Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8468.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.704624\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.704624 | −0.498245 | −0.249122 | − | 0.968472i | \(-0.580142\pi\) | ||||
−0.249122 | + | 0.968472i | \(0.580142\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.50350 | −0.751752 | ||||||||
\(5\) | −1.50350 | −0.672388 | −0.336194 | − | 0.941793i | \(-0.609140\pi\) | ||||
−0.336194 | + | 0.941793i | \(0.609140\pi\) | |||||||
\(6\) | −0.704624 | −0.287662 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.46865 | 0.872801 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.05941 | 0.335014 | ||||||||
\(11\) | −4.26753 | −1.28671 | −0.643355 | − | 0.765568i | \(-0.722458\pi\) | ||||
−0.643355 | + | 0.765568i | \(0.722458\pi\) | |||||||
\(12\) | −1.50350 | −0.434024 | ||||||||
\(13\) | −2.30238 | −0.638567 | −0.319283 | − | 0.947659i | \(-0.603442\pi\) | ||||
−0.319283 | + | 0.947659i | \(0.603442\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.50350 | −0.388203 | ||||||||
\(16\) | 1.26753 | 0.316884 | ||||||||
\(17\) | −0.905744 | −0.219675 | −0.109838 | − | 0.993950i | \(-0.535033\pi\) | ||||
−0.109838 | + | 0.993950i | \(0.535033\pi\) | |||||||
\(18\) | −0.704624 | −0.166082 | ||||||||
\(19\) | −1.17328 | −0.269169 | −0.134584 | − | 0.990902i | \(-0.542970\pi\) | ||||
−0.134584 | + | 0.990902i | \(0.542970\pi\) | |||||||
\(20\) | 2.26053 | 0.505469 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00701 | 0.641096 | ||||||||
\(23\) | −0.893136 | −0.186232 | −0.0931159 | − | 0.995655i | \(-0.529683\pi\) | ||||
−0.0931159 | + | 0.995655i | \(0.529683\pi\) | |||||||
\(24\) | 2.46865 | 0.503912 | ||||||||
\(25\) | −2.73947 | −0.547895 | ||||||||
\(26\) | 1.62232 | 0.318162 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.32694 | 0.617797 | 0.308899 | − | 0.951095i | \(-0.400040\pi\) | ||||
0.308899 | + | 0.951095i | \(0.400040\pi\) | |||||||
\(30\) | 1.05941 | 0.193420 | ||||||||
\(31\) | 3.09426 | 0.555745 | 0.277872 | − | 0.960618i | \(-0.410371\pi\) | ||||
0.277872 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(32\) | −5.83045 | −1.03069 | ||||||||
\(33\) | −4.26753 | −0.742882 | ||||||||
\(34\) | 0.638209 | 0.109452 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50350 | −0.250584 | ||||||||
\(37\) | −2.36179 | −0.388276 | −0.194138 | − | 0.980974i | \(-0.562191\pi\) | ||||
−0.194138 | + | 0.980974i | \(0.562191\pi\) | |||||||
\(38\) | 0.826721 | 0.134112 | ||||||||
\(39\) | −2.30238 | −0.368677 | ||||||||
\(40\) | −3.71163 | −0.586861 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.84305 | −1.19605 | −0.598027 | − | 0.801476i | \(-0.704049\pi\) | ||||
−0.598027 | + | 0.801476i | \(0.704049\pi\) | |||||||
\(44\) | 6.41626 | 0.967287 | ||||||||
\(45\) | −1.50350 | −0.224129 | ||||||||
\(46\) | 0.629325 | 0.0927890 | ||||||||
\(47\) | 1.30567 | 0.190451 | 0.0952257 | − | 0.995456i | \(-0.469643\pi\) | ||||
0.0952257 | + | 0.995456i | \(0.469643\pi\) | |||||||
\(48\) | 1.26753 | 0.182953 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.93030 | 0.272986 | ||||||||
\(51\) | −0.905744 | −0.126830 | ||||||||
\(52\) | 3.46165 | 0.480044 | ||||||||
\(53\) | −6.64894 | −0.913303 | −0.456651 | − | 0.889646i | \(-0.650951\pi\) | ||||
−0.456651 | + | 0.889646i | \(0.650951\pi\) | |||||||
\(54\) | −0.704624 | −0.0958872 | ||||||||
\(55\) | 6.41626 | 0.865168 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.17328 | −0.155405 | ||||||||
\(58\) | −2.34424 | −0.307814 | ||||||||
\(59\) | 0.638209 | 0.0830878 | 0.0415439 | − | 0.999137i | \(-0.486772\pi\) | ||||
0.0415439 | + | 0.999137i | \(0.486772\pi\) | |||||||
\(60\) | 2.26053 | 0.291833 | ||||||||
\(61\) | 9.84305 | 1.26027 | 0.630137 | − | 0.776484i | \(-0.282999\pi\) | ||||
0.630137 | + | 0.776484i | \(0.282999\pi\) | |||||||
\(62\) | −2.18029 | −0.276897 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.57320 | 0.196651 | ||||||||
\(65\) | 3.46165 | 0.429364 | ||||||||
\(66\) | 3.00701 | 0.370137 | ||||||||
\(67\) | −13.4478 | −1.64291 | −0.821457 | − | 0.570271i | \(-0.806838\pi\) | ||||
−0.821457 | + | 0.570271i | \(0.806838\pi\) | |||||||
\(68\) | 1.36179 | 0.165141 | ||||||||
\(69\) | −0.893136 | −0.107521 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.245293 | −0.0291110 | −0.0145555 | − | 0.999894i | \(-0.504633\pi\) | ||||
−0.0145555 | + | 0.999894i | \(0.504633\pi\) | |||||||
\(72\) | 2.46865 | 0.290934 | ||||||||
\(73\) | 2.08725 | 0.244294 | 0.122147 | − | 0.992512i | \(-0.461022\pi\) | ||||
0.122147 | + | 0.992512i | \(0.461022\pi\) | |||||||
\(74\) | 1.66418 | 0.193456 | ||||||||
\(75\) | −2.73947 | −0.316327 | ||||||||
\(76\) | 1.76403 | 0.202348 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.62232 | 0.183691 | ||||||||
\(79\) | −14.5736 | −1.63966 | −0.819832 | − | 0.572605i | \(-0.805933\pi\) | ||||
−0.819832 | + | 0.572605i | \(0.805933\pi\) | |||||||
\(80\) | −1.90574 | −0.213069 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.704624 | −0.0778127 | ||||||||
\(83\) | 6.41626 | 0.704276 | 0.352138 | − | 0.935948i | \(-0.385455\pi\) | ||||
0.352138 | + | 0.935948i | \(0.385455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.36179 | 0.147707 | ||||||||
\(86\) | 5.52641 | 0.595928 | ||||||||
\(87\) | 3.32694 | 0.356685 | ||||||||
\(88\) | −10.5351 | −1.12304 | ||||||||
\(89\) | 1.81149 | 0.192017 | 0.0960087 | − | 0.995380i | \(-0.469392\pi\) | ||||
0.0960087 | + | 0.995380i | \(0.469392\pi\) | |||||||
\(90\) | 1.05941 | 0.111671 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.34283 | 0.140000 | ||||||||
\(93\) | 3.09426 | 0.320859 | ||||||||
\(94\) | −0.920006 | −0.0948914 | ||||||||
\(95\) | 1.76403 | 0.180986 | ||||||||
\(96\) | −5.83045 | −0.595067 | ||||||||
\(97\) | 6.29416 | 0.639075 | 0.319538 | − | 0.947574i | \(-0.396472\pi\) | ||||
0.319538 | + | 0.947574i | \(0.396472\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.26753 | −0.428903 | ||||||||
\(100\) | 4.11881 | 0.411881 | ||||||||
\(101\) | −10.2816 | −1.02305 | −0.511526 | − | 0.859268i | \(-0.670920\pi\) | ||||
−0.511526 | + | 0.859268i | \(0.670920\pi\) | |||||||
\(102\) | 0.638209 | 0.0631922 | ||||||||
\(103\) | 8.68708 | 0.855963 | 0.427982 | − | 0.903787i | \(-0.359225\pi\) | ||||
0.427982 | + | 0.903787i | \(0.359225\pi\) | |||||||
\(104\) | −5.68379 | −0.557342 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.68501 | 0.455048 | ||||||||
\(107\) | 17.9551 | 1.73578 | 0.867890 | − | 0.496756i | \(-0.165476\pi\) | ||||
0.867890 | + | 0.496756i | \(0.165476\pi\) | |||||||
\(108\) | −1.50350 | −0.144675 | ||||||||
\(109\) | −1.29866 | −0.124389 | −0.0621946 | − | 0.998064i | \(-0.519810\pi\) | ||||
−0.0621946 | + | 0.998064i | \(0.519810\pi\) | |||||||
\(110\) | −4.52105 | −0.431065 | ||||||||
\(111\) | −2.36179 | −0.224171 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.46493 | 0.325953 | 0.162977 | − | 0.986630i | \(-0.447890\pi\) | ||||
0.162977 | + | 0.986630i | \(0.447890\pi\) | |||||||
\(114\) | 0.826721 | 0.0774295 | ||||||||
\(115\) | 1.34283 | 0.125220 | ||||||||
\(116\) | −5.00207 | −0.464431 | ||||||||
\(117\) | −2.30238 | −0.212856 | ||||||||
\(118\) | −0.449698 | −0.0413981 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.71163 | −0.338824 | ||||||||
\(121\) | 7.21185 | 0.655623 | ||||||||
\(122\) | −6.93566 | −0.627925 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −4.65223 | −0.417782 | ||||||||
\(125\) | 11.6363 | 1.04079 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.1398 | 0.988501 | 0.494250 | − | 0.869320i | \(-0.335443\pi\) | ||||
0.494250 | + | 0.869320i | \(0.335443\pi\) | |||||||
\(128\) | 10.5524 | 0.932707 | ||||||||
\(129\) | −7.84305 | −0.690542 | ||||||||
\(130\) | −2.43916 | −0.213928 | ||||||||
\(131\) | −4.43850 | −0.387793 | −0.193897 | − | 0.981022i | \(-0.562113\pi\) | ||||
−0.193897 | + | 0.981022i | \(0.562113\pi\) | |||||||
\(132\) | 6.41626 | 0.558464 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.47566 | 0.818573 | ||||||||
\(135\) | −1.50350 | −0.129401 | ||||||||
\(136\) | −2.23597 | −0.191733 | ||||||||
\(137\) | 10.7362 | 0.917255 | 0.458627 | − | 0.888629i | \(-0.348341\pi\) | ||||
0.458627 | + | 0.888629i | \(0.348341\pi\) | |||||||
\(138\) | 0.629325 | 0.0535717 | ||||||||
\(139\) | 12.1836 | 1.03340 | 0.516699 | − | 0.856167i | \(-0.327161\pi\) | ||||
0.516699 | + | 0.856167i | \(0.327161\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.30567 | 0.109957 | ||||||||
\(142\) | 0.172840 | 0.0145044 | ||||||||
\(143\) | 9.82551 | 0.821650 | ||||||||
\(144\) | 1.26753 | 0.105628 | ||||||||
\(145\) | −5.00207 | −0.415399 | ||||||||
\(146\) | −1.47072 | −0.121718 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.55096 | 0.291887 | ||||||||
\(149\) | 6.11716 | 0.501137 | 0.250569 | − | 0.968099i | \(-0.419382\pi\) | ||||
0.250569 | + | 0.968099i | \(0.419382\pi\) | |||||||
\(150\) | 1.93030 | 0.157608 | ||||||||
\(151\) | −8.41626 | −0.684905 | −0.342453 | − | 0.939535i | \(-0.611258\pi\) | ||||
−0.342453 | + | 0.939535i | \(0.611258\pi\) | |||||||
\(152\) | −2.89642 | −0.234931 | ||||||||
\(153\) | −0.905744 | −0.0732251 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.65223 | −0.373676 | ||||||||
\(156\) | 3.46165 | 0.277153 | ||||||||
\(157\) | −8.46372 | −0.675478 | −0.337739 | − | 0.941240i | \(-0.609662\pi\) | ||||
−0.337739 | + | 0.941240i | \(0.609662\pi\) | |||||||
\(158\) | 10.2689 | 0.816953 | ||||||||
\(159\) | −6.64894 | −0.527295 | ||||||||
\(160\) | 8.76610 | 0.693021 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.704624 | −0.0553605 | ||||||||
\(163\) | 8.70603 | 0.681909 | 0.340955 | − | 0.940080i | \(-0.389250\pi\) | ||||
0.340955 | + | 0.940080i | \(0.389250\pi\) | |||||||
\(164\) | −1.50350 | −0.117404 | ||||||||
\(165\) | 6.41626 | 0.499505 | ||||||||
\(166\) | −4.52105 | −0.350902 | ||||||||
\(167\) | −7.09304 | −0.548876 | −0.274438 | − | 0.961605i | \(-0.588492\pi\) | ||||
−0.274438 | + | 0.961605i | \(0.588492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.69903 | −0.592233 | ||||||||
\(170\) | −0.959551 | −0.0735942 | ||||||||
\(171\) | −1.17328 | −0.0897229 | ||||||||
\(172\) | 11.7921 | 0.899137 | ||||||||
\(173\) | 16.8030 | 1.27751 | 0.638756 | − | 0.769409i | \(-0.279449\pi\) | ||||
0.638756 | + | 0.769409i | \(0.279449\pi\) | |||||||
\(174\) | −2.34424 | −0.177717 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.40925 | −0.407737 | ||||||||
\(177\) | 0.638209 | 0.0479708 | ||||||||
\(178\) | −1.27642 | −0.0956716 | ||||||||
\(179\) | 4.85663 | 0.363002 | 0.181501 | − | 0.983391i | \(-0.441904\pi\) | ||||
0.181501 | + | 0.983391i | \(0.441904\pi\) | |||||||
\(180\) | 2.26053 | 0.168490 | ||||||||
\(181\) | −5.94597 | −0.441961 | −0.220980 | − | 0.975278i | \(-0.570926\pi\) | ||||
−0.220980 | + | 0.975278i | \(0.570926\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.84305 | 0.727619 | ||||||||
\(184\) | −2.20484 | −0.162543 | ||||||||
\(185\) | 3.55096 | 0.261072 | ||||||||
\(186\) | −2.18029 | −0.159866 | ||||||||
\(187\) | 3.86530 | 0.282658 | ||||||||
\(188\) | −1.96308 | −0.143172 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.24298 | −0.0901752 | ||||||||
\(191\) | −14.0854 | −1.01918 | −0.509591 | − | 0.860417i | \(-0.670203\pi\) | ||||
−0.509591 | + | 0.860417i | \(0.670203\pi\) | |||||||
\(192\) | 1.57320 | 0.113536 | ||||||||
\(193\) | 9.65924 | 0.695287 | 0.347644 | − | 0.937627i | \(-0.386982\pi\) | ||||
0.347644 | + | 0.937627i | \(0.386982\pi\) | |||||||
\(194\) | −4.43502 | −0.318416 | ||||||||
\(195\) | 3.46165 | 0.247894 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.13984 | −0.0812102 | −0.0406051 | − | 0.999175i | \(-0.512929\pi\) | ||||
−0.0406051 | + | 0.999175i | \(0.512929\pi\) | |||||||
\(198\) | 3.00701 | 0.213699 | ||||||||
\(199\) | −6.81027 | −0.482768 | −0.241384 | − | 0.970430i | \(-0.577601\pi\) | ||||
−0.241384 | + | 0.970430i | \(0.577601\pi\) | |||||||
\(200\) | −6.76282 | −0.478203 | ||||||||
\(201\) | −13.4478 | −0.948536 | ||||||||
\(202\) | 7.24463 | 0.509731 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.36179 | 0.0953444 | ||||||||
\(205\) | −1.50350 | −0.105009 | ||||||||
\(206\) | −6.12113 | −0.426479 | ||||||||
\(207\) | −0.893136 | −0.0620772 | ||||||||
\(208\) | −2.91835 | −0.202351 | ||||||||
\(209\) | 5.00701 | 0.346342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.45439 | 0.237810 | 0.118905 | − | 0.992906i | \(-0.462062\pi\) | ||||
0.118905 | + | 0.992906i | \(0.462062\pi\) | |||||||
\(212\) | 9.99672 | 0.686577 | ||||||||
\(213\) | −0.245293 | −0.0168072 | ||||||||
\(214\) | −12.6516 | −0.864843 | ||||||||
\(215\) | 11.7921 | 0.804212 | ||||||||
\(216\) | 2.46865 | 0.167971 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.915068 | 0.0619762 | ||||||||
\(219\) | 2.08725 | 0.141043 | ||||||||
\(220\) | −9.64687 | −0.650392 | ||||||||
\(221\) | 2.08537 | 0.140277 | ||||||||
\(222\) | 1.66418 | 0.111692 | ||||||||
\(223\) | −3.01195 | −0.201695 | −0.100847 | − | 0.994902i | \(-0.532155\pi\) | ||||
−0.100847 | + | 0.994902i | \(0.532155\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.73947 | −0.182632 | ||||||||
\(226\) | −2.44147 | −0.162404 | ||||||||
\(227\) | −14.0619 | −0.933322 | −0.466661 | − | 0.884436i | \(-0.654543\pi\) | ||||
−0.466661 | + | 0.884436i | \(0.654543\pi\) | |||||||
\(228\) | 1.76403 | 0.116826 | ||||||||
\(229\) | 1.07999 | 0.0713680 | 0.0356840 | − | 0.999363i | \(-0.488639\pi\) | ||||
0.0356840 | + | 0.999363i | \(0.488639\pi\) | |||||||
\(230\) | −0.946193 | −0.0623901 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.21307 | 0.539214 | ||||||||
\(233\) | 5.55030 | 0.363612 | 0.181806 | − | 0.983334i | \(-0.441806\pi\) | ||||
0.181806 | + | 0.983334i | \(0.441806\pi\) | |||||||
\(234\) | 1.62232 | 0.106054 | ||||||||
\(235\) | −1.96308 | −0.128057 | ||||||||
\(236\) | −0.959551 | −0.0624614 | ||||||||
\(237\) | −14.5736 | −0.946660 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.45836 | −0.0943335 | −0.0471668 | − | 0.998887i | \(-0.515019\pi\) | ||||
−0.0471668 | + | 0.998887i | \(0.515019\pi\) | |||||||
\(240\) | −1.90574 | −0.123015 | ||||||||
\(241\) | −1.68335 | −0.108434 | −0.0542172 | − | 0.998529i | \(-0.517266\pi\) | ||||
−0.0542172 | + | 0.998529i | \(0.517266\pi\) | |||||||
\(242\) | −5.08165 | −0.326661 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −14.7991 | −0.947414 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.704624 | −0.0449252 | ||||||||
\(247\) | 2.70134 | 0.171882 | ||||||||
\(248\) | 7.63865 | 0.485055 | ||||||||
\(249\) | 6.41626 | 0.406614 | ||||||||
\(250\) | −8.19924 | −0.518566 | ||||||||
\(251\) | 18.8882 | 1.19221 | 0.596106 | − | 0.802906i | \(-0.296714\pi\) | ||||
0.596106 | + | 0.802906i | \(0.296714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.81149 | 0.239626 | ||||||||
\(254\) | −7.84940 | −0.492515 | ||||||||
\(255\) | 1.36179 | 0.0852786 | ||||||||
\(256\) | −10.5819 | −0.661367 | ||||||||
\(257\) | −15.1796 | −0.946879 | −0.473440 | − | 0.880826i | \(-0.656988\pi\) | ||||
−0.473440 | + | 0.880826i | \(0.656988\pi\) | |||||||
\(258\) | 5.52641 | 0.344059 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.20460 | −0.322776 | ||||||||
\(261\) | 3.32694 | 0.205932 | ||||||||
\(262\) | 3.12747 | 0.193216 | ||||||||
\(263\) | −1.96021 | −0.120872 | −0.0604359 | − | 0.998172i | \(-0.519249\pi\) | ||||
−0.0604359 | + | 0.998172i | \(0.519249\pi\) | |||||||
\(264\) | −10.5351 | −0.648389 | ||||||||
\(265\) | 9.99672 | 0.614093 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.81149 | 0.110861 | ||||||||
\(268\) | 20.2189 | 1.23506 | ||||||||
\(269\) | 30.4771 | 1.85822 | 0.929110 | − | 0.369804i | \(-0.120575\pi\) | ||||
0.929110 | + | 0.369804i | \(0.120575\pi\) | |||||||
\(270\) | 1.05941 | 0.0644734 | ||||||||
\(271\) | −5.84634 | −0.355140 | −0.177570 | − | 0.984108i | \(-0.556824\pi\) | ||||
−0.177570 | + | 0.984108i | \(0.556824\pi\) | |||||||
\(272\) | −1.14806 | −0.0696115 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.56498 | −0.457017 | ||||||||
\(275\) | 11.6908 | 0.704982 | ||||||||
\(276\) | 1.34283 | 0.0808291 | ||||||||
\(277\) | 7.11638 | 0.427582 | 0.213791 | − | 0.976879i | \(-0.431419\pi\) | ||||
0.213791 | + | 0.976879i | \(0.431419\pi\) | |||||||
\(278\) | −8.58484 | −0.514885 | ||||||||
\(279\) | 3.09426 | 0.185248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.47632 | −0.267035 | −0.133518 | − | 0.991046i | \(-0.542627\pi\) | ||||
−0.133518 | + | 0.991046i | \(0.542627\pi\) | |||||||
\(282\) | −0.920006 | −0.0547856 | ||||||||
\(283\) | −0.675569 | −0.0401584 | −0.0200792 | − | 0.999798i | \(-0.506392\pi\) | ||||
−0.0200792 | + | 0.999798i | \(0.506392\pi\) | |||||||
\(284\) | 0.368800 | 0.0218842 | ||||||||
\(285\) | 1.76403 | 0.104492 | ||||||||
\(286\) | −6.92329 | −0.409383 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.83045 | −0.343562 | ||||||||
\(289\) | −16.1796 | −0.951743 | ||||||||
\(290\) | 3.52458 | 0.206971 | ||||||||
\(291\) | 6.29416 | 0.368970 | ||||||||
\(292\) | −3.13818 | −0.183648 | ||||||||
\(293\) | 2.58722 | 0.151147 | 0.0755736 | − | 0.997140i | \(-0.475921\pi\) | ||||
0.0755736 | + | 0.997140i | \(0.475921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.959551 | −0.0558672 | ||||||||
\(296\) | −5.83045 | −0.338888 | ||||||||
\(297\) | −4.26753 | −0.247627 | ||||||||
\(298\) | −4.31030 | −0.249689 | ||||||||
\(299\) | 2.05634 | 0.118921 | ||||||||
\(300\) | 4.11881 | 0.237800 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.93030 | 0.341250 | ||||||||
\(303\) | −10.2816 | −0.590660 | ||||||||
\(304\) | −1.48717 | −0.0852952 | ||||||||
\(305\) | −14.7991 | −0.847393 | ||||||||
\(306\) | 0.638209 | 0.0364840 | ||||||||
\(307\) | 27.0130 | 1.54172 | 0.770858 | − | 0.637007i | \(-0.219828\pi\) | ||||
0.770858 | + | 0.637007i | \(0.219828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.68708 | 0.494191 | ||||||||
\(310\) | 3.27807 | 0.186182 | ||||||||
\(311\) | 29.6830 | 1.68317 | 0.841585 | − | 0.540125i | \(-0.181623\pi\) | ||||
0.841585 | + | 0.540125i | \(0.181623\pi\) | |||||||
\(312\) | −5.68379 | −0.321781 | ||||||||
\(313\) | 14.0091 | 0.791840 | 0.395920 | − | 0.918285i | \(-0.370426\pi\) | ||||
0.395920 | + | 0.918285i | \(0.370426\pi\) | |||||||
\(314\) | 5.96374 | 0.336553 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.9115 | 1.23262 | ||||||||
\(317\) | 21.2836 | 1.19541 | 0.597704 | − | 0.801717i | \(-0.296080\pi\) | ||||
0.597704 | + | 0.801717i | \(0.296080\pi\) | |||||||
\(318\) | 4.68501 | 0.262722 | ||||||||
\(319\) | −14.1978 | −0.794926 | ||||||||
\(320\) | −2.36532 | −0.132225 | ||||||||
\(321\) | 17.9551 | 1.00215 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.06269 | 0.0591297 | ||||||||
\(324\) | −1.50350 | −0.0835280 | ||||||||
\(325\) | 6.30732 | 0.349867 | ||||||||
\(326\) | −6.13448 | −0.339758 | ||||||||
\(327\) | −1.29866 | −0.0718161 | ||||||||
\(328\) | 2.46865 | 0.136309 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.52105 | −0.248876 | ||||||||
\(331\) | 8.80304 | 0.483859 | 0.241930 | − | 0.970294i | \(-0.422220\pi\) | ||||
0.241930 | + | 0.970294i | \(0.422220\pi\) | |||||||
\(332\) | −9.64687 | −0.529441 | ||||||||
\(333\) | −2.36179 | −0.129425 | ||||||||
\(334\) | 4.99793 | 0.273475 | ||||||||
\(335\) | 20.2189 | 1.10467 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.7158 | 1.78214 | 0.891072 | − | 0.453863i | \(-0.149954\pi\) | ||||
0.891072 | + | 0.453863i | \(0.149954\pi\) | |||||||
\(338\) | 5.42492 | 0.295077 | ||||||||
\(339\) | 3.46493 | 0.188189 | ||||||||
\(340\) | −2.04746 | −0.111039 | ||||||||
\(341\) | −13.2048 | −0.715082 | ||||||||
\(342\) | 0.826721 | 0.0447040 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −19.3618 | −1.04392 | ||||||||
\(345\) | 1.34283 | 0.0722957 | ||||||||
\(346\) | −11.8398 | −0.636513 | ||||||||
\(347\) | 32.9033 | 1.76634 | 0.883171 | − | 0.469051i | \(-0.155404\pi\) | ||||
0.883171 | + | 0.469051i | \(0.155404\pi\) | |||||||
\(348\) | −5.00207 | −0.268139 | ||||||||
\(349\) | 32.5250 | 1.74102 | 0.870511 | − | 0.492149i | \(-0.163789\pi\) | ||||
0.870511 | + | 0.492149i | \(0.163789\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.30238 | −0.122892 | ||||||||
\(352\) | 24.8816 | 1.32620 | ||||||||
\(353\) | 7.58131 | 0.403513 | 0.201756 | − | 0.979436i | \(-0.435335\pi\) | ||||
0.201756 | + | 0.979436i | \(0.435335\pi\) | |||||||
\(354\) | −0.449698 | −0.0239012 | ||||||||
\(355\) | 0.368800 | 0.0195738 | ||||||||
\(356\) | −2.72358 | −0.144350 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.42210 | −0.180864 | ||||||||
\(359\) | 24.6482 | 1.30088 | 0.650440 | − | 0.759557i | \(-0.274584\pi\) | ||||
0.650440 | + | 0.759557i | \(0.274584\pi\) | |||||||
\(360\) | −3.71163 | −0.195620 | ||||||||
\(361\) | −17.6234 | −0.927548 | ||||||||
\(362\) | 4.18968 | 0.220205 | ||||||||
\(363\) | 7.21185 | 0.378524 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.13818 | −0.164260 | ||||||||
\(366\) | −6.93566 | −0.362533 | ||||||||
\(367\) | −21.6318 | −1.12917 | −0.564586 | − | 0.825374i | \(-0.690964\pi\) | ||||
−0.564586 | + | 0.825374i | \(0.690964\pi\) | |||||||
\(368\) | −1.13208 | −0.0590138 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −2.50209 | −0.130078 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.65223 | −0.241207 | ||||||||
\(373\) | −32.2405 | −1.66935 | −0.834676 | − | 0.550741i | \(-0.814345\pi\) | ||||
−0.834676 | + | 0.550741i | \(0.814345\pi\) | |||||||
\(374\) | −2.72358 | −0.140833 | ||||||||
\(375\) | 11.6363 | 0.600898 | ||||||||
\(376\) | 3.22325 | 0.166226 | ||||||||
\(377\) | −7.65990 | −0.394505 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8416 | 1.48149 | 0.740747 | − | 0.671784i | \(-0.234472\pi\) | ||||
0.740747 | + | 0.671784i | \(0.234472\pi\) | |||||||
\(380\) | −2.65223 | −0.136056 | ||||||||
\(381\) | 11.1398 | 0.570711 | ||||||||
\(382\) | 9.92490 | 0.507802 | ||||||||
\(383\) | −31.1691 | −1.59267 | −0.796333 | − | 0.604858i | \(-0.793230\pi\) | ||||
−0.796333 | + | 0.604858i | \(0.793230\pi\) | |||||||
\(384\) | 10.5524 | 0.538498 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.80613 | −0.346423 | ||||||||
\(387\) | −7.84305 | −0.398685 | ||||||||
\(388\) | −9.46330 | −0.480426 | ||||||||
\(389\) | 0.0362595 | 0.00183843 | 0.000919215 | − | 1.00000i | \(-0.499707\pi\) | ||||
0.000919215 | 1.00000i | \(0.499707\pi\) | ||||||||
\(390\) | −2.43916 | −0.123512 | ||||||||
\(391\) | 0.808953 | 0.0409105 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.43850 | −0.223893 | ||||||||
\(394\) | 0.803158 | 0.0404625 | ||||||||
\(395\) | 21.9115 | 1.10249 | ||||||||
\(396\) | 6.41626 | 0.322429 | ||||||||
\(397\) | 34.1952 | 1.71621 | 0.858104 | − | 0.513477i | \(-0.171643\pi\) | ||||
0.858104 | + | 0.513477i | \(0.171643\pi\) | |||||||
\(398\) | 4.79868 | 0.240536 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47238 | −0.173619 | ||||||||
\(401\) | 20.3606 | 1.01676 | 0.508379 | − | 0.861133i | \(-0.330245\pi\) | ||||
0.508379 | + | 0.861133i | \(0.330245\pi\) | |||||||
\(402\) | 9.47566 | 0.472603 | ||||||||
\(403\) | −7.12417 | −0.354880 | ||||||||
\(404\) | 15.4584 | 0.769082 | ||||||||
\(405\) | −1.50350 | −0.0747097 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0790 | 0.499599 | ||||||||
\(408\) | −2.23597 | −0.110697 | ||||||||
\(409\) | −10.5257 | −0.520465 | −0.260232 | − | 0.965546i | \(-0.583799\pi\) | ||||
−0.260232 | + | 0.965546i | \(0.583799\pi\) | |||||||
\(410\) | 1.05941 | 0.0523203 | ||||||||
\(411\) | 10.7362 | 0.529577 | ||||||||
\(412\) | −13.0611 | −0.643472 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.629325 | 0.0309297 | ||||||||
\(415\) | −9.64687 | −0.473546 | ||||||||
\(416\) | 13.4239 | 0.658162 | ||||||||
\(417\) | 12.1836 | 0.596632 | ||||||||
\(418\) | −3.52806 | −0.172563 | ||||||||
\(419\) | 27.5895 | 1.34784 | 0.673919 | − | 0.738806i | \(-0.264610\pi\) | ||||
0.673919 | + | 0.738806i | \(0.264610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.0924 | 1.61282 | 0.806412 | − | 0.591354i | \(-0.201406\pi\) | ||||
0.806412 | + | 0.591354i | \(0.201406\pi\) | |||||||
\(422\) | −2.43405 | −0.118488 | ||||||||
\(423\) | 1.30567 | 0.0634838 | ||||||||
\(424\) | −16.4139 | −0.797132 | ||||||||
\(425\) | 2.48126 | 0.120359 | ||||||||
\(426\) | 0.172840 | 0.00837411 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.9955 | −1.30488 | ||||||||
\(429\) | 9.82551 | 0.474380 | ||||||||
\(430\) | −8.30898 | −0.400694 | ||||||||
\(431\) | −4.91044 | −0.236528 | −0.118264 | − | 0.992982i | \(-0.537733\pi\) | ||||
−0.118264 | + | 0.992982i | \(0.537733\pi\) | |||||||
\(432\) | 1.26753 | 0.0609843 | ||||||||
\(433\) | −12.2511 | −0.588750 | −0.294375 | − | 0.955690i | \(-0.595111\pi\) | ||||
−0.294375 | + | 0.955690i | \(0.595111\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.00207 | −0.239831 | ||||||||
\(436\) | 1.95254 | 0.0935098 | ||||||||
\(437\) | 1.04790 | 0.0501277 | ||||||||
\(438\) | −1.47072 | −0.0702740 | ||||||||
\(439\) | −15.5133 | −0.740408 | −0.370204 | − | 0.928951i | \(-0.620712\pi\) | ||||
−0.370204 | + | 0.928951i | \(0.620712\pi\) | |||||||
\(440\) | 15.8395 | 0.755120 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.46940 | −0.0698924 | ||||||||
\(443\) | −18.4525 | −0.876706 | −0.438353 | − | 0.898803i | \(-0.644438\pi\) | ||||
−0.438353 | + | 0.898803i | \(0.644438\pi\) | |||||||
\(444\) | 3.55096 | 0.168521 | ||||||||
\(445\) | −2.72358 | −0.129110 | ||||||||
\(446\) | 2.12229 | 0.100493 | ||||||||
\(447\) | 6.11716 | 0.289332 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.5643 | −0.640140 | −0.320070 | − | 0.947394i | \(-0.603706\pi\) | ||||
−0.320070 | + | 0.947394i | \(0.603706\pi\) | |||||||
\(450\) | 1.93030 | 0.0909952 | ||||||||
\(451\) | −4.26753 | −0.200950 | ||||||||
\(452\) | −5.20954 | −0.245036 | ||||||||
\(453\) | −8.41626 | −0.395430 | ||||||||
\(454\) | 9.90837 | 0.465023 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.89642 | −0.135637 | ||||||||
\(457\) | −7.62298 | −0.356588 | −0.178294 | − | 0.983977i | \(-0.557058\pi\) | ||||
−0.178294 | + | 0.983977i | \(0.557058\pi\) | |||||||
\(458\) | −0.760990 | −0.0355587 | ||||||||
\(459\) | −0.905744 | −0.0422765 | ||||||||
\(460\) | −2.01896 | −0.0941343 | ||||||||
\(461\) | 10.5533 | 0.491518 | 0.245759 | − | 0.969331i | \(-0.420963\pi\) | ||||
0.245759 | + | 0.969331i | \(0.420963\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.4384 | −1.04280 | −0.521400 | − | 0.853312i | \(-0.674590\pi\) | ||||
−0.521400 | + | 0.853312i | \(0.674590\pi\) | |||||||
\(464\) | 4.21701 | 0.195770 | ||||||||
\(465\) | −4.65223 | −0.215742 | ||||||||
\(466\) | −3.91088 | −0.181168 | ||||||||
\(467\) | 25.3453 | 1.17284 | 0.586421 | − | 0.810006i | \(-0.300536\pi\) | ||||
0.586421 | + | 0.810006i | \(0.300536\pi\) | |||||||
\(468\) | 3.46165 | 0.160015 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.38323 | 0.0638038 | ||||||||
\(471\) | −8.46372 | −0.389987 | ||||||||
\(472\) | 1.57552 | 0.0725191 | ||||||||
\(473\) | 33.4705 | 1.53898 | ||||||||
\(474\) | 10.2689 | 0.471668 | ||||||||
\(475\) | 3.21417 | 0.147476 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.64894 | −0.304434 | ||||||||
\(478\) | 1.02760 | 0.0470012 | ||||||||
\(479\) | 37.6491 | 1.72023 | 0.860117 | − | 0.510098i | \(-0.170391\pi\) | ||||
0.860117 | + | 0.510098i | \(0.170391\pi\) | |||||||
\(480\) | 8.76610 | 0.400116 | ||||||||
\(481\) | 5.43775 | 0.247940 | ||||||||
\(482\) | 1.18613 | 0.0540268 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8431 | −0.492866 | ||||||||
\(485\) | −9.46330 | −0.429706 | ||||||||
\(486\) | −0.704624 | −0.0319624 | ||||||||
\(487\) | 7.52337 | 0.340916 | 0.170458 | − | 0.985365i | \(-0.445475\pi\) | ||||
0.170458 | + | 0.985365i | \(0.445475\pi\) | |||||||
\(488\) | 24.2991 | 1.09997 | ||||||||
\(489\) | 8.70603 | 0.393700 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8758 | 0.896982 | 0.448491 | − | 0.893787i | \(-0.351962\pi\) | ||||
0.448491 | + | 0.893787i | \(0.351962\pi\) | |||||||
\(492\) | −1.50350 | −0.0677832 | ||||||||
\(493\) | −3.01336 | −0.135715 | ||||||||
\(494\) | −1.90343 | −0.0856394 | ||||||||
\(495\) | 6.41626 | 0.288389 | ||||||||
\(496\) | 3.92208 | 0.176106 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.52105 | −0.202593 | ||||||||
\(499\) | −37.6127 | −1.68377 | −0.841887 | − | 0.539654i | \(-0.818555\pi\) | ||||
−0.841887 | + | 0.539654i | \(0.818555\pi\) | |||||||
\(500\) | −17.4953 | −0.782413 | ||||||||
\(501\) | −7.09304 | −0.316894 | ||||||||
\(502\) | −13.3091 | −0.594013 | ||||||||
\(503\) | 15.2628 | 0.680536 | 0.340268 | − | 0.940328i | \(-0.389482\pi\) | ||||
0.340268 | + | 0.940328i | \(0.389482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.4584 | 0.687888 | ||||||||
\(506\) | −2.68567 | −0.119392 | ||||||||
\(507\) | −7.69903 | −0.341926 | ||||||||
\(508\) | −16.7488 | −0.743108 | ||||||||
\(509\) | −11.1269 | −0.493192 | −0.246596 | − | 0.969118i | \(-0.579312\pi\) | ||||
−0.246596 | + | 0.969118i | \(0.579312\pi\) | |||||||
\(510\) | −0.959551 | −0.0424896 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13.6485 | −0.603184 | ||||||||
\(513\) | −1.17328 | −0.0518015 | ||||||||
\(514\) | 10.6959 | 0.471777 | ||||||||
\(515\) | −13.0611 | −0.575539 | ||||||||
\(516\) | 11.7921 | 0.519117 | ||||||||
\(517\) | −5.57199 | −0.245056 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.8030 | 0.737572 | ||||||||
\(520\) | 8.54561 | 0.374750 | ||||||||
\(521\) | 17.0795 | 0.748265 | 0.374132 | − | 0.927375i | \(-0.377941\pi\) | ||||
0.374132 | + | 0.927375i | \(0.377941\pi\) | |||||||
\(522\) | −2.34424 | −0.102605 | ||||||||
\(523\) | 23.7322 | 1.03774 | 0.518869 | − | 0.854854i | \(-0.326353\pi\) | ||||
0.518869 | + | 0.854854i | \(0.326353\pi\) | |||||||
\(524\) | 6.67330 | 0.291525 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.38121 | 0.0602237 | ||||||||
\(527\) | −2.80260 | −0.122083 | ||||||||
\(528\) | −5.40925 | −0.235407 | ||||||||
\(529\) | −22.2023 | −0.965318 | ||||||||
\(530\) | −7.04393 | −0.305969 | ||||||||
\(531\) | 0.638209 | 0.0276959 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.30238 | −0.0997273 | ||||||||
\(534\) | −1.27642 | −0.0552360 | ||||||||
\(535\) | −26.9955 | −1.16712 | ||||||||
\(536\) | −33.1980 | −1.43394 | ||||||||
\(537\) | 4.85663 | 0.209579 | ||||||||
\(538\) | −21.4749 | −0.925848 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.26053 | 0.0972775 | ||||||||
\(541\) | −27.4226 | −1.17899 | −0.589495 | − | 0.807772i | \(-0.700673\pi\) | ||||
−0.589495 | + | 0.807772i | \(0.700673\pi\) | |||||||
\(542\) | 4.11947 | 0.176946 | ||||||||
\(543\) | −5.94597 | −0.255166 | ||||||||
\(544\) | 5.28089 | 0.226416 | ||||||||
\(545\) | 1.95254 | 0.0836377 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2333 | −0.907871 | −0.453936 | − | 0.891034i | \(-0.649980\pi\) | ||||
−0.453936 | + | 0.891034i | \(0.649980\pi\) | |||||||
\(548\) | −16.1419 | −0.689548 | ||||||||
\(549\) | 9.84305 | 0.420091 | ||||||||
\(550\) | −8.23762 | −0.351253 | ||||||||
\(551\) | −3.90343 | −0.166292 | ||||||||
\(552\) | −2.20484 | −0.0938444 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.01438 | −0.213040 | ||||||||
\(555\) | 3.55096 | 0.150730 | ||||||||
\(556\) | −18.3181 | −0.776859 | ||||||||
\(557\) | 26.6920 | 1.13098 | 0.565489 | − | 0.824756i | \(-0.308688\pi\) | ||||
0.565489 | + | 0.824756i | \(0.308688\pi\) | |||||||
\(558\) | −2.18029 | −0.0922990 | ||||||||
\(559\) | 18.0577 | 0.763760 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.86530 | 0.163193 | ||||||||
\(562\) | 3.15413 | 0.133049 | ||||||||
\(563\) | −5.72358 | −0.241220 | −0.120610 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120610 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(564\) | −1.96308 | −0.0826606 | ||||||||
\(565\) | −5.20954 | −0.219167 | ||||||||
\(566\) | 0.476022 | 0.0200087 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.605544 | −0.0254081 | ||||||||
\(569\) | 33.3248 | 1.39705 | 0.698523 | − | 0.715587i | \(-0.253841\pi\) | ||||
0.698523 | + | 0.715587i | \(0.253841\pi\) | |||||||
\(570\) | −1.24298 | −0.0520626 | ||||||||
\(571\) | 8.54252 | 0.357493 | 0.178747 | − | 0.983895i | \(-0.442796\pi\) | ||||
0.178747 | + | 0.983895i | \(0.442796\pi\) | |||||||
\(572\) | −14.7727 | −0.617677 | ||||||||
\(573\) | −14.0854 | −0.588425 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.44672 | 0.102035 | ||||||||
\(576\) | 1.57320 | 0.0655502 | ||||||||
\(577\) | −6.13581 | −0.255437 | −0.127718 | − | 0.991810i | \(-0.540765\pi\) | ||||
−0.127718 | + | 0.991810i | \(0.540765\pi\) | |||||||
\(578\) | 11.4006 | 0.474201 | ||||||||
\(579\) | 9.65924 | 0.401424 | ||||||||
\(580\) | 7.52064 | 0.312277 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.43502 | −0.183837 | ||||||||
\(583\) | 28.3746 | 1.17516 | ||||||||
\(584\) | 5.15269 | 0.213220 | ||||||||
\(585\) | 3.46165 | 0.143121 | ||||||||
\(586\) | −1.82302 | −0.0753083 | ||||||||
\(587\) | −39.5794 | −1.63362 | −0.816809 | − | 0.576908i | \(-0.804259\pi\) | ||||
−0.816809 | + | 0.576908i | \(0.804259\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.63043 | −0.149589 | ||||||||
\(590\) | 0.676123 | 0.0278355 | ||||||||
\(591\) | −1.13984 | −0.0468867 | ||||||||
\(592\) | −2.99365 | −0.123038 | ||||||||
\(593\) | −15.4883 | −0.636027 | −0.318014 | − | 0.948086i | \(-0.603016\pi\) | ||||
−0.318014 | + | 0.948086i | \(0.603016\pi\) | |||||||
\(594\) | 3.00701 | 0.123379 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.19717 | −0.376731 | ||||||||
\(597\) | −6.81027 | −0.278726 | ||||||||
\(598\) | −1.44895 | −0.0592519 | ||||||||
\(599\) | 4.22806 | 0.172754 | 0.0863768 | − | 0.996263i | \(-0.472471\pi\) | ||||
0.0863768 | + | 0.996263i | \(0.472471\pi\) | |||||||
\(600\) | −6.76282 | −0.276091 | ||||||||
\(601\) | −35.7858 | −1.45973 | −0.729867 | − | 0.683589i | \(-0.760418\pi\) | ||||
−0.729867 | + | 0.683589i | \(0.760418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.4478 | −0.547638 | ||||||||
\(604\) | 12.6539 | 0.514879 | ||||||||
\(605\) | −10.8431 | −0.440833 | ||||||||
\(606\) | 7.24463 | 0.294293 | ||||||||
\(607\) | 3.30743 | 0.134244 | 0.0671222 | − | 0.997745i | \(-0.478618\pi\) | ||||
0.0671222 | + | 0.997745i | \(0.478618\pi\) | |||||||
\(608\) | 6.84074 | 0.277429 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.4278 | 0.422209 | ||||||||
\(611\) | −3.00615 | −0.121616 | ||||||||
\(612\) | 1.36179 | 0.0550471 | ||||||||
\(613\) | 21.8254 | 0.881519 | 0.440760 | − | 0.897625i | \(-0.354709\pi\) | ||||
0.440760 | + | 0.897625i | \(0.354709\pi\) | |||||||
\(614\) | −19.0341 | −0.768152 | ||||||||
\(615\) | −1.50350 | −0.0606272 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.3792 | 1.46457 | 0.732286 | − | 0.680997i | \(-0.238453\pi\) | ||||
0.732286 | + | 0.680997i | \(0.238453\pi\) | |||||||
\(618\) | −6.12113 | −0.246228 | ||||||||
\(619\) | 33.3671 | 1.34114 | 0.670568 | − | 0.741848i | \(-0.266051\pi\) | ||||
0.670568 | + | 0.741848i | \(0.266051\pi\) | |||||||
\(620\) | 6.99464 | 0.280912 | ||||||||
\(621\) | −0.893136 | −0.0358403 | ||||||||
\(622\) | −20.9154 | −0.838630 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.91835 | −0.116828 | ||||||||
\(625\) | −3.79791 | −0.151916 | ||||||||
\(626\) | −9.87114 | −0.394530 | ||||||||
\(627\) | 5.00701 | 0.199961 | ||||||||
\(628\) | 12.7252 | 0.507792 | ||||||||
\(629\) | 2.13918 | 0.0852946 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8563 | 1.42742 | 0.713708 | − | 0.700443i | \(-0.247014\pi\) | ||||
0.713708 | + | 0.700443i | \(0.247014\pi\) | |||||||
\(632\) | −35.9773 | −1.43110 | ||||||||
\(633\) | 3.45439 | 0.137300 | ||||||||
\(634\) | −14.9970 | −0.595605 | ||||||||
\(635\) | −16.7488 | −0.664656 | ||||||||
\(636\) | 9.99672 | 0.396396 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.0041 | 0.396068 | ||||||||
\(639\) | −0.245293 | −0.00970365 | ||||||||
\(640\) | −15.8655 | −0.627141 | ||||||||
\(641\) | 29.4974 | 1.16508 | 0.582538 | − | 0.812803i | \(-0.302060\pi\) | ||||
0.582538 | + | 0.812803i | \(0.302060\pi\) | |||||||
\(642\) | −12.6516 | −0.499318 | ||||||||
\(643\) | −39.6993 | −1.56559 | −0.782795 | − | 0.622280i | \(-0.786207\pi\) | ||||
−0.782795 | + | 0.622280i | \(0.786207\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.7921 | 0.464312 | ||||||||
\(646\) | −0.748798 | −0.0294611 | ||||||||
\(647\) | −28.2158 | −1.10928 | −0.554638 | − | 0.832092i | \(-0.687143\pi\) | ||||
−0.554638 | + | 0.832092i | \(0.687143\pi\) | |||||||
\(648\) | 2.46865 | 0.0969779 | ||||||||
\(649\) | −2.72358 | −0.106910 | ||||||||
\(650\) | −4.44429 | −0.174320 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.0896 | −0.512627 | ||||||||
\(653\) | 23.1901 | 0.907497 | 0.453748 | − | 0.891130i | \(-0.350086\pi\) | ||||
0.453748 | + | 0.891130i | \(0.350086\pi\) | |||||||
\(654\) | 0.915068 | 0.0357820 | ||||||||
\(655\) | 6.67330 | 0.260748 | ||||||||
\(656\) | 1.26753 | 0.0494889 | ||||||||
\(657\) | 2.08725 | 0.0814313 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5515 | −0.566847 | −0.283423 | − | 0.958995i | \(-0.591470\pi\) | ||||
−0.283423 | + | 0.958995i | \(0.591470\pi\) | |||||||
\(660\) | −9.64687 | −0.375504 | ||||||||
\(661\) | 26.5326 | 1.03200 | 0.516000 | − | 0.856589i | \(-0.327420\pi\) | ||||
0.516000 | + | 0.856589i | \(0.327420\pi\) | |||||||
\(662\) | −6.20284 | −0.241080 | ||||||||
\(663\) | 2.08537 | 0.0809891 | ||||||||
\(664\) | 15.8395 | 0.614693 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.66418 | 0.0644855 | ||||||||
\(667\) | −2.97141 | −0.115053 | ||||||||
\(668\) | 10.6644 | 0.412619 | ||||||||
\(669\) | −3.01195 | −0.116449 | ||||||||
\(670\) | −14.2467 | −0.550398 | ||||||||
\(671\) | −42.0056 | −1.62161 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.9600 | −0.692307 | −0.346153 | − | 0.938178i | \(-0.612512\pi\) | ||||
−0.346153 | + | 0.938178i | \(0.612512\pi\) | |||||||
\(674\) | −23.0523 | −0.887943 | ||||||||
\(675\) | −2.73947 | −0.105442 | ||||||||
\(676\) | 11.5755 | 0.445212 | ||||||||
\(677\) | 7.79090 | 0.299429 | 0.149714 | − | 0.988729i | \(-0.452165\pi\) | ||||
0.149714 | + | 0.988729i | \(0.452165\pi\) | |||||||
\(678\) | −2.44147 | −0.0937643 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.36179 | 0.128919 | ||||||||
\(681\) | −14.0619 | −0.538854 | ||||||||
\(682\) | 9.30445 | 0.356286 | ||||||||
\(683\) | −4.27880 | −0.163724 | −0.0818618 | − | 0.996644i | \(-0.526087\pi\) | ||||
−0.0818618 | + | 0.996644i | \(0.526087\pi\) | |||||||
\(684\) | 1.76403 | 0.0674494 | ||||||||
\(685\) | −16.1419 | −0.616751 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.07999 | 0.0412043 | ||||||||
\(688\) | −9.94134 | −0.379010 | ||||||||
\(689\) | 15.3084 | 0.583204 | ||||||||
\(690\) | −0.946193 | −0.0360210 | ||||||||
\(691\) | 23.8218 | 0.906222 | 0.453111 | − | 0.891454i | \(-0.350314\pi\) | ||||
0.453111 | + | 0.891454i | \(0.350314\pi\) | |||||||
\(692\) | −25.2635 | −0.960372 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.1845 | −0.880071 | ||||||||
\(695\) | −18.3181 | −0.694843 | ||||||||
\(696\) | 8.21307 | 0.311316 | ||||||||
\(697\) | −0.905744 | −0.0343075 | ||||||||
\(698\) | −22.9179 | −0.867455 | ||||||||
\(699\) | 5.55030 | 0.209932 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.77225 | 0.369093 | 0.184546 | − | 0.982824i | \(-0.440918\pi\) | ||||
0.184546 | + | 0.982824i | \(0.440918\pi\) | |||||||
\(702\) | 1.62232 | 0.0612304 | ||||||||
\(703\) | 2.77104 | 0.104512 | ||||||||
\(704\) | −6.71370 | −0.253032 | ||||||||
\(705\) | −1.96308 | −0.0739339 | ||||||||
\(706\) | −5.34198 | −0.201048 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.959551 | −0.0360621 | ||||||||
\(709\) | −7.96953 | −0.299302 | −0.149651 | − | 0.988739i | \(-0.547815\pi\) | ||||
−0.149651 | + | 0.988739i | \(0.547815\pi\) | |||||||
\(710\) | −0.259865 | −0.00975256 | ||||||||
\(711\) | −14.5736 | −0.546554 | ||||||||
\(712\) | 4.47194 | 0.167593 | ||||||||
\(713\) | −2.76359 | −0.103497 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.7727 | −0.552467 | ||||||||
\(716\) | −7.30197 | −0.272887 | ||||||||
\(717\) | −1.45836 | −0.0544635 | ||||||||
\(718\) | −17.3677 | −0.648157 | ||||||||
\(719\) | −3.66691 | −0.136753 | −0.0683763 | − | 0.997660i | \(-0.521782\pi\) | ||||
−0.0683763 | + | 0.997660i | \(0.521782\pi\) | |||||||
\(720\) | −1.90574 | −0.0710229 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.4179 | 0.462146 | ||||||||
\(723\) | −1.68335 | −0.0626046 | ||||||||
\(724\) | 8.93980 | 0.332245 | ||||||||
\(725\) | −9.11407 | −0.338488 | ||||||||
\(726\) | −5.08165 | −0.188598 | ||||||||
\(727\) | −40.3400 | −1.49613 | −0.748064 | − | 0.663627i | \(-0.769016\pi\) | ||||
−0.748064 | + | 0.663627i | \(0.769016\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.21124 | 0.0818417 | ||||||||
\(731\) | 7.10380 | 0.262744 | ||||||||
\(732\) | −14.7991 | −0.546990 | ||||||||
\(733\) | −35.1684 | −1.29898 | −0.649488 | − | 0.760372i | \(-0.725017\pi\) | ||||
−0.649488 | + | 0.760372i | \(0.725017\pi\) | |||||||
\(734\) | 15.2423 | 0.562604 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.20738 | 0.191947 | ||||||||
\(737\) | 57.3891 | 2.11395 | ||||||||
\(738\) | −0.704624 | −0.0259376 | ||||||||
\(739\) | 1.71767 | 0.0631856 | 0.0315928 | − | 0.999501i | \(-0.489942\pi\) | ||||
0.0315928 | + | 0.999501i | \(0.489942\pi\) | |||||||
\(740\) | −5.33889 | −0.196261 | ||||||||
\(741\) | 2.70134 | 0.0992362 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.4571 | −0.750500 | −0.375250 | − | 0.926924i | \(-0.622443\pi\) | ||||
−0.375250 | + | 0.926924i | \(0.622443\pi\) | |||||||
\(744\) | 7.63865 | 0.280046 | ||||||||
\(745\) | −9.19717 | −0.336958 | ||||||||
\(746\) | 22.7175 | 0.831746 | ||||||||
\(747\) | 6.41626 | 0.234759 | ||||||||
\(748\) | −5.81149 | −0.212489 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.19924 | −0.299394 | ||||||||
\(751\) | 20.4502 | 0.746238 | 0.373119 | − | 0.927783i | \(-0.378288\pi\) | ||||
0.373119 | + | 0.927783i | \(0.378288\pi\) | |||||||
\(752\) | 1.65498 | 0.0603510 | ||||||||
\(753\) | 18.8882 | 0.688324 | ||||||||
\(754\) | 5.39735 | 0.196560 | ||||||||
\(755\) | 12.6539 | 0.460522 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4022 | 1.03230 | 0.516148 | − | 0.856499i | \(-0.327365\pi\) | ||||
0.516148 | + | 0.856499i | \(0.327365\pi\) | |||||||
\(758\) | −20.3225 | −0.738147 | ||||||||
\(759\) | 3.81149 | 0.138348 | ||||||||
\(760\) | 4.35478 | 0.157965 | ||||||||
\(761\) | 10.0943 | 0.365916 | 0.182958 | − | 0.983121i | \(-0.441433\pi\) | ||||
0.182958 | + | 0.983121i | \(0.441433\pi\) | |||||||
\(762\) | −7.84940 | −0.284354 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.1774 | 0.766172 | ||||||||
\(765\) | 1.36179 | 0.0492356 | ||||||||
\(766\) | 21.9625 | 0.793537 | ||||||||
\(767\) | −1.46940 | −0.0530571 | ||||||||
\(768\) | −10.5819 | −0.381840 | ||||||||
\(769\) | −39.5682 | −1.42687 | −0.713434 | − | 0.700723i | \(-0.752861\pi\) | ||||
−0.713434 | + | 0.700723i | \(0.752861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.1796 | −0.546681 | ||||||||
\(772\) | −14.5227 | −0.522684 | ||||||||
\(773\) | −13.6450 | −0.490776 | −0.245388 | − | 0.969425i | \(-0.578915\pi\) | ||||
−0.245388 | + | 0.969425i | \(0.578915\pi\) | |||||||
\(774\) | 5.52641 | 0.198643 | ||||||||
\(775\) | −8.47663 | −0.304490 | ||||||||
\(776\) | 15.5381 | 0.557786 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.0255493 | −0.000915988 0 | ||||||||
\(779\) | −1.17328 | −0.0420371 | ||||||||
\(780\) | −5.20460 | −0.186355 | ||||||||
\(781\) | 1.04680 | 0.0374574 | ||||||||
\(782\) | −0.570008 | −0.0203834 | ||||||||
\(783\) | 3.32694 | 0.118895 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.7252 | 0.454183 | ||||||||
\(786\) | 3.12747 | 0.111553 | ||||||||
\(787\) | −6.72052 | −0.239561 | −0.119780 | − | 0.992800i | \(-0.538219\pi\) | ||||
−0.119780 | + | 0.992800i | \(0.538219\pi\) | |||||||
\(788\) | 1.71375 | 0.0610499 | ||||||||
\(789\) | −1.96021 | −0.0697854 | ||||||||
\(790\) | −15.4394 | −0.549309 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.5351 | −0.374347 | ||||||||
\(793\) | −22.6625 | −0.804769 | ||||||||
\(794\) | −24.0948 | −0.855091 | ||||||||
\(795\) | 9.99672 | 0.354547 | ||||||||
\(796\) | 10.2393 | 0.362922 | ||||||||
\(797\) | −1.63942 | −0.0580714 | −0.0290357 | − | 0.999578i | \(-0.509244\pi\) | ||||
−0.0290357 | + | 0.999578i | \(0.509244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.18260 | −0.0418375 | ||||||||
\(800\) | 15.9724 | 0.564708 | ||||||||
\(801\) | 1.81149 | 0.0640058 | ||||||||
\(802\) | −14.3466 | −0.506595 | ||||||||
\(803\) | −8.90740 | −0.314335 | ||||||||
\(804\) | 20.2189 | 0.713064 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.01986 | 0.176817 | ||||||||
\(807\) | 30.4771 | 1.07284 | ||||||||
\(808\) | −25.3816 | −0.892922 | ||||||||
\(809\) | −28.1798 | −0.990750 | −0.495375 | − | 0.868679i | \(-0.664969\pi\) | ||||
−0.495375 | + | 0.868679i | \(0.664969\pi\) | |||||||
\(810\) | 1.05941 | 0.0372237 | ||||||||
\(811\) | −22.2848 | −0.782526 | −0.391263 | − | 0.920279i | \(-0.627962\pi\) | ||||
−0.391263 | + | 0.920279i | \(0.627962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.84634 | −0.205040 | ||||||||
\(814\) | −7.10193 | −0.248922 | ||||||||
\(815\) | −13.0896 | −0.458507 | ||||||||
\(816\) | −1.14806 | −0.0401902 | ||||||||
\(817\) | 9.20209 | 0.321940 | ||||||||
\(818\) | 7.41670 | 0.259319 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.26053 | 0.0789410 | ||||||||
\(821\) | −29.0974 | −1.01551 | −0.507753 | − | 0.861503i | \(-0.669524\pi\) | ||||
−0.507753 | + | 0.861503i | \(0.669524\pi\) | |||||||
\(822\) | −7.56498 | −0.263859 | ||||||||
\(823\) | −28.7398 | −1.00181 | −0.500903 | − | 0.865503i | \(-0.666999\pi\) | ||||
−0.500903 | + | 0.865503i | \(0.666999\pi\) | |||||||
\(824\) | 21.4454 | 0.747086 | ||||||||
\(825\) | 11.6908 | 0.407021 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.5448 | 1.34033 | 0.670167 | − | 0.742211i | \(-0.266223\pi\) | ||||
0.670167 | + | 0.742211i | \(0.266223\pi\) | |||||||
\(828\) | 1.34283 | 0.0466667 | ||||||||
\(829\) | −42.9541 | −1.49186 | −0.745928 | − | 0.666026i | \(-0.767994\pi\) | ||||
−0.745928 | + | 0.666026i | \(0.767994\pi\) | |||||||
\(830\) | 6.79742 | 0.235942 | ||||||||
\(831\) | 7.11638 | 0.246865 | ||||||||
\(832\) | −3.62212 | −0.125574 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.58484 | −0.297269 | ||||||||
\(835\) | 10.6644 | 0.369057 | ||||||||
\(836\) | −7.52806 | −0.260363 | ||||||||
\(837\) | 3.09426 | 0.106953 | ||||||||
\(838\) | −19.4403 | −0.671553 | ||||||||
\(839\) | −12.5023 | −0.431627 | −0.215813 | − | 0.976435i | \(-0.569240\pi\) | ||||
−0.215813 | + | 0.976435i | \(0.569240\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9315 | −0.618326 | ||||||||
\(842\) | −23.3177 | −0.803581 | ||||||||
\(843\) | −4.47632 | −0.154173 | ||||||||
\(844\) | −5.19369 | −0.178774 | ||||||||
\(845\) | 11.5755 | 0.398210 | ||||||||
\(846\) | −0.920006 | −0.0316305 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.42777 | −0.289411 | ||||||||
\(849\) | −0.675569 | −0.0231855 | ||||||||
\(850\) | −1.74836 | −0.0599682 | ||||||||
\(851\) | 2.10940 | 0.0723093 | ||||||||
\(852\) | 0.368800 | 0.0126349 | ||||||||
\(853\) | −0.740028 | −0.0253381 | −0.0126690 | − | 0.999920i | \(-0.504033\pi\) | ||||
−0.0126690 | + | 0.999920i | \(0.504033\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.76403 | 0.0603286 | ||||||||
\(856\) | 44.3248 | 1.51499 | ||||||||
\(857\) | 55.2205 | 1.88630 | 0.943148 | − | 0.332374i | \(-0.107850\pi\) | ||||
0.943148 | + | 0.332374i | \(0.107850\pi\) | |||||||
\(858\) | −6.92329 | −0.236357 | ||||||||
\(859\) | −48.3612 | −1.65006 | −0.825032 | − | 0.565087i | \(-0.808843\pi\) | ||||
−0.825032 | + | 0.565087i | \(0.808843\pi\) | |||||||
\(860\) | −17.7294 | −0.604568 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.46001 | 0.117849 | ||||||||
\(863\) | −34.7431 | −1.18267 | −0.591334 | − | 0.806427i | \(-0.701399\pi\) | ||||
−0.591334 | + | 0.806427i | \(0.701399\pi\) | |||||||
\(864\) | −5.83045 | −0.198356 | ||||||||
\(865\) | −25.2635 | −0.858983 | ||||||||
\(866\) | 8.63241 | 0.293341 | ||||||||
\(867\) | −16.1796 | −0.549489 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 62.1935 | 2.10977 | ||||||||
\(870\) | 3.52458 | 0.119494 | ||||||||
\(871\) | 30.9621 | 1.04911 | ||||||||
\(872\) | −3.20594 | −0.108567 | ||||||||
\(873\) | 6.29416 | 0.213025 | ||||||||
\(874\) | −0.738374 | −0.0249759 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.13818 | −0.106029 | ||||||||
\(877\) | −32.5538 | −1.09926 | −0.549632 | − | 0.835407i | \(-0.685232\pi\) | ||||
−0.549632 | + | 0.835407i | \(0.685232\pi\) | |||||||
\(878\) | 10.9310 | 0.368904 | ||||||||
\(879\) | 2.58722 | 0.0872648 | ||||||||
\(880\) | 8.13283 | 0.274158 | ||||||||
\(881\) | −3.54142 | −0.119313 | −0.0596567 | − | 0.998219i | \(-0.519001\pi\) | ||||
−0.0596567 | + | 0.998219i | \(0.519001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.3909 | 1.15735 | 0.578673 | − | 0.815559i | \(-0.303571\pi\) | ||||
0.578673 | + | 0.815559i | \(0.303571\pi\) | |||||||
\(884\) | −3.13537 | −0.105454 | ||||||||
\(885\) | −0.959551 | −0.0322549 | ||||||||
\(886\) | 13.0021 | 0.436814 | ||||||||
\(887\) | −10.8911 | −0.365686 | −0.182843 | − | 0.983142i | \(-0.558530\pi\) | ||||
−0.182843 | + | 0.983142i | \(0.558530\pi\) | |||||||
\(888\) | −5.83045 | −0.195657 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.91910 | 0.0643284 | ||||||||
\(891\) | −4.26753 | −0.142968 | ||||||||
\(892\) | 4.52848 | 0.151625 | ||||||||
\(893\) | −1.53191 | −0.0512636 | ||||||||
\(894\) | −4.31030 | −0.144158 | ||||||||
\(895\) | −7.30197 | −0.244078 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.05634 | 0.0686593 | ||||||||
\(898\) | 9.55775 | 0.318946 | ||||||||
\(899\) | 10.2944 | 0.343338 | ||||||||
\(900\) | 4.11881 | 0.137294 | ||||||||
\(901\) | 6.02224 | 0.200630 | ||||||||
\(902\) | 3.00701 | 0.100122 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.55372 | 0.284492 | ||||||||
\(905\) | 8.93980 | 0.297169 | ||||||||
\(906\) | 5.93030 | 0.197021 | ||||||||
\(907\) | −32.4770 | −1.07838 | −0.539190 | − | 0.842184i | \(-0.681269\pi\) | ||||
−0.539190 | + | 0.842184i | \(0.681269\pi\) | |||||||
\(908\) | 21.1422 | 0.701627 | ||||||||
\(909\) | −10.2816 | −0.341018 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4670 | 0.479314 | 0.239657 | − | 0.970858i | \(-0.422965\pi\) | ||||
0.239657 | + | 0.970858i | \(0.422965\pi\) | |||||||
\(912\) | −1.48717 | −0.0492452 | ||||||||
\(913\) | −27.3816 | −0.906199 | ||||||||
\(914\) | 5.37134 | 0.177668 | ||||||||
\(915\) | −14.7991 | −0.489242 | ||||||||
\(916\) | −1.62378 | −0.0536510 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.638209 | 0.0210641 | ||||||||
\(919\) | −21.8298 | −0.720097 | −0.360049 | − | 0.932934i | \(-0.617240\pi\) | ||||
−0.360049 | + | 0.932934i | \(0.617240\pi\) | |||||||
\(920\) | 3.31499 | 0.109292 | ||||||||
\(921\) | 27.0130 | 0.890110 | ||||||||
\(922\) | −7.43614 | −0.244896 | ||||||||
\(923\) | 0.564759 | 0.0185893 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.47006 | 0.212734 | ||||||||
\(926\) | 15.8106 | 0.519570 | ||||||||
\(927\) | 8.68708 | 0.285321 | ||||||||
\(928\) | −19.3975 | −0.636756 | ||||||||
\(929\) | −11.2589 | −0.369392 | −0.184696 | − | 0.982796i | \(-0.559130\pi\) | ||||
−0.184696 | + | 0.982796i | \(0.559130\pi\) | |||||||
\(930\) | 3.27807 | 0.107492 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.34490 | −0.273346 | ||||||||
\(933\) | 29.6830 | 0.971778 | ||||||||
\(934\) | −17.8589 | −0.584363 | ||||||||
\(935\) | −5.81149 | −0.190056 | ||||||||
\(936\) | −5.68379 | −0.185781 | ||||||||
\(937\) | −27.7504 | −0.906566 | −0.453283 | − | 0.891367i | \(-0.649747\pi\) | ||||
−0.453283 | + | 0.891367i | \(0.649747\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0091 | 0.457169 | ||||||||
\(940\) | 2.95150 | 0.0962673 | ||||||||
\(941\) | 27.2563 | 0.888531 | 0.444266 | − | 0.895895i | \(-0.353465\pi\) | ||||
0.444266 | + | 0.895895i | \(0.353465\pi\) | |||||||
\(942\) | 5.96374 | 0.194309 | ||||||||
\(943\) | −0.893136 | −0.0290845 | ||||||||
\(944\) | 0.808953 | 0.0263292 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.5841 | −0.766786 | ||||||||
\(947\) | −16.0528 | −0.521645 | −0.260823 | − | 0.965387i | \(-0.583994\pi\) | ||||
−0.260823 | + | 0.965387i | \(0.583994\pi\) | |||||||
\(948\) | 21.9115 | 0.711654 | ||||||||
\(949\) | −4.80564 | −0.155998 | ||||||||
\(950\) | −2.26478 | −0.0734792 | ||||||||
\(951\) | 21.2836 | 0.690169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.62507 | −0.149821 | −0.0749104 | − | 0.997190i | \(-0.523867\pi\) | ||||
−0.0749104 | + | 0.997190i | \(0.523867\pi\) | |||||||
\(954\) | 4.68501 | 0.151683 | ||||||||
\(955\) | 21.1774 | 0.685285 | ||||||||
\(956\) | 2.19265 | 0.0709154 | ||||||||
\(957\) | −14.1978 | −0.458951 | ||||||||
\(958\) | −26.5285 | −0.857097 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.36532 | −0.0763404 | ||||||||
\(961\) | −21.4256 | −0.691148 | ||||||||
\(962\) | −3.83157 | −0.123535 | ||||||||
\(963\) | 17.9551 | 0.578593 | ||||||||
\(964\) | 2.53093 | 0.0815157 | ||||||||
\(965\) | −14.5227 | −0.467502 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.867236 | 0.0278884 | 0.0139442 | − | 0.999903i | \(-0.495561\pi\) | ||||
0.0139442 | + | 0.999903i | \(0.495561\pi\) | |||||||
\(968\) | 17.8036 | 0.572229 | ||||||||
\(969\) | 1.06269 | 0.0341385 | ||||||||
\(970\) | 6.66807 | 0.214099 | ||||||||
\(971\) | 45.9188 | 1.47360 | 0.736802 | − | 0.676109i | \(-0.236335\pi\) | ||||
0.736802 | + | 0.676109i | \(0.236335\pi\) | |||||||
\(972\) | −1.50350 | −0.0482249 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.30115 | −0.169860 | ||||||||
\(975\) | 6.30732 | 0.201996 | ||||||||
\(976\) | 12.4764 | 0.399360 | ||||||||
\(977\) | −0.727989 | −0.0232904 | −0.0116452 | − | 0.999932i | \(-0.503707\pi\) | ||||
−0.0116452 | + | 0.999932i | \(0.503707\pi\) | |||||||
\(978\) | −6.13448 | −0.196159 | ||||||||
\(979\) | −7.73059 | −0.247071 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.29866 | −0.0414630 | ||||||||
\(982\) | −14.0050 | −0.446916 | ||||||||
\(983\) | 26.3436 | 0.840230 | 0.420115 | − | 0.907471i | \(-0.361990\pi\) | ||||
0.420115 | + | 0.907471i | \(0.361990\pi\) | |||||||
\(984\) | 2.46865 | 0.0786978 | ||||||||
\(985\) | 1.71375 | 0.0546047 | ||||||||
\(986\) | 2.12329 | 0.0676192 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.06148 | −0.129213 | ||||||||
\(989\) | 7.00491 | 0.222743 | ||||||||
\(990\) | −4.52105 | −0.143688 | ||||||||
\(991\) | 29.2465 | 0.929044 | 0.464522 | − | 0.885561i | \(-0.346226\pi\) | ||||
0.464522 | + | 0.885561i | \(0.346226\pi\) | |||||||
\(992\) | −18.0409 | −0.572799 | ||||||||
\(993\) | 8.80304 | 0.279356 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.2393 | 0.324607 | ||||||||
\(996\) | −9.64687 | −0.305673 | ||||||||
\(997\) | 43.6374 | 1.38201 | 0.691005 | − | 0.722850i | \(-0.257168\pi\) | ||||
0.691005 | + | 0.722850i | \(0.257168\pi\) | |||||||
\(998\) | 26.5028 | 0.838931 | ||||||||
\(999\) | −2.36179 | −0.0747237 |
(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 | 6027.2.a.u.1.2 | 4 | ||
7.6 | odd | 2 | 861.2.a.i.1.2 | ✓ | 4 | ||
21.20 | even | 2 | 2583.2.a.o.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.a.i.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
2583.2.a.o.1.3 | 4 | 21.20 | even | 2 | |||
6027.2.a.u.1.2 | 4 | 1.1 | even | 1 | trivial |