Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 49 x^{14} + 130 x^{13} + 932 x^{12} - 2028 x^{11} - 8965 x^{10} + 14400 x^{9} + \cdots + 3888 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.86734\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.86734 | −0.835100 | −0.417550 | − | 0.908654i | \(-0.637111\pi\) | ||||
−0.417550 | + | 0.908654i | \(0.637111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.84365 | −1.83073 | −0.915364 | − | 0.402627i | \(-0.868097\pi\) | ||||
−0.915364 | + | 0.402627i | \(0.868097\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.93713 | −1.48860 | −0.744301 | − | 0.667844i | \(-0.767217\pi\) | ||||
−0.744301 | + | 0.667844i | \(0.767217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.86190 | 0.793747 | 0.396873 | − | 0.917873i | \(-0.370095\pi\) | ||||
0.396873 | + | 0.917873i | \(0.370095\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.86734 | −0.482145 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.10878 | 0.753989 | 0.376995 | − | 0.926215i | \(-0.376958\pi\) | ||||
0.376995 | + | 0.926215i | \(0.376958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94897 | −0.447124 | −0.223562 | − | 0.974690i | \(-0.571769\pi\) | ||||
−0.223562 | + | 0.974690i | \(0.571769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.84365 | −1.05697 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.51304 | −0.302609 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.41813 | −0.973126 | −0.486563 | − | 0.873646i | \(-0.661750\pi\) | ||||
−0.486563 | + | 0.873646i | \(0.661750\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.93713 | −0.859445 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.04474 | 1.52884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.81511 | −1.12040 | −0.560198 | − | 0.828358i | \(-0.689275\pi\) | ||||
−0.560198 | + | 0.828358i | \(0.689275\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.86190 | 0.458270 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1828 | 1.59029 | 0.795145 | − | 0.606420i | \(-0.207395\pi\) | ||||
0.795145 | + | 0.606420i | \(0.207395\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.21385 | −0.490108 | −0.245054 | − | 0.969509i | \(-0.578806\pi\) | ||||
−0.245054 | + | 0.969509i | \(0.578806\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.86734 | −0.278367 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.3322 | −1.79884 | −0.899420 | − | 0.437085i | \(-0.856011\pi\) | ||||
−0.899420 | + | 0.437085i | \(0.856011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.4610 | 2.35157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.10878 | 0.435316 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.4625 | −1.84922 | −0.924610 | − | 0.380915i | \(-0.875609\pi\) | ||||
−0.924610 | + | 0.380915i | \(0.875609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.21930 | 1.24313 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.94897 | −0.258147 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.37852 | 0.179468 | 0.0897342 | − | 0.995966i | \(-0.471398\pi\) | ||||
0.0897342 | + | 0.995966i | \(0.471398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.44631 | −0.697329 | −0.348664 | − | 0.937248i | \(-0.613365\pi\) | ||||
−0.348664 | + | 0.937248i | \(0.613365\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.84365 | −0.610243 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.34413 | −0.662858 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.14327 | −0.506181 | −0.253090 | − | 0.967443i | \(-0.581447\pi\) | ||||
−0.253090 | + | 0.967443i | \(0.581447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2781 | −1.21979 | −0.609895 | − | 0.792482i | \(-0.708788\pi\) | ||||
−0.609895 | + | 0.792482i | \(0.708788\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.90515 | −0.574105 | −0.287052 | − | 0.957915i | \(-0.592675\pi\) | ||||
−0.287052 | + | 0.957915i | \(0.592675\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.51304 | −0.174711 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.9138 | 2.72523 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3997 | 1.17006 | 0.585029 | − | 0.811013i | \(-0.301083\pi\) | ||||
0.585029 | + | 0.811013i | \(0.301083\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7262 | 1.50665 | 0.753324 | − | 0.657649i | \(-0.228449\pi\) | ||||
0.753324 | + | 0.657649i | \(0.228449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.80514 | −0.629656 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.89306 | −0.200664 | −0.100332 | − | 0.994954i | \(-0.531991\pi\) | ||||
−0.100332 | + | 0.994954i | \(0.531991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.8620 | −1.45313 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.41813 | −0.561834 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.63939 | 0.373393 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.06388 | 0.615693 | 0.307847 | − | 0.951436i | \(-0.400392\pi\) | ||||
0.307847 | + | 0.951436i | \(0.400392\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.93713 | −0.496201 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.91628 | 0.787699 | 0.393850 | − | 0.919175i | \(-0.371143\pi\) | ||||
0.393850 | + | 0.919175i | \(0.371143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.03978 | 0.890716 | 0.445358 | − | 0.895353i | \(-0.353076\pi\) | ||||
0.445358 | + | 0.895353i | \(0.353076\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.04474 | 0.882676 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.79071 | −0.946504 | −0.473252 | − | 0.880927i | \(-0.656920\pi\) | ||||
−0.473252 | + | 0.880927i | \(0.656920\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4248 | 1.38164 | 0.690822 | − | 0.723025i | \(-0.257249\pi\) | ||||
0.690822 | + | 0.723025i | \(0.257249\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.81511 | −0.646861 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00311 | 0.564725 | 0.282363 | − | 0.959308i | \(-0.408882\pi\) | ||||
0.282363 | + | 0.959308i | \(0.408882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.86734 | −0.174130 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.86190 | 0.264582 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.0578 | −1.38035 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.3753 | 1.21594 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.1828 | 0.918154 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1621 | 1.08781 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.05286 | −0.359633 | −0.179816 | − | 0.983700i | \(-0.557550\pi\) | ||||
−0.179816 | + | 0.983700i | \(0.557550\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.21385 | −0.282964 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.69396 | 0.322742 | 0.161371 | − | 0.986894i | \(-0.448408\pi\) | ||||
0.161371 | + | 0.986894i | \(0.448408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.44013 | 0.818563 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.86734 | −0.160715 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.8480 | −1.26855 | −0.634274 | − | 0.773109i | \(-0.718701\pi\) | ||||
−0.634274 | + | 0.773109i | \(0.718701\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.753509 | −0.0639118 | −0.0319559 | − | 0.999489i | \(-0.510174\pi\) | ||||
−0.0319559 | + | 0.999489i | \(0.510174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.3322 | −1.03856 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.1296 | −1.18157 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.86734 | 0.155074 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.4610 | 1.35768 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.0823 | 1.56328 | 0.781641 | − | 0.623729i | \(-0.214383\pi\) | ||||
0.781641 | + | 0.623729i | \(0.214383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9551 | 0.972895 | 0.486448 | − | 0.873710i | \(-0.338292\pi\) | ||||
0.486448 | + | 0.873710i | \(0.338292\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.10878 | 0.251330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.1175 | 0.812657 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.855906 | 0.0683088 | 0.0341544 | − | 0.999417i | \(-0.489126\pi\) | ||||
0.0341544 | + | 0.999417i | \(0.489126\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.4625 | −1.06765 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.84365 | −0.381733 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.9613 | 1.48516 | 0.742580 | − | 0.669757i | \(-0.233602\pi\) | ||||
0.742580 | + | 0.669757i | \(0.233602\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.21930 | 0.717722 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.5645 | −1.28180 | −0.640900 | − | 0.767625i | \(-0.721439\pi\) | ||||
−0.640900 | + | 0.767625i | \(0.721439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.80956 | −0.369966 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.94897 | −0.149041 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.8644 | 1.81438 | 0.907189 | − | 0.420723i | \(-0.138224\pi\) | ||||
0.907189 | + | 0.420723i | \(0.138224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.32865 | 0.553994 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.37852 | 0.103616 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2293 | 0.914062 | 0.457031 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457031 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6427 | 0.865393 | 0.432696 | − | 0.901540i | \(-0.357562\pi\) | ||||
0.432696 | + | 0.901540i | \(0.357562\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.44631 | −0.402603 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.7261 | 0.935643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.3484 | −1.12239 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.84365 | −0.352324 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.9093 | −1.65766 | −0.828829 | − | 0.559502i | \(-0.810992\pi\) | ||||
−0.828829 | + | 0.559502i | \(0.810992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.0630 | 1.37219 | 0.686094 | − | 0.727513i | \(-0.259324\pi\) | ||||
0.686094 | + | 0.727513i | \(0.259324\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.34413 | −0.382701 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.4760 | −0.888880 | −0.444440 | − | 0.895809i | \(-0.646597\pi\) | ||||
−0.444440 | + | 0.895809i | \(0.646597\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.5233 | −1.45486 | −0.727428 | − | 0.686184i | \(-0.759284\pi\) | ||||
−0.727428 | + | 0.686184i | \(0.759284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.14327 | −0.292244 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.84365 | 0.339958 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0148 | −1.32805 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.62233 | 0.665590 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.5670 | 1.20936 | 0.604682 | − | 0.796467i | \(-0.293300\pi\) | ||||
0.604682 | + | 0.796467i | \(0.293300\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.2781 | −0.704246 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.00136 | 0.409289 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.2436 | 1.78153 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.90515 | −0.331460 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.89699 | 0.598477 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.8503 | 0.994451 | 0.497225 | − | 0.867621i | \(-0.334352\pi\) | ||||
0.497225 | + | 0.867621i | \(0.334352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.51304 | −0.100870 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.04076 | −0.533684 | −0.266842 | − | 0.963740i | \(-0.585980\pi\) | ||||
−0.266842 | + | 0.963740i | \(0.585980\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8993 | 0.852409 | 0.426204 | − | 0.904627i | \(-0.359850\pi\) | ||||
0.426204 | + | 0.904627i | \(0.359850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.9138 | 1.57341 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.3045 | 1.59224 | 0.796120 | − | 0.605138i | \(-0.206882\pi\) | ||||
0.796120 | + | 0.605138i | \(0.206882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.0285 | 1.50221 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.3997 | 0.675533 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.62036 | −0.298867 | −0.149433 | − | 0.988772i | \(-0.547745\pi\) | ||||
−0.149433 | + | 0.988772i | \(0.547745\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3930 | 0.669472 | 0.334736 | − | 0.942312i | \(-0.391353\pi\) | ||||
0.334736 | + | 0.942312i | \(0.391353\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30.7382 | −1.96379 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.57775 | −0.354904 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.7262 | 0.869864 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.33210 | 0.210320 | 0.105160 | − | 0.994455i | \(-0.466464\pi\) | ||||
0.105160 | + | 0.994455i | \(0.466464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.93713 | −0.310395 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.80514 | −0.363532 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.5424 | −0.844749 | −0.422375 | − | 0.906421i | \(-0.638803\pi\) | ||||
−0.422375 | + | 0.906421i | \(0.638803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.0100 | 2.05114 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.2268 | 1.43222 | 0.716112 | − | 0.697986i | \(-0.245920\pi\) | ||||
0.716112 | + | 0.697986i | \(0.245920\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.1391 | 1.54428 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.89306 | −0.115854 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5605 | 1.00971 | 0.504855 | − | 0.863204i | \(-0.331546\pi\) | ||||
0.504855 | + | 0.863204i | \(0.331546\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.2844 | 1.71815 | 0.859077 | − | 0.511847i | \(-0.171038\pi\) | ||||
0.859077 | + | 0.511847i | \(0.171038\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.8620 | −0.838968 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.47010 | 0.450464 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.3786 | 0.683675 | 0.341838 | − | 0.939759i | \(-0.388951\pi\) | ||||
0.341838 | + | 0.939759i | \(0.388951\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.41813 | −0.324375 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.08816 | 0.482499 | 0.241249 | − | 0.970463i | \(-0.422443\pi\) | ||||
0.241249 | + | 0.970463i | \(0.422443\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.42987 | 0.441660 | 0.220830 | − | 0.975312i | \(-0.429123\pi\) | ||||
0.220830 | + | 0.975312i | \(0.429123\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.63939 | 0.215579 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −49.3220 | −2.91139 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.33551 | −0.431500 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.06388 | 0.355471 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1144 | −0.649312 | −0.324656 | − | 0.945832i | \(-0.605249\pi\) | ||||
−0.324656 | + | 0.945832i | \(0.605249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.57417 | −0.149874 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.93713 | −0.286482 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.86190 | 0.165508 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.5668 | 0.897255 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.91628 | 0.454778 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.1701 | 0.582339 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.59206 | 0.376229 | 0.188114 | − | 0.982147i | \(-0.439762\pi\) | ||||
0.188114 | + | 0.982147i | \(0.439762\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.03978 | 0.514255 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.87943 | 0.106573 | 0.0532863 | − | 0.998579i | \(-0.483030\pi\) | ||||
0.0532863 | + | 0.998579i | \(0.483030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.4792 | 1.44017 | 0.720086 | − | 0.693885i | \(-0.244102\pi\) | ||||
0.720086 | + | 0.693885i | \(0.244102\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.04474 | 0.509613 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.0671 | −0.677755 | −0.338878 | − | 0.940830i | \(-0.610047\pi\) | ||||
−0.338878 | + | 0.940830i | \(0.610047\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.93713 | 0.276426 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.79071 | −0.546464 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.05891 | −0.337127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.33017 | −0.240195 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.4248 | 0.797693 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 59.7330 | 3.29319 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.5193 | −1.89735 | −0.948676 | − | 0.316251i | \(-0.897576\pi\) | ||||
−0.948676 | + | 0.316251i | \(0.897576\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.81511 | −0.373466 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.73689 | 0.422711 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.8494 | −1.35364 | −0.676818 | − | 0.736151i | \(-0.736641\pi\) | ||||
−0.676818 | + | 0.736151i | \(0.736641\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00311 | 0.326044 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.7501 | 1.44860 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −45.8256 | −2.47435 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.86734 | −0.100534 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.8748 | 0.852205 | 0.426103 | − | 0.904675i | \(-0.359886\pi\) | ||||
0.426103 | + | 0.904675i | \(0.359886\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.4659 | 0.827873 | 0.413936 | − | 0.910306i | \(-0.364154\pi\) | ||||
0.413936 | + | 0.910306i | \(0.364154\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.86190 | 0.152757 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.502338 | −0.0267368 | −0.0133684 | − | 0.999911i | \(-0.504255\pi\) | ||||
−0.0133684 | + | 0.999911i | \(0.504255\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.1928 | 1.01865 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.0578 | −0.796945 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.7686 | −1.36001 | −0.680007 | − | 0.733205i | \(-0.738023\pi\) | ||||
−0.680007 | + | 0.733205i | \(0.738023\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2015 | −0.800080 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.3753 | 0.702021 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.15959 | 0.479435 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.9152 | 1.45716 | 0.728581 | − | 0.684960i | \(-0.240180\pi\) | ||||
0.728581 | + | 0.684960i | \(0.240180\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.1828 | 0.530096 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 65.2078 | 3.38542 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.6994 | −1.84844 | −0.924222 | − | 0.381856i | \(-0.875285\pi\) | ||||
−0.924222 | + | 0.381856i | \(0.875285\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.1621 | 0.628046 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.86190 | −0.147395 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.69150 | 0.0868864 | 0.0434432 | − | 0.999056i | \(-0.486167\pi\) | ||||
0.0434432 | + | 0.999056i | \(0.486167\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.05286 | −0.207634 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.91105 | −0.506431 | −0.253216 | − | 0.967410i | \(-0.581488\pi\) | ||||
−0.253216 | + | 0.967410i | \(0.581488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −44.6551 | −2.27583 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.21385 | −0.163369 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.1451 | 1.17350 | 0.586752 | − | 0.809767i | \(-0.300406\pi\) | ||||
0.586752 | + | 0.809767i | \(0.300406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.10878 | 0.157218 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.69396 | 0.186335 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.4198 | −0.977115 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4833 | −0.676708 | −0.338354 | − | 0.941019i | \(-0.609870\pi\) | ||||
−0.338354 | + | 0.941019i | \(0.609870\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.44013 | 0.472598 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −39.5347 | −1.97427 | −0.987133 | − | 0.159900i | \(-0.948883\pi\) | ||||
−0.987133 | + | 0.159900i | \(0.948883\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.5061 | −0.772415 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.86734 | −0.0927888 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.6471 | 1.66782 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.56923 | 0.423721 | 0.211860 | − | 0.977300i | \(-0.432048\pi\) | ||||
0.211860 | + | 0.977300i | \(0.432048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.8480 | −0.732396 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.67708 | −0.328558 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.6315 | −1.25820 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.753509 | −0.0368995 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1207 | −0.885254 | −0.442627 | − | 0.896706i | \(-0.645953\pi\) | ||||
−0.442627 | + | 0.896706i | \(0.645953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.8733 | −1.11477 | −0.557387 | − | 0.830253i | \(-0.688196\pi\) | ||||
−0.557387 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.3322 | −0.599614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.70371 | −0.228164 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.3800 | 1.27662 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.1296 | −0.682182 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.8383 | −0.811074 | −0.405537 | − | 0.914079i | \(-0.632916\pi\) | ||||
−0.405537 | + | 0.914079i | \(0.632916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.6268 | 1.61600 | 0.808001 | − | 0.589181i | \(-0.200550\pi\) | ||||
0.808001 | + | 0.589181i | \(0.200550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.86734 | 0.0895321 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.94897 | −0.0932319 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.3416 | −0.875396 | −0.437698 | − | 0.899122i | \(-0.644206\pi\) | ||||
−0.437698 | + | 0.899122i | \(0.644206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.4610 | 0.783855 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0952 | −1.14480 | −0.572400 | − | 0.819975i | \(-0.693987\pi\) | ||||
−0.572400 | + | 0.819975i | \(0.693987\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.53499 | 0.167575 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.0823 | 0.902561 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.45100 | 0.210056 | 0.105028 | − | 0.994469i | \(-0.466507\pi\) | ||||
0.105028 | + | 0.994469i | \(0.466507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −50.2739 | −2.36731 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.9551 | 0.561701 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.8851 | 1.21351 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6804 | −1.10772 | −0.553860 | − | 0.832610i | \(-0.686846\pi\) | ||||
−0.553860 | + | 0.832610i | \(0.686846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.10878 | 0.145105 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.913736 | −0.0425569 | −0.0212785 | − | 0.999774i | \(-0.506774\pi\) | ||||
−0.0212785 | + | 0.999774i | \(0.506774\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5722 | 0.584279 | 0.292139 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292139 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.1175 | 0.469188 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.2992 | −0.615415 | −0.307708 | − | 0.951481i | \(-0.599562\pi\) | ||||
−0.307708 | + | 0.951481i | \(0.599562\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0686 | 0.926680 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.855906 | 0.0394381 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.8672 | 0.729576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.94888 | 0.135304 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4625 | −0.616407 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.7874 | 1.36102 | 0.680512 | − | 0.732737i | \(-0.261758\pi\) | ||||
0.680512 | + | 0.732737i | \(0.261758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.5041 | −0.889312 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.84365 | −0.220394 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.3233 | −0.514165 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.21942 | −0.0552574 | −0.0276287 | − | 0.999618i | \(-0.508796\pi\) | ||||
−0.0276287 | + | 0.999618i | \(0.508796\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.9613 | 0.857458 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.5778 | 1.60560 | 0.802802 | − | 0.596246i | \(-0.203342\pi\) | ||||
0.802802 | + | 0.596246i | \(0.203342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.10878 | −0.140012 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.21930 | 0.414377 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 49.7837 | 2.23310 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1010 | −0.541716 | −0.270858 | − | 0.962619i | \(-0.587307\pi\) | ||||
−0.270858 | + | 0.962619i | \(0.587307\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.5645 | −0.740047 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.26150 | 0.100835 | 0.0504176 | − | 0.998728i | \(-0.483945\pi\) | ||||
0.0504176 | + | 0.998728i | \(0.483945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.7824 | −0.657807 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.80956 | −0.213600 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.5346 | −1.39775 | −0.698874 | − | 0.715245i | \(-0.746315\pi\) | ||||
−0.698874 | + | 0.715245i | \(0.746315\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.7589 | 1.05103 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.94897 | −0.0860491 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.8803 | −0.743837 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 60.8859 | 2.67776 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.8644 | 1.04753 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6095 | 0.552434 | 0.276217 | − | 0.961095i | \(-0.410919\pi\) | ||||
0.276217 | + | 0.961095i | \(0.410919\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.7998 | −1.21560 | −0.607800 | − | 0.794090i | \(-0.707948\pi\) | ||||
−0.607800 | + | 0.794090i | \(0.707948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.32865 | 0.319849 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.8438 | −0.733726 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.37852 | 0.0598228 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.1422 | 1.26229 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.2826 | 0.790425 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.2293 | 0.527734 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −81.2699 | −3.50054 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.3620 | −1.43435 | −0.717173 | − | 0.696895i | \(-0.754564\pi\) | ||||
−0.717173 | + | 0.696895i | \(0.754564\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.6427 | 0.499635 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.9360 | −1.15381 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.9906 | 1.70988 | 0.854938 | − | 0.518731i | \(-0.173595\pi\) | ||||
0.854938 | + | 0.518731i | \(0.173595\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.44631 | −0.232443 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.94897 | 0.0830289 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −50.3725 | −2.14206 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.7261 | 0.540194 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.84277 | −0.289937 | −0.144969 | − | 0.989436i | \(-0.546308\pi\) | ||||
−0.144969 | + | 0.989436i | \(0.546308\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.19771 | −0.389022 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.3484 | −0.648012 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.9084 | 0.628313 | 0.314156 | − | 0.949371i | \(-0.398278\pi\) | ||||
0.314156 | + | 0.949371i | \(0.398278\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.2099 | −0.471602 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.84365 | −0.203414 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.3870 | 1.19004 | 0.595022 | − | 0.803709i | \(-0.297143\pi\) | ||||
0.595022 | + | 0.803709i | \(0.297143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.9532 | −1.04426 | −0.522129 | − | 0.852866i | \(-0.674862\pi\) | ||||
−0.522129 | + | 0.852866i | \(0.674862\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.9093 | −0.957049 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.51304 | −0.0630983 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.5385 | 1.52112 | 0.760558 | − | 0.649270i | \(-0.224925\pi\) | ||||
0.760558 | + | 0.649270i | \(0.224925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.0630 | 0.792233 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −66.4850 | −2.75826 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 66.4663 | 2.75275 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.34413 | −0.220953 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.4432 | −0.926331 | −0.463166 | − | 0.886272i | \(-0.653286\pi\) | ||||
−0.463166 | + | 0.886272i | \(0.653286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5598 | 0.435108 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4760 | −0.513195 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.3577 | −1.53410 | −0.767049 | − | 0.641589i | \(-0.778276\pi\) | ||||
−0.767049 | + | 0.641589i | \(0.778276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.1181 | 1.15273 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.5233 | −0.839961 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.50787 | 0.184187 | 0.0920933 | − | 0.995750i | \(-0.470644\pi\) | ||||
0.0920933 | + | 0.995750i | \(0.470644\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.9181 | −0.812476 | −0.406238 | − | 0.913767i | \(-0.633160\pi\) | ||||
−0.406238 | + | 0.913767i | \(0.633160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.14327 | −0.168727 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.9762 | −1.01543 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.3046 | 0.621193 | 0.310596 | − | 0.950542i | \(-0.399471\pi\) | ||||
0.310596 | + | 0.950542i | \(0.399471\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.84365 | 0.196275 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.2936 | −1.42782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.9131 | −1.57168 | −0.785842 | − | 0.618427i | \(-0.787770\pi\) | ||||
−0.785842 | + | 0.618427i | \(0.787770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −19.0148 | −0.766750 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.8410 | −1.48316 | −0.741581 | − | 0.670863i | \(-0.765924\pi\) | ||||
−0.741581 | + | 0.670863i | \(0.765924\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.7922 | 1.92093 | 0.960464 | − | 0.278403i | \(-0.0898050\pi\) | ||||
0.960464 | + | 0.278403i | \(0.0898050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.16935 | 0.367362 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.1455 | −0.605819 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.62233 | 0.384279 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.1866 | −0.844767 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.4766 | −0.536495 | −0.268248 | − | 0.963350i | \(-0.586445\pi\) | ||||
−0.268248 | + | 0.963350i | \(0.586445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.5670 | 0.698226 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.56806 | 0.300329 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.1095 | 1.86655 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.2781 | −0.406597 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.8240 | −1.53345 | −0.766727 | − | 0.641973i | \(-0.778116\pi\) | ||||
−0.766727 | + | 0.641973i | \(0.778116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.2647 | 1.66676 | 0.833379 | − | 0.552702i | \(-0.186403\pi\) | ||||
0.833379 | + | 0.552702i | \(0.186403\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00136 | 0.236303 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.5267 | 0.492475 | 0.246237 | − | 0.969210i | \(-0.420806\pi\) | ||||
0.246237 | + | 0.969210i | \(0.420806\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.80595 | −0.267157 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.2436 | 1.02857 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.1492 | −0.475436 | −0.237718 | − | 0.971334i | \(-0.576399\pi\) | ||||
−0.237718 | + | 0.971334i | \(0.576399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.89787 | −0.269522 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.90515 | −0.191368 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.9303 | −1.59442 | −0.797210 | − | 0.603703i | \(-0.793691\pi\) | ||||
−0.797210 | + | 0.603703i | \(0.793691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.80196 | −0.225670 | −0.112835 | − | 0.993614i | \(-0.535993\pi\) | ||||
−0.112835 | + | 0.993614i | \(0.535993\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.89699 | 0.345531 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.6279 | −0.683582 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.8503 | 0.574146 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.8892 | 1.03804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.0266 | −1.04180 | −0.520899 | − | 0.853618i | \(-0.674403\pi\) | ||||
−0.520899 | + | 0.853618i | \(0.674403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.51304 | −0.0582371 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.3630 | −0.475148 | −0.237574 | − | 0.971369i | \(-0.576352\pi\) | ||||
−0.237574 | + | 0.971369i | \(0.576352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.3713 | −1.12717 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.04076 | −0.308123 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8193 | 0.681836 | 0.340918 | − | 0.940093i | \(-0.389262\pi\) | ||||
0.340918 | + | 0.940093i | \(0.389262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.7262 | 1.05936 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.8993 | 0.492138 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.5283 | −1.46781 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.55059 | 0.0970290 | 0.0485145 | − | 0.998822i | \(-0.484551\pi\) | ||||
0.0485145 | + | 0.998822i | \(0.484551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.9138 | 0.908408 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.40706 | 0.0533727 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.6561 | 1.19906 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.3045 | 0.919281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.99753 | −0.226524 | −0.113262 | − | 0.993565i | \(-0.536130\pi\) | ||||
−0.113262 | + | 0.993565i | \(0.536130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2824 | 0.500957 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.0285 | 0.867302 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.3437 | −1.44206 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.3497 | −0.764250 | −0.382125 | − | 0.924111i | \(-0.624808\pi\) | ||||
−0.382125 | + | 0.924111i | \(0.624808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.3997 | 0.390019 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.41813 | −0.202911 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.3847 | 0.986731 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.62036 | −0.172551 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.7200 | −0.698139 | −0.349069 | − | 0.937097i | \(-0.613502\pi\) | ||||
−0.349069 | + | 0.937097i | \(0.613502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.7855 | −1.63066 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.3930 | 0.386520 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.51304 | 0.0561930 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.6322 | 0.839381 | 0.419691 | − | 0.907667i | \(-0.362139\pi\) | ||||
0.419691 | + | 0.907667i | \(0.362139\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.99115 | −0.369536 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.5871 | 1.05589 | 0.527945 | − | 0.849279i | \(-0.322963\pi\) | ||||
0.527945 | + | 0.849279i | \(0.322963\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −30.7382 | −1.13380 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.4559 | 0.753502 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0224 | 0.883679 | 0.441839 | − | 0.897094i | \(-0.354326\pi\) | ||||
0.441839 | + | 0.897094i | \(0.354326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.57775 | −0.204904 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.7880 | −1.12950 | −0.564752 | − | 0.825261i | \(-0.691028\pi\) | ||||
−0.564752 | + | 0.825261i | \(0.691028\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.6331 | −1.30550 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.7262 | 0.502216 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 47.4228 | 1.73279 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.5105 | 1.36878 | 0.684388 | − | 0.729118i | \(-0.260070\pi\) | ||||
0.684388 | + | 0.729118i | \(0.260070\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.33210 | 0.121429 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.3243 | −0.812464 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.92889 | −0.0701067 | −0.0350533 | − | 0.999385i | \(-0.511160\pi\) | ||||
−0.0350533 | + | 0.999385i | \(0.511160\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.93713 | −0.179207 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.2430 | −0.480059 | −0.240030 | − | 0.970766i | \(-0.577157\pi\) | ||||
−0.240030 | + | 0.970766i | \(0.577157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −69.8687 | −2.52942 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.80514 | −0.209885 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.94519 | 0.142452 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.5343 | 0.740485 | 0.370242 | − | 0.928935i | \(-0.379275\pi\) | ||||
0.370242 | + | 0.928935i | \(0.379275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.5424 | −0.487716 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.422817 | 0.0152077 | 0.00760384 | − | 0.999971i | \(-0.497580\pi\) | ||||
0.00760384 | + | 0.999971i | \(0.497580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.19787 | 0.294476 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 33.0100 | 1.18423 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.8460 | −0.711057 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.7445 | 1.81578 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.59827 | −0.0570446 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.8110 | 1.81122 | 0.905608 | − | 0.424116i | \(-0.139415\pi\) | ||||
0.905608 | + | 0.424116i | \(0.139415\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.2268 | 0.826895 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.0770 | −1.03386 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.5868 | −0.553502 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.1391 | 0.891592 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.0840 | −0.534303 | −0.267151 | − | 0.963655i | \(-0.586082\pi\) | ||||
−0.267151 | + | 0.963655i | \(0.586082\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.3382 | −1.35631 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.89306 | −0.0668882 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.2174 | 0.854613 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.04474 | 0.318785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.5605 | 0.582957 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.8924 | −1.01580 | −0.507902 | − | 0.861415i | \(-0.669579\pi\) | ||||
−0.507902 | + | 0.861415i | \(0.669579\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.2287 | −0.394294 | −0.197147 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197147 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.2844 | 0.991977 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.4071 | −1.24026 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.26370 | 0.219139 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.8620 | −0.484378 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.1064 | 1.08562 | 0.542811 | − | 0.839855i | \(-0.317360\pi\) | ||||
0.542811 | + | 0.839855i | \(0.317360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.8374 | −0.517198 | −0.258599 | − | 0.965985i | \(-0.583261\pi\) | ||||
−0.258599 | + | 0.965985i | \(0.583261\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.47010 | 0.260075 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.1314 | 0.978224 | 0.489112 | − | 0.872221i | \(-0.337321\pi\) | ||||
0.489112 | + | 0.872221i | \(0.337321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.6051 | 1.02823 | 0.514113 | − | 0.857722i | \(-0.328121\pi\) | ||||
0.514113 | + | 0.857722i | \(0.328121\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.3786 | 0.394720 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 51.1734 | 1.77305 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.9315 | 1.07043 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.41813 | −0.187278 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.4631 | 1.29337 | 0.646684 | − | 0.762758i | \(-0.276155\pi\) | ||||
0.646684 | + | 0.762758i | \(0.276155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.08816 | 0.278571 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.98107 | 0.308958 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −64.7852 | −2.22605 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.42987 | 0.254993 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.81511 | −0.233619 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.37850 | −0.286874 | −0.143437 | − | 0.989659i | \(-0.545815\pi\) | ||||
−0.143437 | + | 0.989659i | \(0.545815\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.63939 | 0.124464 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.4602 | −1.79201 | −0.896003 | − | 0.444047i | \(-0.853542\pi\) | ||||
−0.896003 | + | 0.444047i | \(0.853542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.570326 | 0.0194593 | 0.00972964 | − | 0.999953i | \(-0.496903\pi\) | ||||
0.00972964 | + | 0.999953i | \(0.496903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −49.3220 | −1.68089 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.9161 | 0.746034 | 0.373017 | − | 0.927825i | \(-0.378323\pi\) | ||||
0.373017 | + | 0.927825i | \(0.378323\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.5630 | −1.51519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.33551 | −0.249127 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.3447 | −1.74175 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.8576 | −0.401780 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.06388 | 0.205231 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −58.9088 | −1.99148 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.4269 | 1.33135 | 0.665676 | − | 0.746241i | \(-0.268143\pi\) | ||||
0.665676 | + | 0.746241i | \(0.268143\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.1144 | −0.374881 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.7692 | −0.362824 | −0.181412 | − | 0.983407i | \(-0.558067\pi\) | ||||
−0.181412 | + | 0.983407i | \(0.558067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.56188 | −0.220825 | −0.110412 | − | 0.993886i | \(-0.535217\pi\) | ||||
−0.110412 | + | 0.993886i | \(0.535217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.57417 | −0.0865298 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.2217 | −0.914016 | −0.457008 | − | 0.889463i | \(-0.651079\pi\) | ||||
−0.457008 | + | 0.889463i | \(0.651079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.6306 | 0.658390 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.93713 | −0.165400 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.0352 | 0.804306 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.8363 | −0.763333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.86190 | 0.0955559 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.41813 | 0.180705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.8520 | −1.39429 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.5668 | 0.518030 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.7408 | −0.722689 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.2816 | −0.407804 | −0.203902 | − | 0.978991i | \(-0.565362\pi\) | ||||
−0.203902 | + | 0.978991i | \(0.565362\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.91628 | 0.262566 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.9611 | −1.09205 | −0.546025 | − | 0.837769i | \(-0.683860\pi\) | ||||
−0.546025 | + | 0.837769i | \(0.683860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −67.7682 | −2.24280 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.1701 | 0.336213 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.8922 | −0.590854 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.3611 | −1.59528 | −0.797642 | − | 0.603131i | \(-0.793920\pi\) | ||||
−0.797642 | + | 0.603131i | \(0.793920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.59206 | 0.217216 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.4149 | −0.968204 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.3116 | 0.339042 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.03978 | 0.296905 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.4504 | 1.45837 | 0.729185 | − | 0.684316i | \(-0.239899\pi\) | ||||
0.729185 | + | 0.684316i | \(0.239899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.0819 | −1.05144 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.87943 | 0.0615297 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.6608 | 0.937307 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.4331 | 0.700190 | 0.350095 | − | 0.936714i | \(-0.386149\pi\) | ||||
0.350095 | + | 0.936714i | \(0.386149\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.4792 | 0.831483 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.6533 | 0.510282 | 0.255141 | − | 0.966904i | \(-0.417878\pi\) | ||||
0.255141 | + | 0.966904i | \(0.417878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1828 | 0.331598 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.04474 | 0.294225 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.8996 | 0.484173 | 0.242087 | − | 0.970255i | \(-0.422168\pi\) | ||||
0.242087 | + | 0.970255i | \(0.422168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0380 | −0.455694 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0671 | −0.391302 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.3059 | 1.40281 | 0.701407 | − | 0.712761i | \(-0.252555\pi\) | ||||
0.701407 | + | 0.712761i | \(0.252555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.7794 | 1.38431 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.93713 | 0.159595 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 71.9184 | 2.32237 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.64382 | −0.0530265 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.79071 | −0.315501 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.5972 | −1.14591 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.8380 | −1.05600 | −0.527999 | − | 0.849245i | \(-0.677057\pi\) | ||||
−0.527999 | + | 0.849245i | \(0.677057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.05891 | −0.194640 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.2710 | −1.06772 | −0.533859 | − | 0.845574i | \(-0.679259\pi\) | ||||
−0.533859 | + | 0.845574i | \(0.679259\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.64973 | 0.117005 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.33017 | −0.138676 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.8741 | 1.72359 | 0.861793 | − | 0.507260i | \(-0.169342\pi\) | ||||
0.861793 | + | 0.507260i | \(0.169342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.34631 | 0.298709 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4248 | 0.460548 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.9078 | −0.890120 | −0.445060 | − | 0.895501i | \(-0.646818\pi\) | ||||
−0.445060 | + | 0.895501i | \(0.646818\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.2970 | 0.742303 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 59.7330 | 1.90132 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.21385 | −0.102195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.94439 | 0.157064 | 0.0785318 | − | 0.996912i | \(-0.474977\pi\) | ||||
0.0785318 | + | 0.996912i | \(0.474977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.5193 | −1.09544 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.3239 | 1.21495 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.56994 | 0.113061 | 0.0565306 | − | 0.998401i | \(-0.481996\pi\) | ||||
0.0565306 | + | 0.998401i | \(0.481996\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.81511 | −0.215620 |
(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 | 8004.2.a.j.1.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.j.1.5 | ✓ | 16 | 1.1 | even | 1 | trivial |