | ||||||||
\(971\) | 28.9214 | 0.928131 | 0.464065 | − | 0.885801i | \(-0.346390\pi\) | ||||
0.464065 | + | 0.885801i | \(0.346390\pi\) | |||||||
\(972\) | 11.6559 | 0.373863 | ||||||||
\(973\) | −20.8094 | −0.667118 | ||||||||
\(974\) | 18.6872 | 0.598777 | ||||||||
\(975\) | −0.356080 | −0.0114037 | ||||||||
\(976\) | −5.43170 | −0.173865 | ||||||||
\(977\) | 60.4037 | 1.93249 | 0.966243 | − | 0.257631i | \(-0.0829419\pi\) | ||||
0.966243 | + | 0.257631i | \(0.0829419\pi\) | |||||||
\(978\) | 1.02643 | 0.0328217 | ||||||||
\(979\) | −78.6172 | −2.51262 | ||||||||
\(980\) | −2.85512 | −0.0912034 | ||||||||
\(981\) | 35.6287 | 1.13754 | ||||||||
\(982\) | −31.2379 | −0.996841 | ||||||||
\(983\) | 6.35674 | 0.202748 | 0.101374 | − | 0.994848i | \(-0.467676\pi\) | ||||
0.101374 | + | 0.994848i | \(0.467676\pi\) | |||||||
\(984\) | −1.59866 | −0.0509635 | ||||||||
\(985\) | 62.2852 | 1.98457 | ||||||||
\(986\) | −27.6447 | −0.880385 | ||||||||
\(987\) | −0.282943 | −0.00900617 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.7074 | −1.26262 | ||||||||
\(990\) | −40.6450 | −1.29178 | ||||||||
\(991\) | 53.6557 | 1.70443 | 0.852215 | − | 0.523192i | \(-0.175259\pi\) | ||||
0.852215 | + | 0.523192i | \(0.175259\pi\) | |||||||
\(992\) | −5.68999 | −0.180657 | ||||||||
\(993\) | −0.924946 | −0.0293523 | ||||||||
\(994\) | 3.04026 | 0.0964313 | ||||||||
\(995\) | 8.80969 | 0.279286 | ||||||||
\(996\) | 5.82206 | 0.184479 | ||||||||
\(997\) | −26.8958 | −0.851798 | −0.425899 | − | 0.904771i | \(-0.640042\pi\) | ||||
−0.425899 | + | 0.904771i | \(0.640042\pi\) | |||||||
\(998\) | 11.4120 | 0.361240 | ||||||||
\(999\) | 8.16175 | 0.258226 |
(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 | 5054.2.a.z.1.4 | ✓ | 6 | |
19.18 | odd | 2 | 5054.2.a.be.1.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.z.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
5054.2.a.be.1.3 | yes | 6 | 19.18 | odd | 2 |