Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1710) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.03528 | 0.391298 | 0.195649 | − | 0.980674i | \(-0.437319\pi\) | ||||
0.195649 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.86370 | 1.16495 | 0.582475 | − | 0.812848i | \(-0.302084\pi\) | ||||
0.582475 | + | 0.812848i | \(0.302084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.03528 | −0.287134 | −0.143567 | − | 0.989641i | \(-0.545857\pi\) | ||||
−0.143567 | + | 0.989641i | \(0.545857\pi\) | |||||||
\(14\) | −1.03528 | −0.276689 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.46410 | 1.81031 | 0.905155 | − | 0.425081i | \(-0.139754\pi\) | ||||
0.905155 | + | 0.425081i | \(0.139754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.86370 | −0.823744 | ||||||||
\(23\) | −1.46410 | −0.305286 | −0.152643 | − | 0.988281i | \(-0.548779\pi\) | ||||
−0.152643 | + | 0.988281i | \(0.548779\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.03528 | 0.203034 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.03528 | 0.195649 | ||||||||
\(29\) | −9.52056 | −1.76792 | −0.883962 | − | 0.467560i | \(-0.845133\pi\) | ||||
−0.883962 | + | 0.467560i | \(0.845133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.92820 | 0.525921 | 0.262960 | − | 0.964807i | \(-0.415301\pi\) | ||||
0.262960 | + | 0.964807i | \(0.415301\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.46410 | −1.28008 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.69213 | 1.10018 | 0.550090 | − | 0.835106i | \(-0.314594\pi\) | ||||
0.550090 | + | 0.835106i | \(0.314594\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.69213 | −1.04514 | −0.522568 | − | 0.852598i | \(-0.675026\pi\) | ||||
−0.522568 | + | 0.852598i | \(0.675026\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.79315 | 0.273453 | 0.136726 | − | 0.990609i | \(-0.456342\pi\) | ||||
0.136726 | + | 0.990609i | \(0.456342\pi\) | |||||||
\(44\) | 3.86370 | 0.582475 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.46410 | 0.215870 | ||||||||
\(47\) | 9.46410 | 1.38048 | 0.690241 | − | 0.723580i | \(-0.257505\pi\) | ||||
0.690241 | + | 0.723580i | \(0.257505\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.92820 | −0.846886 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.03528 | −0.143567 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.03528 | −0.138345 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.52056 | 1.25011 | ||||||||
\(59\) | 12.6264 | 1.64382 | 0.821908 | − | 0.569621i | \(-0.192910\pi\) | ||||
0.821908 | + | 0.569621i | \(0.192910\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | −2.92820 | −0.371882 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.58630 | −0.438137 | −0.219068 | − | 0.975710i | \(-0.570302\pi\) | ||||
−0.219068 | + | 0.975710i | \(0.570302\pi\) | |||||||
\(68\) | 7.46410 | 0.905155 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.4548 | 1.83415 | 0.917074 | − | 0.398716i | \(-0.130544\pi\) | ||||
0.917074 | + | 0.398716i | \(0.130544\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3843 | 1.56651 | 0.783255 | − | 0.621701i | \(-0.213558\pi\) | ||||
0.783255 | + | 0.621701i | \(0.213558\pi\) | |||||||
\(74\) | −6.69213 | −0.777944 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.69213 | 0.739022 | ||||||||
\(83\) | −4.39230 | −0.482118 | −0.241059 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241059 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.79315 | −0.193360 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.86370 | −0.411872 | ||||||||
\(89\) | −1.03528 | −0.109739 | −0.0548695 | − | 0.998494i | \(-0.517474\pi\) | ||||
−0.0548695 | + | 0.998494i | \(0.517474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.07180 | −0.112355 | ||||||||
\(92\) | −1.46410 | −0.152643 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.46410 | −0.976148 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.2480 | −1.75127 | −0.875633 | − | 0.482978i | \(-0.839555\pi\) | ||||
−0.875633 | + | 0.482978i | \(0.839555\pi\) | |||||||
\(98\) | 5.92820 | 0.598839 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.757875 | 0.0754114 | 0.0377057 | − | 0.999289i | \(-0.487995\pi\) | ||||
0.0377057 | + | 0.999289i | \(0.487995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89898 | 0.482711 | 0.241355 | − | 0.970437i | \(-0.422408\pi\) | ||||
0.241355 | + | 0.970437i | \(0.422408\pi\) | |||||||
\(104\) | 1.03528 | 0.101517 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 10.9282 | 1.05647 | 0.528235 | − | 0.849098i | \(-0.322854\pi\) | ||||
0.528235 | + | 0.849098i | \(0.322854\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.92820 | −0.472036 | −0.236018 | − | 0.971749i | \(-0.575842\pi\) | ||||
−0.236018 | + | 0.971749i | \(0.575842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.03528 | 0.0978244 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.52056 | −0.883962 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.6264 | −1.16235 | ||||||||
\(119\) | 7.72741 | 0.708370 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.92820 | 0.357109 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.92820 | 0.262960 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.48528 | −0.752947 | −0.376473 | − | 0.926427i | \(-0.622863\pi\) | ||||
−0.376473 | + | 0.926427i | \(0.622863\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5911 | 1.01272 | 0.506360 | − | 0.862322i | \(-0.330991\pi\) | ||||
0.506360 | + | 0.862322i | \(0.330991\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.03528 | −0.0897698 | ||||||||
\(134\) | 3.58630 | 0.309809 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.46410 | −0.640041 | ||||||||
\(137\) | 7.46410 | 0.637701 | 0.318851 | − | 0.947805i | \(-0.396703\pi\) | ||||
0.318851 | + | 0.947805i | \(0.396703\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.4548 | −1.29694 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.3843 | −1.10769 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.69213 | 0.550090 | ||||||||
\(149\) | 9.04008 | 0.740593 | 0.370296 | − | 0.928914i | \(-0.379256\pi\) | ||||
0.370296 | + | 0.928914i | \(0.379256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.8564 | −1.77865 | −0.889325 | − | 0.457277i | \(-0.848825\pi\) | ||||
−0.889325 | + | 0.457277i | \(0.848825\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.00000 | −0.322329 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1421 | −1.12867 | −0.564333 | − | 0.825547i | \(-0.690866\pi\) | ||||
−0.564333 | + | 0.825547i | \(0.690866\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.51575 | −0.119458 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.7637 | −1.46969 | −0.734844 | − | 0.678236i | \(-0.762745\pi\) | ||||
−0.734844 | + | 0.678236i | \(0.762745\pi\) | |||||||
\(164\) | −6.69213 | −0.522568 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.39230 | 0.340909 | ||||||||
\(167\) | −2.92820 | −0.226591 | −0.113296 | − | 0.993561i | \(-0.536141\pi\) | ||||
−0.113296 | + | 0.993561i | \(0.536141\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9282 | −0.917554 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.79315 | 0.136726 | ||||||||
\(173\) | 18.7846 | 1.42817 | 0.714084 | − | 0.700060i | \(-0.246844\pi\) | ||||
0.714084 | + | 0.700060i | \(0.246844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.86370 | 0.291238 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.03528 | 0.0775972 | ||||||||
\(179\) | −22.4243 | −1.67607 | −0.838037 | − | 0.545613i | \(-0.816297\pi\) | ||||
−0.838037 | + | 0.545613i | \(0.816297\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.85641 | −0.583962 | −0.291981 | − | 0.956424i | \(-0.594314\pi\) | ||||
−0.291981 | + | 0.956424i | \(0.594314\pi\) | |||||||
\(182\) | 1.07180 | 0.0794469 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.46410 | 0.107935 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.8391 | 2.10892 | ||||||||
\(188\) | 9.46410 | 0.690241 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.55103 | 0.184586 | 0.0922929 | − | 0.995732i | \(-0.470580\pi\) | ||||
0.0922929 | + | 0.995732i | \(0.470580\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.93426 | 0.427157 | 0.213579 | − | 0.976926i | \(-0.431488\pi\) | ||||
0.213579 | + | 0.976926i | \(0.431488\pi\) | |||||||
\(194\) | 17.2480 | 1.23833 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.92820 | −0.423443 | ||||||||
\(197\) | 16.5359 | 1.17813 | 0.589067 | − | 0.808084i | \(-0.299495\pi\) | ||||
0.589067 | + | 0.808084i | \(0.299495\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.9282 | 1.90889 | 0.954445 | − | 0.298387i | \(-0.0964487\pi\) | ||||
0.954445 | + | 0.298387i | \(0.0964487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.757875 | −0.0533239 | ||||||||
\(203\) | −9.85641 | −0.691784 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.89898 | −0.341328 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.03528 | −0.0717835 | ||||||||
\(209\) | −3.86370 | −0.267258 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.85641 | 0.678543 | 0.339272 | − | 0.940688i | \(-0.389819\pi\) | ||||
0.339272 | + | 0.940688i | \(0.389819\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.9282 | −0.747037 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.03150 | 0.205792 | ||||||||
\(218\) | 4.92820 | 0.333780 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.72741 | −0.519802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.757875 | 0.0507510 | 0.0253755 | − | 0.999678i | \(-0.491922\pi\) | ||||
0.0253755 | + | 0.999678i | \(0.491922\pi\) | |||||||
\(224\) | −1.03528 | −0.0691723 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 25.8564 | 1.71615 | 0.858075 | − | 0.513524i | \(-0.171660\pi\) | ||||
0.858075 | + | 0.513524i | \(0.171660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.8564 | 1.57648 | 0.788238 | − | 0.615371i | \(-0.210994\pi\) | ||||
0.788238 | + | 0.615371i | \(0.210994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.52056 | 0.625055 | ||||||||
\(233\) | 19.4641 | 1.27514 | 0.637568 | − | 0.770394i | \(-0.279941\pi\) | ||||
0.637568 | + | 0.770394i | \(0.279941\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.6264 | 0.821908 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.72741 | −0.500893 | ||||||||
\(239\) | −18.0058 | −1.16470 | −0.582350 | − | 0.812938i | \(-0.697867\pi\) | ||||
−0.582350 | + | 0.812938i | \(0.697867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | −3.92820 | −0.252514 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.03528 | 0.0658730 | ||||||||
\(248\) | −2.92820 | −0.185941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.5302 | −1.61145 | −0.805725 | − | 0.592290i | \(-0.798224\pi\) | ||||
−0.805725 | + | 0.592290i | \(0.798224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.65685 | −0.355643 | ||||||||
\(254\) | 8.48528 | 0.532414 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.7846 | −1.17175 | −0.585876 | − | 0.810401i | \(-0.699249\pi\) | ||||
−0.585876 | + | 0.810401i | \(0.699249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.92820 | 0.430498 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.5911 | −0.716101 | ||||||||
\(263\) | −15.3205 | −0.944703 | −0.472351 | − | 0.881410i | \(-0.656595\pi\) | ||||
−0.472351 | + | 0.881410i | \(0.656595\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.03528 | 0.0634769 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.58630 | −0.219068 | ||||||||
\(269\) | −12.1459 | −0.740549 | −0.370275 | − | 0.928922i | \(-0.620736\pi\) | ||||
−0.370275 | + | 0.928922i | \(0.620736\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.92820 | −0.177876 | −0.0889378 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889378 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(272\) | 7.46410 | 0.452578 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.46410 | −0.450923 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.31268 | −0.0788712 | −0.0394356 | − | 0.999222i | \(-0.512556\pi\) | ||||
−0.0394356 | + | 0.999222i | \(0.512556\pi\) | |||||||
\(278\) | 6.92820 | 0.415526 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.7017 | −1.35427 | −0.677136 | − | 0.735858i | \(-0.736779\pi\) | ||||
−0.677136 | + | 0.735858i | \(0.736779\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.3185 | 1.14837 | 0.574183 | − | 0.818727i | \(-0.305320\pi\) | ||||
0.574183 | + | 0.818727i | \(0.305320\pi\) | |||||||
\(284\) | 15.4548 | 0.917074 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | −6.92820 | −0.408959 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.3843 | 0.783255 | ||||||||
\(293\) | 7.85641 | 0.458976 | 0.229488 | − | 0.973311i | \(-0.426295\pi\) | ||||
0.229488 | + | 0.973311i | \(0.426295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.69213 | −0.388972 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.04008 | −0.523678 | ||||||||
\(299\) | 1.51575 | 0.0876581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.85641 | 0.107001 | ||||||||
\(302\) | 21.8564 | 1.25769 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.8685 | 0.677372 | 0.338686 | − | 0.940900i | \(-0.390018\pi\) | ||||
0.338686 | + | 0.940900i | \(0.390018\pi\) | |||||||
\(308\) | 4.00000 | 0.227921 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.69213 | 0.379476 | 0.189738 | − | 0.981835i | \(-0.439236\pi\) | ||||
0.189738 | + | 0.981835i | \(0.439236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5959 | −1.10763 | −0.553813 | − | 0.832641i | \(-0.686828\pi\) | ||||
−0.553813 | + | 0.832641i | \(0.686828\pi\) | |||||||
\(314\) | 14.1421 | 0.798087 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.7846 | −2.05954 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.51575 | 0.0844694 | ||||||||
\(323\) | −7.46410 | −0.415314 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.7637 | 1.03923 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.69213 | 0.369511 | ||||||||
\(329\) | 9.79796 | 0.540179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.8564 | −0.761617 | −0.380808 | − | 0.924654i | \(-0.624354\pi\) | ||||
−0.380808 | + | 0.924654i | \(0.624354\pi\) | |||||||
\(332\) | −4.39230 | −0.241059 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.92820 | 0.160224 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.86370 | 0.210469 | 0.105235 | − | 0.994447i | \(-0.466441\pi\) | ||||
0.105235 | + | 0.994447i | \(0.466441\pi\) | |||||||
\(338\) | 11.9282 | 0.648809 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.3137 | 0.612672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.3843 | −0.722682 | ||||||||
\(344\) | −1.79315 | −0.0966802 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.7846 | −1.00987 | ||||||||
\(347\) | 25.4641 | 1.36698 | 0.683492 | − | 0.729958i | \(-0.260460\pi\) | ||||
0.683492 | + | 0.729958i | \(0.260460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.8564 | 1.70523 | 0.852617 | − | 0.522536i | \(-0.175014\pi\) | ||||
0.852617 | + | 0.522536i | \(0.175014\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.86370 | −0.205936 | ||||||||
\(353\) | −13.3205 | −0.708979 | −0.354490 | − | 0.935060i | \(-0.615345\pi\) | ||||
−0.354490 | + | 0.935060i | \(0.615345\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.03528 | −0.0548695 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.4243 | 1.18516 | ||||||||
\(359\) | 9.31749 | 0.491758 | 0.245879 | − | 0.969301i | \(-0.420923\pi\) | ||||
0.245879 | + | 0.969301i | \(0.420923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 7.85641 | 0.412924 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.07180 | −0.0561774 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0764 | 1.04798 | 0.523990 | − | 0.851725i | \(-0.324443\pi\) | ||||
0.523990 | + | 0.851725i | \(0.324443\pi\) | |||||||
\(368\) | −1.46410 | −0.0763216 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.21166 | 0.322493 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.480473 | 0.0248780 | 0.0124390 | − | 0.999923i | \(-0.496040\pi\) | ||||
0.0124390 | + | 0.999923i | \(0.496040\pi\) | |||||||
\(374\) | −28.8391 | −1.49123 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.46410 | −0.488074 | ||||||||
\(377\) | 9.85641 | 0.507631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.7128 | 1.01258 | 0.506290 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506290 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.55103 | −0.130522 | ||||||||
\(383\) | −9.07180 | −0.463547 | −0.231774 | − | 0.972770i | \(-0.574453\pi\) | ||||
−0.231774 | + | 0.972770i | \(0.574453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.93426 | −0.302046 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.2480 | −0.875633 | ||||||||
\(389\) | 19.7990 | 1.00385 | 0.501924 | − | 0.864912i | \(-0.332626\pi\) | ||||
0.501924 | + | 0.864912i | \(0.332626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.9282 | −0.552663 | ||||||||
\(392\) | 5.92820 | 0.299419 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.5359 | −0.833067 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.31268 | 0.0658814 | 0.0329407 | − | 0.999457i | \(-0.489513\pi\) | ||||
0.0329407 | + | 0.999457i | \(0.489513\pi\) | |||||||
\(398\) | −26.9282 | −1.34979 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.62158 | −0.230791 | −0.115395 | − | 0.993320i | \(-0.536813\pi\) | ||||
−0.115395 | + | 0.993320i | \(0.536813\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.03150 | −0.151010 | ||||||||
\(404\) | 0.757875 | 0.0377057 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.85641 | 0.489165 | ||||||||
\(407\) | 25.8564 | 1.28165 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.07180 | −0.349678 | −0.174839 | − | 0.984597i | \(-0.555940\pi\) | ||||
−0.174839 | + | 0.984597i | \(0.555940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.89898 | 0.241355 | ||||||||
\(413\) | 13.0718 | 0.643221 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.03528 | 0.0507586 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.86370 | 0.188980 | ||||||||
\(419\) | −24.4206 | −1.19302 | −0.596511 | − | 0.802605i | \(-0.703447\pi\) | ||||
−0.596511 | + | 0.802605i | \(0.703447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.7128 | −1.25317 | −0.626583 | − | 0.779355i | \(-0.715547\pi\) | ||||
−0.626583 | + | 0.779355i | \(0.715547\pi\) | |||||||
\(422\) | −9.85641 | −0.479802 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.07055 | −0.100201 | ||||||||
\(428\) | 10.9282 | 0.528235 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.0117 | 1.73462 | 0.867311 | − | 0.497767i | \(-0.165847\pi\) | ||||
0.867311 | + | 0.497767i | \(0.165847\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.6617 | −0.656538 | −0.328269 | − | 0.944584i | \(-0.606465\pi\) | ||||
−0.328269 | + | 0.944584i | \(0.606465\pi\) | |||||||
\(434\) | −3.03150 | −0.145517 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.92820 | −0.236018 | ||||||||
\(437\) | 1.46410 | 0.0700375 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.0000 | 0.954548 | 0.477274 | − | 0.878755i | \(-0.341625\pi\) | ||||
0.477274 | + | 0.878755i | \(0.341625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.72741 | 0.367555 | ||||||||
\(443\) | −4.39230 | −0.208685 | −0.104342 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104342 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.757875 | −0.0358864 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.03528 | 0.0489122 | ||||||||
\(449\) | −3.66063 | −0.172756 | −0.0863779 | − | 0.996262i | \(-0.527529\pi\) | ||||
−0.0863779 | + | 0.996262i | \(0.527529\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.8564 | −1.21753 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −25.8564 | −1.21350 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.9411 | 1.58770 | 0.793849 | − | 0.608114i | \(-0.208074\pi\) | ||||
0.793849 | + | 0.608114i | \(0.208074\pi\) | |||||||
\(458\) | −23.8564 | −1.11474 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.7284 | −0.825696 | −0.412848 | − | 0.910800i | \(-0.635466\pi\) | ||||
−0.412848 | + | 0.910800i | \(0.635466\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.0155 | 1.58083 | 0.790416 | − | 0.612570i | \(-0.209864\pi\) | ||||
0.790416 | + | 0.612570i | \(0.209864\pi\) | |||||||
\(464\) | −9.52056 | −0.441981 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.4641 | −0.901657 | ||||||||
\(467\) | 9.46410 | 0.437946 | 0.218973 | − | 0.975731i | \(-0.429729\pi\) | ||||
0.218973 | + | 0.975731i | \(0.429729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.71281 | −0.171442 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.6264 | −0.581177 | ||||||||
\(473\) | 6.92820 | 0.318559 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.72741 | 0.354185 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0058 | 0.823568 | ||||||||
\(479\) | −31.3901 | −1.43425 | −0.717125 | − | 0.696944i | \(-0.754542\pi\) | ||||
−0.717125 | + | 0.696944i | \(0.754542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.92820 | −0.315899 | ||||||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.92820 | 0.178555 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.0106 | −1.17865 | −0.589327 | − | 0.807894i | \(-0.700607\pi\) | ||||
−0.589327 | + | 0.807894i | \(0.700607\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7322 | 0.709985 | 0.354992 | − | 0.934869i | \(-0.384483\pi\) | ||||
0.354992 | + | 0.934869i | \(0.384483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −71.0624 | −3.20049 | ||||||||
\(494\) | −1.03528 | −0.0465793 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.92820 | 0.131480 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.85641 | −0.0831042 | −0.0415521 | − | 0.999136i | \(-0.513230\pi\) | ||||
−0.0415521 | + | 0.999136i | \(0.513230\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.5302 | 1.13947 | ||||||||
\(503\) | 23.3205 | 1.03981 | 0.519905 | − | 0.854224i | \(-0.325967\pi\) | ||||
0.519905 | + | 0.854224i | \(0.325967\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.65685 | 0.251478 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.48528 | −0.376473 | ||||||||
\(509\) | 22.3500 | 0.990647 | 0.495324 | − | 0.868709i | \(-0.335050\pi\) | ||||
0.495324 | + | 0.868709i | \(0.335050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8564 | 0.612971 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.7846 | 0.828554 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.5665 | 1.60819 | ||||||||
\(518\) | −6.92820 | −0.304408 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.62158 | −0.202475 | −0.101238 | − | 0.994862i | \(-0.532280\pi\) | ||||
−0.101238 | + | 0.994862i | \(0.532280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.17260 | −0.313636 | −0.156818 | − | 0.987628i | \(-0.550124\pi\) | ||||
−0.156818 | + | 0.987628i | \(0.550124\pi\) | |||||||
\(524\) | 11.5911 | 0.506360 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.3205 | 0.668006 | ||||||||
\(527\) | 21.8564 | 0.952080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8564 | −0.906800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.03528 | −0.0448849 | ||||||||
\(533\) | 6.92820 | 0.300094 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.58630 | 0.154905 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.1459 | 0.523647 | ||||||||
\(539\) | −22.9048 | −0.986580 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.0000 | 1.11783 | 0.558914 | − | 0.829226i | \(-0.311218\pi\) | ||||
0.558914 | + | 0.829226i | \(0.311218\pi\) | |||||||
\(542\) | 2.92820 | 0.125777 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.46410 | −0.320021 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.6370 | −1.65200 | −0.826000 | − | 0.563670i | \(-0.809389\pi\) | ||||
−0.826000 | + | 0.563670i | \(0.809389\pi\) | |||||||
\(548\) | 7.46410 | 0.318851 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.52056 | 0.405589 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.14110 | −0.176098 | ||||||||
\(554\) | 1.31268 | 0.0557703 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.92820 | −0.293821 | ||||||||
\(557\) | 24.5359 | 1.03962 | 0.519810 | − | 0.854282i | \(-0.326003\pi\) | ||||
0.519810 | + | 0.854282i | \(0.326003\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.85641 | −0.0785176 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.7017 | 0.957615 | ||||||||
\(563\) | −1.85641 | −0.0782382 | −0.0391191 | − | 0.999235i | \(-0.512455\pi\) | ||||
−0.0391191 | + | 0.999235i | \(0.512455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19.3185 | −0.812018 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.4548 | −0.648470 | ||||||||
\(569\) | −9.72363 | −0.407636 | −0.203818 | − | 0.979009i | \(-0.565335\pi\) | ||||
−0.203818 | + | 0.979009i | \(0.565335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.07180 | 0.0448533 | 0.0224266 | − | 0.999748i | \(-0.492861\pi\) | ||||
0.0224266 | + | 0.999748i | \(0.492861\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.92820 | 0.289178 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.65685 | −0.235498 | −0.117749 | − | 0.993043i | \(-0.537568\pi\) | ||||
−0.117749 | + | 0.993043i | \(0.537568\pi\) | |||||||
\(578\) | −38.7128 | −1.61024 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.54725 | −0.188652 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.1822 | 0.960109 | ||||||||
\(584\) | −13.3843 | −0.553845 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.85641 | −0.324545 | ||||||||
\(587\) | 3.60770 | 0.148906 | 0.0744528 | − | 0.997225i | \(-0.476279\pi\) | ||||
0.0744528 | + | 0.997225i | \(0.476279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.92820 | −0.120655 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.69213 | 0.275045 | ||||||||
\(593\) | −11.4641 | −0.470774 | −0.235387 | − | 0.971902i | \(-0.575636\pi\) | ||||
−0.235387 | + | 0.971902i | \(0.575636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.04008 | 0.370296 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.51575 | −0.0619836 | ||||||||
\(599\) | 30.3548 | 1.24026 | 0.620132 | − | 0.784497i | \(-0.287079\pi\) | ||||
0.620132 | + | 0.784497i | \(0.287079\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.7846 | 0.929404 | 0.464702 | − | 0.885467i | \(-0.346162\pi\) | ||||
0.464702 | + | 0.885467i | \(0.346162\pi\) | |||||||
\(602\) | −1.85641 | −0.0756615 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.8564 | −0.889325 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.9791 | −0.932695 | −0.466347 | − | 0.884602i | \(-0.654430\pi\) | ||||
−0.466347 | + | 0.884602i | \(0.654430\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.79796 | −0.396383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.0518 | 1.81962 | 0.909812 | − | 0.415021i | \(-0.136226\pi\) | ||||
0.909812 | + | 0.415021i | \(0.136226\pi\) | |||||||
\(614\) | −11.8685 | −0.478974 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | −20.2487 | −0.815182 | −0.407591 | − | 0.913165i | \(-0.633631\pi\) | ||||
−0.407591 | + | 0.913165i | \(0.633631\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6410 | 1.39234 | 0.696170 | − | 0.717877i | \(-0.254886\pi\) | ||||
0.696170 | + | 0.717877i | \(0.254886\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.69213 | −0.268330 | ||||||||
\(623\) | −1.07180 | −0.0429406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.5959 | 0.783210 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.1421 | −0.564333 | ||||||||
\(629\) | 49.9507 | 1.99167 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.85641 | −0.233140 | −0.116570 | − | 0.993182i | \(-0.537190\pi\) | ||||
−0.116570 | + | 0.993182i | \(0.537190\pi\) | |||||||
\(632\) | 4.00000 | 0.159111 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.0000 | −0.556011 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.13733 | 0.243170 | ||||||||
\(638\) | 36.7846 | 1.45632 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.55103 | −0.100759 | −0.0503797 | − | 0.998730i | \(-0.516043\pi\) | ||||
−0.0503797 | + | 0.998730i | \(0.516043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.3500 | 0.881399 | 0.440699 | − | 0.897655i | \(-0.354731\pi\) | ||||
0.440699 | + | 0.897655i | \(0.354731\pi\) | |||||||
\(644\) | −1.51575 | −0.0597289 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.46410 | 0.293671 | ||||||||
\(647\) | 6.53590 | 0.256953 | 0.128476 | − | 0.991713i | \(-0.458991\pi\) | ||||
0.128476 | + | 0.991713i | \(0.458991\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.7846 | 1.91496 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.7637 | −0.734844 | ||||||||
\(653\) | 24.2487 | 0.948925 | 0.474463 | − | 0.880276i | \(-0.342642\pi\) | ||||
0.474463 | + | 0.880276i | \(0.342642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.69213 | −0.261284 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.79796 | −0.381964 | ||||||||
\(659\) | 9.04008 | 0.352152 | 0.176076 | − | 0.984377i | \(-0.443660\pi\) | ||||
0.176076 | + | 0.984377i | \(0.443660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7846 | 1.19738 | 0.598691 | − | 0.800980i | \(-0.295688\pi\) | ||||
0.598691 | + | 0.800980i | \(0.295688\pi\) | |||||||
\(662\) | 13.8564 | 0.538545 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.39230 | 0.170454 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.9391 | 0.539723 | ||||||||
\(668\) | −2.92820 | −0.113296 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.72741 | −0.298313 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.1480 | 1.23921 | 0.619607 | − | 0.784912i | \(-0.287292\pi\) | ||||
0.619607 | + | 0.784912i | \(0.287292\pi\) | |||||||
\(674\) | −3.86370 | −0.148824 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.9282 | −0.458777 | ||||||||
\(677\) | −32.6410 | −1.25450 | −0.627248 | − | 0.778820i | \(-0.715819\pi\) | ||||
−0.627248 | + | 0.778820i | \(0.715819\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.8564 | −0.685266 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.3137 | −0.433224 | ||||||||
\(683\) | 5.07180 | 0.194067 | 0.0970335 | − | 0.995281i | \(-0.469065\pi\) | ||||
0.0970335 | + | 0.995281i | \(0.469065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.3843 | 0.511013 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.79315 | 0.0683632 | ||||||||
\(689\) | −6.21166 | −0.236645 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.0718 | 0.953776 | 0.476888 | − | 0.878964i | \(-0.341765\pi\) | ||||
0.476888 | + | 0.878964i | \(0.341765\pi\) | |||||||
\(692\) | 18.7846 | 0.714084 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.4641 | −0.966604 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.9507 | −1.89202 | ||||||||
\(698\) | −31.8564 | −1.20578 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.4655 | −1.56613 | −0.783064 | − | 0.621941i | \(-0.786345\pi\) | ||||
−0.783064 | + | 0.621941i | \(0.786345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.69213 | −0.252398 | ||||||||
\(704\) | 3.86370 | 0.145619 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.3205 | 0.501324 | ||||||||
\(707\) | 0.784610 | 0.0295083 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.8564 | 0.595500 | 0.297750 | − | 0.954644i | \(-0.403764\pi\) | ||||
0.297750 | + | 0.954644i | \(0.403764\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.03528 | 0.0387986 | ||||||||
\(713\) | −4.28719 | −0.160556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.4243 | −0.838037 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.31749 | −0.347725 | ||||||||
\(719\) | 26.8429 | 1.00107 | 0.500535 | − | 0.865716i | \(-0.333137\pi\) | ||||
0.500535 | + | 0.865716i | \(0.333137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.07180 | 0.188884 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.85641 | −0.291981 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.2784 | 0.381206 | 0.190603 | − | 0.981667i | \(-0.438956\pi\) | ||||
0.190603 | + | 0.981667i | \(0.438956\pi\) | |||||||
\(728\) | 1.07180 | 0.0397234 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.3843 | 0.495035 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0716 | 0.445874 | 0.222937 | − | 0.974833i | \(-0.428436\pi\) | ||||
0.222937 | + | 0.974833i | \(0.428436\pi\) | |||||||
\(734\) | −20.0764 | −0.741033 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.46410 | 0.0539675 | ||||||||
\(737\) | −13.8564 | −0.510407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.7128 | −1.16657 | −0.583287 | − | 0.812266i | \(-0.698234\pi\) | ||||
−0.583287 | + | 0.812266i | \(0.698234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.21166 | −0.228037 | ||||||||
\(743\) | 34.6410 | 1.27086 | 0.635428 | − | 0.772160i | \(-0.280824\pi\) | ||||
0.635428 | + | 0.772160i | \(0.280824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.480473 | −0.0175914 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 28.8391 | 1.05446 | ||||||||
\(749\) | 11.3137 | 0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.8564 | −0.797552 | −0.398776 | − | 0.917048i | \(-0.630565\pi\) | ||||
−0.398776 | + | 0.917048i | \(0.630565\pi\) | |||||||
\(752\) | 9.46410 | 0.345120 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.85641 | −0.358949 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.1538 | −1.82287 | −0.911436 | − | 0.411443i | \(-0.865025\pi\) | ||||
−0.911436 | + | 0.411443i | \(0.865025\pi\) | |||||||
\(758\) | −19.7128 | −0.716002 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.21166 | 0.225172 | 0.112586 | − | 0.993642i | \(-0.464087\pi\) | ||||
0.112586 | + | 0.993642i | \(0.464087\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.10205 | −0.184707 | ||||||||
\(764\) | 2.55103 | 0.0922929 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.07180 | 0.327777 | ||||||||
\(767\) | −13.0718 | −0.471995 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.14359 | 0.293665 | 0.146833 | − | 0.989161i | \(-0.453092\pi\) | ||||
0.146833 | + | 0.989161i | \(0.453092\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.93426 | 0.213579 | ||||||||
\(773\) | 19.8564 | 0.714185 | 0.357093 | − | 0.934069i | \(-0.383768\pi\) | ||||
0.357093 | + | 0.934069i | \(0.383768\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.2480 | 0.619166 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.7990 | −0.709828 | ||||||||
\(779\) | 6.69213 | 0.239770 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.7128 | 2.13669 | ||||||||
\(782\) | 10.9282 | 0.390792 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.92820 | −0.211722 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.7685 | −0.954195 | −0.477097 | − | 0.878850i | \(-0.658311\pi\) | ||||
−0.477097 | + | 0.878850i | \(0.658311\pi\) | |||||||
\(788\) | 16.5359 | 0.589067 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.21166 | 0.220861 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.07055 | 0.0735275 | ||||||||
\(794\) | −1.31268 | −0.0465852 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.9282 | 0.954445 | ||||||||
\(797\) | −28.6410 | −1.01452 | −0.507258 | − | 0.861794i | \(-0.669341\pi\) | ||||
−0.507258 | + | 0.861794i | \(0.669341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 70.6410 | 2.49910 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.62158 | 0.163194 | ||||||||
\(803\) | 51.7128 | 1.82491 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.03150 | 0.106780 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.757875 | −0.0266619 | ||||||||
\(809\) | 33.5350 | 1.17903 | 0.589514 | − | 0.807758i | \(-0.299319\pi\) | ||||
0.589514 | + | 0.807758i | \(0.299319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 56.4974 | 1.98389 | 0.991946 | − | 0.126658i | \(-0.0404251\pi\) | ||||
0.991946 | + | 0.126658i | \(0.0404251\pi\) | |||||||
\(812\) | −9.85641 | −0.345892 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.8564 | −0.906267 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.79315 | −0.0627344 | ||||||||
\(818\) | 7.07180 | 0.247260 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.3244 | 1.30263 | 0.651314 | − | 0.758808i | \(-0.274218\pi\) | ||||
0.651314 | + | 0.758808i | \(0.274218\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.6819 | −1.94095 | −0.970475 | − | 0.241202i | \(-0.922458\pi\) | ||||
−0.970475 | + | 0.241202i | \(0.922458\pi\) | |||||||
\(824\) | −4.89898 | −0.170664 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.0718 | −0.454826 | ||||||||
\(827\) | −6.92820 | −0.240917 | −0.120459 | − | 0.992718i | \(-0.538437\pi\) | ||||
−0.120459 | + | 0.992718i | \(0.538437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.7846 | −0.930268 | −0.465134 | − | 0.885240i | \(-0.653994\pi\) | ||||
−0.465134 | + | 0.885240i | \(0.653994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.03528 | −0.0358917 | ||||||||
\(833\) | −44.2487 | −1.53313 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.86370 | −0.133629 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.4206 | 0.843595 | ||||||||
\(839\) | 28.2843 | 0.976481 | 0.488241 | − | 0.872709i | \(-0.337639\pi\) | ||||
0.488241 | + | 0.872709i | \(0.337639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.6410 | 2.12555 | ||||||||
\(842\) | 25.7128 | 0.886122 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.85641 | 0.339272 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.06678 | 0.139736 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.79796 | −0.335870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.6969 | −0.503214 | −0.251607 | − | 0.967830i | \(-0.580959\pi\) | ||||
−0.251607 | + | 0.967830i | \(0.580959\pi\) | |||||||
\(854\) | 2.07055 | 0.0708528 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.9282 | −0.373518 | ||||||||
\(857\) | −52.6410 | −1.79818 | −0.899091 | − | 0.437761i | \(-0.855772\pi\) | ||||
−0.899091 | + | 0.437761i | \(0.855772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.7846 | 1.25507 | 0.627537 | − | 0.778586i | \(-0.284063\pi\) | ||||
0.627537 | + | 0.778586i | \(0.284063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.0117 | −1.22656 | ||||||||
\(863\) | −20.7846 | −0.707516 | −0.353758 | − | 0.935337i | \(-0.615096\pi\) | ||||
−0.353758 | + | 0.935337i | \(0.615096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.6617 | 0.464242 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.03150 | 0.102896 | ||||||||
\(869\) | −15.4548 | −0.524269 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.71281 | 0.125804 | ||||||||
\(872\) | 4.92820 | 0.166890 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.46410 | −0.0495240 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.8134 | 1.47947 | 0.739737 | − | 0.672896i | \(-0.234950\pi\) | ||||
0.739737 | + | 0.672896i | \(0.234950\pi\) | |||||||
\(878\) | −20.0000 | −0.674967 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.3528 | −0.348793 | −0.174397 | − | 0.984675i | \(-0.555798\pi\) | ||||
−0.174397 | + | 0.984675i | \(0.555798\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.0144 | −0.808150 | −0.404075 | − | 0.914726i | \(-0.632406\pi\) | ||||
−0.404075 | + | 0.914726i | \(0.632406\pi\) | |||||||
\(884\) | −7.72741 | −0.259901 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.39230 | 0.147562 | ||||||||
\(887\) | 39.7128 | 1.33343 | 0.666713 | − | 0.745315i | \(-0.267701\pi\) | ||||
0.666713 | + | 0.745315i | \(0.267701\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.78461 | −0.294626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.757875 | 0.0253755 | ||||||||
\(893\) | −9.46410 | −0.316704 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.03528 | −0.0345861 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.66063 | 0.122157 | ||||||||
\(899\) | −27.8781 | −0.929788 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7846 | 1.49199 | ||||||||
\(902\) | 25.8564 | 0.860924 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.62536 | 0.0871735 | 0.0435867 | − | 0.999050i | \(-0.486122\pi\) | ||||
0.0435867 | + | 0.999050i | \(0.486122\pi\) | |||||||
\(908\) | 25.8564 | 0.858075 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.2548 | −1.49936 | −0.749680 | − | 0.661801i | \(-0.769792\pi\) | ||||
−0.749680 | + | 0.661801i | \(0.769792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.9706 | −0.561644 | ||||||||
\(914\) | −33.9411 | −1.12267 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.8564 | 0.788238 | ||||||||
\(917\) | 12.0000 | 0.396275 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7128 | −0.914161 | −0.457081 | − | 0.889425i | \(-0.651105\pi\) | ||||
−0.457081 | + | 0.889425i | \(0.651105\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.7284 | 0.583855 | ||||||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34.0155 | −1.11782 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.52056 | 0.312528 | ||||||||
\(929\) | −11.3137 | −0.371191 | −0.185595 | − | 0.982626i | \(-0.559421\pi\) | ||||
−0.185595 | + | 0.982626i | \(0.559421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.92820 | 0.194289 | ||||||||
\(932\) | 19.4641 | 0.637568 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.46410 | −0.309675 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.3548 | −0.991649 | −0.495824 | − | 0.868423i | \(-0.665134\pi\) | ||||
−0.495824 | + | 0.868423i | \(0.665134\pi\) | |||||||
\(938\) | 3.71281 | 0.121228 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.8343 | −0.679178 | −0.339589 | − | 0.940574i | \(-0.610288\pi\) | ||||
−0.339589 | + | 0.940574i | \(0.610288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.79796 | 0.319065 | ||||||||
\(944\) | 12.6264 | 0.410954 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.92820 | −0.225255 | ||||||||
\(947\) | 37.1769 | 1.20809 | 0.604044 | − | 0.796951i | \(-0.293555\pi\) | ||||
0.604044 | + | 0.796951i | \(0.293555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.8564 | −0.449798 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.72741 | −0.250447 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0058 | −0.582350 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.3901 | 1.01417 | ||||||||
\(959\) | 7.72741 | 0.249531 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.4256 | −0.723407 | ||||||||
\(962\) | 6.92820 | 0.223374 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.0000 | 0.322078 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.55103 | −0.0820355 | −0.0410177 | − | 0.999158i | \(-0.513060\pi\) | ||||
−0.0410177 | + | 0.999158i | \(0.513060\pi\) | |||||||
\(968\) | −3.92820 | −0.126257 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.9010 | −0.799112 | −0.399556 | − | 0.916709i | \(-0.630836\pi\) | ||||
−0.399556 | + | 0.916709i | \(0.630836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.17260 | −0.229943 | ||||||||
\(974\) | 26.0106 | 0.833435 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | −49.7128 | −1.59045 | −0.795227 | − | 0.606312i | \(-0.792648\pi\) | ||||
−0.795227 | + | 0.606312i | \(0.792648\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00000 | −0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.7322 | −0.502035 | ||||||||
\(983\) | 48.7846 | 1.55599 | 0.777994 | − | 0.628272i | \(-0.216238\pi\) | ||||
0.777994 | + | 0.628272i | \(0.216238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 71.0624 | 2.26309 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.03528 | 0.0329365 | ||||||||
\(989\) | −2.62536 | −0.0834814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.7846 | 0.660245 | 0.330122 | − | 0.943938i | \(-0.392910\pi\) | ||||
0.330122 | + | 0.943938i | \(0.392910\pi\) | |||||||
\(992\) | −2.92820 | −0.0929705 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.0000 | −0.507489 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.31268 | 0.0415729 | 0.0207865 | − | 0.999784i | \(-0.493383\pi\) | ||||
0.0207865 | + | 0.999784i | \(0.493383\pi\) | |||||||
\(998\) | 1.85641 | 0.0587635 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8550.2.a.cu.1.3 | 4 | ||
3.2 | odd | 2 | 8550.2.a.cv.1.3 | 4 | |||
5.2 | odd | 4 | 1710.2.d.g.1369.3 | yes | 8 | ||
5.3 | odd | 4 | 1710.2.d.g.1369.8 | yes | 8 | ||
5.4 | even | 2 | 8550.2.a.cv.1.2 | 4 | |||
15.2 | even | 4 | 1710.2.d.g.1369.6 | yes | 8 | ||
15.8 | even | 4 | 1710.2.d.g.1369.1 | ✓ | 8 | ||
15.14 | odd | 2 | inner | 8550.2.a.cu.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1710.2.d.g.1369.1 | ✓ | 8 | 15.8 | even | 4 | ||
1710.2.d.g.1369.3 | yes | 8 | 5.2 | odd | 4 | ||
1710.2.d.g.1369.6 | yes | 8 | 15.2 | even | 4 | ||
1710.2.d.g.1369.8 | yes | 8 | 5.3 | odd | 4 | ||
8550.2.a.cu.1.2 | 4 | 15.14 | odd | 2 | inner | ||
8550.2.a.cu.1.3 | 4 | 1.1 | even | 1 | trivial | ||
8550.2.a.cv.1.2 | 4 | 5.4 | even | 2 | |||
8550.2.a.cv.1.3 | 4 | 3.2 | odd | 2 |