Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, 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("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.253565184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 20x^{3} + 22x^{2} - 32x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.84742\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | 2.84742 | 1.64396 | 0.821980 | − | 0.569516i | \(-0.192869\pi\) | ||||
0.821980 | + | 0.569516i | \(0.192869\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.145034 | 0.0548179 | 0.0274089 | − | 0.999624i | \(-0.491274\pi\) | ||||
0.0274089 | + | 0.999624i | \(0.491274\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.10782 | 1.70261 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.71774 | −1.72396 | −0.861982 | − | 0.506938i | \(-0.830777\pi\) | ||||
−0.861982 | + | 0.506938i | \(0.830777\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.24345 | −1.45427 | −0.727136 | − | 0.686493i | \(-0.759149\pi\) | ||||
−0.727136 | + | 0.686493i | \(0.759149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.15378 | −1.73505 | −0.867524 | − | 0.497396i | \(-0.834290\pi\) | ||||
−0.867524 | + | 0.497396i | \(0.834290\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.412974 | 0.0901184 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.622762 | 0.129855 | 0.0649274 | − | 0.997890i | \(-0.479318\pi\) | ||||
0.0649274 | + | 0.997890i | \(0.479318\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.00186 | 1.15506 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.46811 | −1.01540 | −0.507702 | − | 0.861533i | \(-0.669505\pi\) | ||||
−0.507702 | + | 0.861533i | \(0.669505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.77513 | −0.678033 | −0.339017 | − | 0.940780i | \(-0.610094\pi\) | ||||
−0.339017 | + | 0.940780i | \(0.610094\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −16.2808 | −2.83413 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.03553 | 0.827836 | 0.413918 | − | 0.910314i | \(-0.364160\pi\) | ||||
0.413918 | + | 0.910314i | \(0.364160\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.9303 | −2.39077 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.77513 | 0.901924 | 0.450962 | − | 0.892543i | \(-0.351081\pi\) | ||||
0.450962 | + | 0.892543i | \(0.351081\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.32308 | 0.506765 | 0.253382 | − | 0.967366i | \(-0.418457\pi\) | ||||
0.253382 | + | 0.967366i | \(0.418457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.85683 | −0.854306 | −0.427153 | − | 0.904179i | \(-0.640483\pi\) | ||||
−0.427153 | + | 0.904179i | \(0.640483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.97897 | −0.996995 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20.3699 | −2.85235 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.97219 | 0.957704 | 0.478852 | − | 0.877896i | \(-0.341053\pi\) | ||||
0.478852 | + | 0.877896i | \(0.341053\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.84742 | 0.377150 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.09089 | 1.18353 | 0.591767 | − | 0.806109i | \(-0.298431\pi\) | ||||
0.591767 | + | 0.806109i | \(0.298431\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.16707 | −1.04569 | −0.522843 | − | 0.852429i | \(-0.675129\pi\) | ||||
−0.522843 | + | 0.852429i | \(0.675129\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.740810 | 0.0933333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6583 | −1.66863 | −0.834313 | − | 0.551291i | \(-0.814135\pi\) | ||||
−0.834313 | + | 0.551291i | \(0.814135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.77327 | 0.213476 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.41484 | 0.286588 | 0.143294 | − | 0.989680i | \(-0.454230\pi\) | ||||
0.143294 | + | 0.989680i | \(0.454230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.44385 | −0.871237 | −0.435619 | − | 0.900131i | \(-0.643470\pi\) | ||||
−0.435619 | + | 0.900131i | \(0.643470\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.829270 | −0.0945041 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.69485 | −1.09076 | −0.545378 | − | 0.838190i | \(-0.683614\pi\) | ||||
−0.545378 | + | 0.838190i | \(0.683614\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.76638 | 0.196264 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.17116 | 0.238316 | 0.119158 | − | 0.992875i | \(-0.461981\pi\) | ||||
0.119158 | + | 0.992875i | \(0.461981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.5700 | −1.66928 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.90782 | 0.414228 | 0.207114 | − | 0.978317i | \(-0.433593\pi\) | ||||
0.207114 | + | 0.978317i | \(0.433593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.760481 | −0.0797201 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.7494 | −1.11466 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.98328 | −0.505976 | −0.252988 | − | 0.967469i | \(-0.581413\pi\) | ||||
−0.252988 | + | 0.967469i | \(0.581413\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −29.2052 | −2.93524 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.35148 | −0.532493 | −0.266246 | − | 0.963905i | \(-0.585783\pi\) | ||||
−0.266246 | + | 0.963905i | \(0.585783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.59495 | 0.354221 | 0.177111 | − | 0.984191i | \(-0.443325\pi\) | ||||
0.177111 | + | 0.984191i | \(0.443325\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3518 | 1.48412 | 0.742059 | − | 0.670335i | \(-0.233850\pi\) | ||||
0.742059 | + | 0.670335i | \(0.233850\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.20105 | 0.210823 | 0.105411 | − | 0.994429i | \(-0.466384\pi\) | ||||
0.105411 | + | 0.994429i | \(0.466384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.3383 | 1.36093 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.3613 | 1.16286 | 0.581428 | − | 0.813598i | \(-0.302494\pi\) | ||||
0.581428 | + | 0.813598i | \(0.302494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −26.7826 | −2.47605 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.03754 | −0.0951116 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.6926 | 1.97205 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.4442 | 1.48273 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.0907 | −1.60529 | −0.802644 | − | 0.596459i | \(-0.796574\pi\) | ||||
−0.802644 | + | 0.596459i | \(0.796574\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.46222 | 0.833102 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1244 | 1.05931 | 0.529655 | − | 0.848213i | \(-0.322321\pi\) | ||||
0.529655 | + | 0.848213i | \(0.322321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.145034 | 0.0125761 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.0385 | 1.71201 | 0.856004 | − | 0.516969i | \(-0.172940\pi\) | ||||
0.856004 | + | 0.516969i | \(0.172940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3996 | 0.966905 | 0.483452 | − | 0.875371i | \(-0.339383\pi\) | ||||
0.483452 | + | 0.875371i | \(0.339383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.6769 | −1.40445 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.9807 | 2.50711 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19.8721 | −1.63902 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.5818 | −1.27651 | −0.638257 | − | 0.769823i | \(-0.720344\pi\) | ||||
−0.638257 | + | 0.769823i | \(0.720344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.3717 | 1.82058 | 0.910292 | − | 0.413966i | \(-0.135857\pi\) | ||||
0.910292 | + | 0.413966i | \(0.135857\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −36.5403 | −2.95410 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.1047 | −1.84395 | −0.921976 | − | 0.387246i | \(-0.873426\pi\) | ||||
−0.921976 | + | 0.387246i | \(0.873426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.8528 | 1.57443 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0903219 | 0.00711836 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3524 | −0.889186 | −0.444593 | − | 0.895733i | \(-0.646652\pi\) | ||||
−0.444593 | + | 0.895733i | \(0.646652\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.09989 | −0.472024 | −0.236012 | − | 0.971750i | \(-0.575840\pi\) | ||||
−0.236012 | + | 0.971750i | \(0.575840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4938 | 1.11491 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.10782 | 0.390605 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8951 | 0.828338 | 0.414169 | − | 0.910200i | \(-0.364072\pi\) | ||||
0.414169 | + | 0.910200i | \(0.364072\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.8856 | 1.94568 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.46123 | 0.333448 | 0.166724 | − | 0.986004i | \(-0.446681\pi\) | ||||
0.166724 | + | 0.986004i | \(0.446681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.58784 | 0.266682 | 0.133341 | − | 0.991070i | \(-0.457429\pi\) | ||||
0.133341 | + | 0.991070i | \(0.457429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.2551 | −1.71907 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 40.9035 | 2.99116 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.870477 | 0.0633179 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00777 | 0.579422 | 0.289711 | − | 0.957114i | \(-0.406441\pi\) | ||||
0.289711 | + | 0.957114i | \(0.406441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.45641 | 0.104835 | 0.0524173 | − | 0.998625i | \(-0.483307\pi\) | ||||
0.0524173 | + | 0.998625i | \(0.483307\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.3510 | −1.87743 | −0.938716 | − | 0.344692i | \(-0.887983\pi\) | ||||
−0.938716 | + | 0.344692i | \(0.887983\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.1739 | 0.862985 | 0.431492 | − | 0.902117i | \(-0.357987\pi\) | ||||
0.431492 | + | 0.902117i | \(0.357987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −38.8909 | −2.74316 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.793065 | −0.0556622 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.18096 | 0.221092 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.71774 | −0.395505 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5088 | −1.34304 | −0.671521 | − | 0.740985i | \(-0.734359\pi\) | ||||
−0.671521 | + | 0.740985i | \(0.734359\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.87606 | 0.471140 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.547524 | −0.0371683 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.1958 | −1.43228 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.5105 | 2.52323 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.9208 | −0.999168 | −0.499584 | − | 0.866265i | \(-0.666514\pi\) | ||||
−0.499584 | + | 0.866265i | \(0.666514\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.4422 | −0.892192 | −0.446096 | − | 0.894985i | \(-0.647186\pi\) | ||||
−0.446096 | + | 0.894985i | \(0.647186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.36620 | −0.486772 | −0.243386 | − | 0.969929i | \(-0.578258\pi\) | ||||
−0.243386 | + | 0.969929i | \(0.578258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.36128 | −0.155361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.24405 | −0.278037 | −0.139018 | − | 0.990290i | \(-0.544395\pi\) | ||||
−0.139018 | + | 0.990290i | \(0.544395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.6053 | −1.79316 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3387 | −0.992176 | −0.496088 | − | 0.868272i | \(-0.665231\pi\) | ||||
−0.496088 | + | 0.868272i | \(0.665231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.7026 | 1.72006 | 0.860032 | − | 0.510240i | \(-0.170443\pi\) | ||||
0.860032 | + | 0.510240i | \(0.170443\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.9760 | −0.832408 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.24345 | −0.333633 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.18221 | 0.391781 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.64463 | 0.230047 | 0.115023 | − | 0.993363i | \(-0.463306\pi\) | ||||
0.115023 | + | 0.993363i | \(0.463306\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.56079 | −0.223865 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.71103 | −0.605757 | −0.302879 | − | 0.953029i | \(-0.597948\pi\) | ||||
−0.302879 | + | 0.953029i | \(0.597948\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.730325 | 0.0453802 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.9302 | −1.72883 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.82052 | 0.112258 | 0.0561290 | − | 0.998424i | \(-0.482124\pi\) | ||||
0.0561290 | + | 0.998424i | \(0.482124\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.1272 | 0.680974 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.6353 | 1.31913 | 0.659563 | − | 0.751649i | \(-0.270741\pi\) | ||||
0.659563 | + | 0.751649i | \(0.270741\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.54436 | −0.458287 | −0.229144 | − | 0.973393i | \(-0.573593\pi\) | ||||
−0.229144 | + | 0.973393i | \(0.573593\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.16541 | −0.131057 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5559 | 0.754410 | 0.377205 | − | 0.926130i | \(-0.376885\pi\) | ||||
0.377205 | + | 0.926130i | \(0.376885\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.2827 | −1.15442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.1947 | 1.32403 | 0.662013 | − | 0.749493i | \(-0.269703\pi\) | ||||
0.662013 | + | 0.749493i | \(0.269703\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.6171 | −1.22556 | −0.612779 | − | 0.790254i | \(-0.709948\pi\) | ||||
−0.612779 | + | 0.790254i | \(0.709948\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.837592 | 0.0494415 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.1766 | 2.01039 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.1895 | −0.831804 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.1421 | −1.29356 | −0.646778 | − | 0.762679i | \(-0.723884\pi\) | ||||
−0.646778 | + | 0.762679i | \(0.723884\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −34.3171 | −1.99128 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.26542 | −0.188844 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.481961 | 0.0277798 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.2379 | −0.875397 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.80060 | 0.102766 | 0.0513828 | − | 0.998679i | \(-0.483637\pi\) | ||||
0.0513828 | + | 0.998679i | \(0.483637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.2364 | 0.582326 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.26554 | −0.525401 | −0.262700 | − | 0.964877i | \(-0.584613\pi\) | ||||
−0.262700 | + | 0.964877i | \(0.584613\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.29779 | 0.242925 | 0.121463 | − | 0.992596i | \(-0.461242\pi\) | ||||
0.121463 | + | 0.992596i | \(0.461242\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.61065 | 0.258960 | 0.129480 | − | 0.991582i | \(-0.458669\pi\) | ||||
0.129480 | + | 0.991582i | \(0.458669\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.2653 | 1.75052 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 43.7132 | 2.43983 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.15378 | −0.398047 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.26734 | 0.346584 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.849442 | −0.0468312 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.934366 | −0.0513574 | −0.0256787 | − | 0.999670i | \(-0.508175\pi\) | ||||
−0.0256787 | + | 0.999670i | \(0.508175\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.7206 | 1.40948 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.8588 | −1.62651 | −0.813256 | − | 0.581905i | \(-0.802307\pi\) | ||||
−0.813256 | + | 0.581905i | \(0.802307\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 35.1980 | 1.91169 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.5852 | 1.16891 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.02743 | −0.109471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.6502 | −0.571732 | −0.285866 | − | 0.958270i | \(-0.592281\pi\) | ||||
−0.285866 | + | 0.958270i | \(0.592281\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.3479 | 1.57096 | 0.785480 | − | 0.618888i | \(-0.212416\pi\) | ||||
0.785480 | + | 0.618888i | \(0.212416\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31.4705 | −1.67977 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.3847 | 0.765619 | 0.382810 | − | 0.923827i | \(-0.374957\pi\) | ||||
0.382810 | + | 0.923827i | \(0.374957\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.95433 | −0.156360 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.23773 | −0.118103 | −0.0590514 | − | 0.998255i | \(-0.518808\pi\) | ||||
−0.0590514 | + | 0.998255i | \(0.518808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 61.7680 | 3.24198 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.636873 | 0.0332445 | 0.0166222 | − | 0.999862i | \(-0.494709\pi\) | ||||
0.0166222 | + | 0.999862i | \(0.494709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.4983 | 1.53562 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.01121 | 0.0524993 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.2358 | −0.840655 | −0.420328 | − | 0.907372i | \(-0.638085\pi\) | ||||
−0.420328 | + | 0.907372i | \(0.638085\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.6718 | 1.47667 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.9624 | −0.922667 | −0.461333 | − | 0.887227i | \(-0.652629\pi\) | ||||
−0.461333 | + | 0.887227i | \(0.652629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −51.5118 | −2.63903 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.06305 | −0.207612 | −0.103806 | − | 0.994598i | \(-0.533102\pi\) | ||||
−0.103806 | + | 0.994598i | \(0.533102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.9737 | 0.862822 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.7507 | −1.45772 | −0.728859 | − | 0.684663i | \(-0.759949\pi\) | ||||
−0.728859 | + | 0.684663i | \(0.759949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.45510 | −0.225304 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 34.5232 | 1.74147 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.6518 | 0.584786 | 0.292393 | − | 0.956298i | \(-0.405548\pi\) | ||||
0.292393 | + | 0.956298i | \(0.405548\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.412974 | 0.0206746 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.98190 | 0.0989716 | 0.0494858 | − | 0.998775i | \(-0.484242\pi\) | ||||
0.0494858 | + | 0.998775i | \(0.484242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.7947 | 0.986045 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.7919 | −1.42716 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3984 | 1.30532 | 0.652660 | − | 0.757651i | \(-0.273653\pi\) | ||||
0.652660 | + | 0.757651i | \(0.273653\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 57.0582 | 2.81447 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.31849 | 0.0648788 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.4596 | 1.58955 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.3134 | −0.796963 | −0.398481 | − | 0.917176i | \(-0.630463\pi\) | ||||
−0.398481 | + | 0.917176i | \(0.630463\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.90815 | −0.0929976 | −0.0464988 | − | 0.998918i | \(-0.514806\pi\) | ||||
−0.0464988 | + | 0.998918i | \(0.514806\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.9156 | −1.45455 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.18451 | −0.0573223 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 85.3678 | 4.12160 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.9013 | 0.669600 | 0.334800 | − | 0.942289i | \(-0.391331\pi\) | ||||
0.334800 | + | 0.942289i | \(0.391331\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.93885 | 0.237346 | 0.118673 | − | 0.992933i | \(-0.462136\pi\) | ||||
0.118673 | + | 0.992933i | \(0.462136\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.622762 | 0.0297907 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.0918 | −0.863473 | −0.431736 | − | 0.902000i | \(-0.642099\pi\) | ||||
−0.431736 | + | 0.902000i | \(0.642099\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.6473 | −1.69749 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.13690 | −0.386596 | −0.193298 | − | 0.981140i | \(-0.561918\pi\) | ||||
−0.193298 | + | 0.981140i | \(0.561918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −44.3681 | −2.09854 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9187 | 0.940020 | 0.470010 | − | 0.882661i | \(-0.344250\pi\) | ||||
0.470010 | + | 0.882661i | \(0.344250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.0207 | −1.55488 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 63.7018 | 2.99297 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.4434 | −1.00308 | −0.501540 | − | 0.865134i | \(-0.667233\pi\) | ||||
−0.501540 | + | 0.865134i | \(0.667233\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −42.9360 | −2.00408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.2325 | 0.523148 | 0.261574 | − | 0.965183i | \(-0.415758\pi\) | ||||
0.261574 | + | 0.965183i | \(0.415758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.8262 | −1.75793 | −0.878967 | − | 0.476882i | \(-0.841767\pi\) | ||||
−0.878967 | + | 0.476882i | \(0.841767\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.3388 | 1.40391 | 0.701955 | − | 0.712221i | \(-0.252311\pi\) | ||||
0.701955 | + | 0.712221i | \(0.252311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.98092 | −0.0914705 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −65.7888 | −3.03139 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.0005 | −0.873645 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 35.6127 | 1.63059 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.3121 | −1.61345 | −0.806725 | − | 0.590927i | \(-0.798762\pi\) | ||||
−0.806725 | + | 0.590927i | \(0.798762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.4035 | −1.20390 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.257185 | 0.0117023 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.88482 | −0.311981 | −0.155991 | − | 0.987759i | \(-0.549857\pi\) | ||||
−0.155991 | + | 0.987759i | \(0.549857\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.3250 | −1.46179 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1116 | −0.456328 | −0.228164 | − | 0.973623i | \(-0.573272\pi\) | ||||
−0.228164 | + | 0.973623i | \(0.573272\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.1177 | 1.76177 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.350234 | 0.0157102 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.4594 | −1.63215 | −0.816074 | − | 0.577947i | \(-0.803854\pi\) | ||||
−0.816074 | + | 0.577947i | \(0.803854\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3690 | −0.775989 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.00269 | −0.401410 | −0.200705 | − | 0.979652i | \(-0.564323\pi\) | ||||
−0.200705 | + | 0.979652i | \(0.564323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 41.2700 | 1.83286 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3542 | 0.458943 | 0.229471 | − | 0.973315i | \(-0.426300\pi\) | ||||
0.229471 | + | 0.973315i | \(0.426300\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.07961 | −0.0477594 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.00186 | 0.264989 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.4878 | 1.47279 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.0229 | 1.36175 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.5209 | 0.504738 | 0.252369 | − | 0.967631i | \(-0.418790\pi\) | ||||
0.252369 | + | 0.967631i | \(0.418790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0131 | −1.05002 | −0.525009 | − | 0.851097i | \(-0.675938\pi\) | ||||
−0.525009 | + | 0.851097i | \(0.675938\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.0065 | 1.17642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6122 | −0.983138 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 46.4347 | 2.01509 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.2816 | −1.31164 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.7030 | 0.548175 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 39.9039 | 1.71878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.5131 | −1.48383 | −0.741916 | − | 0.670492i | \(-0.766083\pi\) | ||||
−0.741916 | + | 0.670492i | \(0.766083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.2161 | 0.438415 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.89383 | 0.166488 | 0.0832441 | − | 0.996529i | \(-0.473472\pi\) | ||||
0.0832441 | + | 0.996529i | \(0.473472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −41.7159 | −1.78039 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.46811 | −0.232949 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.40609 | −0.0597929 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.1816 | 0.473779 | 0.236889 | − | 0.971537i | \(-0.423872\pi\) | ||||
0.236889 | + | 0.971537i | \(0.423872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.4244 | −0.736974 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 116.470 | 4.91735 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.54455 | −0.107240 | −0.0536200 | − | 0.998561i | \(-0.517076\pi\) | ||||
−0.0536200 | + | 0.998561i | \(0.517076\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.256186 | 0.0107588 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.09511 | 0.0878314 | 0.0439157 | − | 0.999035i | \(-0.486017\pi\) | ||||
0.0439157 | + | 0.999035i | \(0.486017\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.2358 | 1.51642 | 0.758211 | − | 0.652009i | \(-0.226074\pi\) | ||||
0.758211 | + | 0.652009i | \(0.226074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.8015 | 0.952547 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.5756 | 0.648419 | 0.324209 | − | 0.945985i | \(-0.394902\pi\) | ||||
0.324209 | + | 0.945985i | \(0.394902\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.14702 | 0.172344 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.314893 | 0.0130639 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.8652 | −1.65105 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.54894 | 0.352853 | 0.176426 | − | 0.984314i | \(-0.443546\pi\) | ||||
0.176426 | + | 0.984314i | \(0.443546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.77513 | −0.155551 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −75.0325 | −3.08642 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.1005 | 1.03075 | 0.515377 | − | 0.856964i | \(-0.327652\pi\) | ||||
0.515377 | + | 0.856964i | \(0.327652\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.6642 | 1.41871 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.9528 | −1.01954 | −0.509772 | − | 0.860310i | \(-0.670270\pi\) | ||||
−0.509772 | + | 0.860310i | \(0.670270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.9744 | 0.488445 | 0.244223 | − | 0.969719i | \(-0.421467\pi\) | ||||
0.244223 | + | 0.969719i | \(0.421467\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −69.7641 | −2.84101 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.89412 | 0.279824 | 0.139912 | − | 0.990164i | \(-0.455318\pi\) | ||||
0.139912 | + | 0.990164i | \(0.455318\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.25819 | −0.0915065 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.7100 | 1.24239 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.8193 | −1.04283 | −0.521416 | − | 0.853303i | \(-0.674596\pi\) | ||||
−0.521416 | + | 0.853303i | \(0.674596\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.7584 | 0.634408 | 0.317204 | − | 0.948357i | \(-0.397256\pi\) | ||||
0.317204 | + | 0.948357i | \(0.397256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.9111 | −1.04145 | −0.520727 | − | 0.853723i | \(-0.674339\pi\) | ||||
−0.520727 | + | 0.853723i | \(0.674339\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.73773 | 0.149990 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.566768 | 0.0227071 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.2808 | −0.650194 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.0231 | −1.43633 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.86287 | −0.273207 | −0.136603 | − | 0.990626i | \(-0.543619\pi\) | ||||
−0.136603 | + | 0.990626i | \(0.543619\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −55.5499 | −2.20791 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.5939 | 1.44990 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.3346 | 0.487947 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.4136 | −1.39875 | −0.699376 | − | 0.714754i | \(-0.746539\pi\) | ||||
−0.699376 | + | 0.714754i | \(0.746539\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.6618 | −1.09088 | −0.545438 | − | 0.838151i | \(-0.683637\pi\) | ||||
−0.545438 | + | 0.838151i | \(0.683637\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.0871 | −1.14353 | −0.571765 | − | 0.820417i | \(-0.693741\pi\) | ||||
−0.571765 | + | 0.820417i | \(0.693741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.9794 | −2.04037 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.55903 | −0.0611033 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.7798 | 0.891444 | 0.445722 | − | 0.895171i | \(-0.352947\pi\) | ||||
0.445722 | + | 0.895171i | \(0.352947\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −38.0219 | −1.48337 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.5698 | −0.528605 | −0.264302 | − | 0.964440i | \(-0.585142\pi\) | ||||
−0.264302 | + | 0.964440i | \(0.585142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.4318 | 1.84489 | 0.922443 | − | 0.386134i | \(-0.126190\pi\) | ||||
0.922443 | + | 0.386134i | \(0.126190\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 106.808 | 4.14809 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.40533 | −0.131855 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −42.4857 | −1.64259 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.6972 | 1.80273 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.71398 | 0.181711 | 0.0908553 | − | 0.995864i | \(-0.471040\pi\) | ||||
0.0908553 | + | 0.995864i | \(0.471040\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.5524 | −1.63542 | −0.817711 | − | 0.575629i | \(-0.804757\pi\) | ||||
−0.817711 | + | 0.575629i | \(0.804757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.722747 | −0.0277365 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.2757 | −1.46673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.6186 | 1.32464 | 0.662321 | − | 0.749220i | \(-0.269571\pi\) | ||||
0.662321 | + | 0.749220i | \(0.269571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.9747 | −0.800235 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.5584 | −1.39276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4131 | 0.852636 | 0.426318 | − | 0.904573i | \(-0.359811\pi\) | ||||
0.426318 | + | 0.904573i | \(0.359811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.23576 | −0.160903 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.3140 | −1.56488 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0846 | −0.457082 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.3599 | −1.14668 | −0.573339 | − | 0.819318i | \(-0.694352\pi\) | ||||
−0.573339 | + | 0.819318i | \(0.694352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.03553 | 0.189919 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.776149 | −0.0291901 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.2281 | −0.421679 | −0.210839 | − | 0.977521i | \(-0.567620\pi\) | ||||
−0.210839 | + | 0.977521i | \(0.567620\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −49.5196 | −1.85713 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.35101 | −0.0880459 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −43.6757 | −1.63110 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.4485 | −1.02366 | −0.511829 | − | 0.859088i | \(-0.671032\pi\) | ||||
−0.511829 | + | 0.859088i | \(0.671032\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.521392 | 0.0194177 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 76.0336 | 2.82772 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.2650 | 0.640323 | 0.320162 | − | 0.947363i | \(-0.396263\pi\) | ||||
0.320162 | + | 0.947363i | \(0.396263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.2472 | −1.56471 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.7726 | −0.879261 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6789 | 0.579112 | 0.289556 | − | 0.957161i | \(-0.406492\pi\) | ||||
0.289556 | + | 0.957161i | \(0.406492\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 78.0946 | 2.87665 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.7761 | 1.75747 | 0.878737 | − | 0.477307i | \(-0.158387\pi\) | ||||
0.878737 | + | 0.477307i | \(0.158387\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.9303 | −0.548479 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.5789 | −1.37864 | −0.689318 | − | 0.724459i | \(-0.742090\pi\) | ||||
−0.689318 | + | 0.724459i | \(0.742090\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.0899 | 0.405758 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.22654 | 0.0813561 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.4411 | 1.84062 | 0.920311 | − | 0.391188i | \(-0.127936\pi\) | ||||
0.920311 | + | 0.391188i | \(0.127936\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.3778 | 0.378188 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8756 | −0.395280 | −0.197640 | − | 0.980275i | \(-0.563328\pi\) | ||||
−0.197640 | + | 0.980275i | \(0.563328\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.1391 | −0.368026 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.7675 | 0.390322 | 0.195161 | − | 0.980771i | \(-0.437477\pi\) | ||||
0.195161 | + | 0.980771i | \(0.437477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.319229 | 0.0115569 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −47.6677 | −1.72118 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.76320 | −0.0635827 | −0.0317914 | − | 0.999495i | \(-0.510121\pi\) | ||||
−0.0317914 | + | 0.999495i | \(0.510121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.6514 | −0.995841 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.5661 | −0.955517 | −0.477759 | − | 0.878491i | \(-0.658551\pi\) | ||||
−0.477759 | + | 0.878491i | \(0.658551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.07954 | 0.0746032 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.77513 | 0.206915 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8074 | −0.494068 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32.8189 | −1.17285 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.4557 | −1.22821 | −0.614106 | − | 0.789223i | \(-0.710483\pi\) | ||||
−0.614106 | + | 0.789223i | \(0.710483\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.18379 | 0.184548 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.79282 | 0.0637453 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.8236 | 1.52071 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5121 | 0.407779 | 0.203890 | − | 0.978994i | \(-0.434642\pi\) | ||||
0.203890 | + | 0.978994i | \(0.434642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.8985 | 1.48226 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.9604 | 0.705267 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.5621 | 1.50198 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 61.6048 | 2.16859 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.7367 | 1.25643 | 0.628217 | − | 0.778038i | \(-0.283785\pi\) | ||||
0.628217 | + | 0.778038i | \(0.283785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.4425 | −1.66593 | −0.832966 | − | 0.553324i | \(-0.813359\pi\) | ||||
−0.832966 | + | 0.553324i | \(0.813359\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.4820 | −0.753406 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.32308 | 0.116260 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.88440 | −0.135732 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.70237 | −0.199014 | −0.0995070 | − | 0.995037i | \(-0.531727\pi\) | ||||
−0.0995070 | + | 0.995037i | \(0.531727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.37125 | 0.117514 | 0.0587572 | − | 0.998272i | \(-0.481286\pi\) | ||||
0.0587572 | + | 0.998272i | \(0.481286\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.22704 | 0.112215 | 0.0561075 | − | 0.998425i | \(-0.482131\pi\) | ||||
0.0561075 | + | 0.998425i | \(0.482131\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5746 | 0.367273 | 0.183636 | − | 0.982994i | \(-0.441213\pi\) | ||||
0.183636 | + | 0.982994i | \(0.441213\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.7519 | 1.24022 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 49.9260 | 1.72983 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.6578 | −0.783168 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.5214 | 1.77872 | 0.889359 | − | 0.457210i | \(-0.151151\pi\) | ||||
0.889359 | + | 0.457210i | \(0.151151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.900274 | 0.0310439 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 63.1977 | 2.17665 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.14617 | 0.108104 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −58.7055 | −2.01477 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.13593 | 0.107498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.3074 | 0.489874 | 0.244937 | − | 0.969539i | \(-0.421233\pi\) | ||||
0.244937 | + | 0.969539i | \(0.421233\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.55632 | −0.121482 | −0.0607408 | − | 0.998154i | \(-0.519346\pi\) | ||||
−0.0607408 | + | 0.998154i | \(0.519346\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.8084 | 0.471135 | 0.235568 | − | 0.971858i | \(-0.424305\pi\) | ||||
0.235568 | + | 0.971858i | \(0.424305\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.38498 | 0.0812799 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.3476 | −0.386277 | −0.193139 | − | 0.981171i | \(-0.561867\pi\) | ||||
−0.193139 | + | 0.981171i | \(0.561867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 97.3154 | 3.30500 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 55.4327 | 1.88042 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 71.6166 | 2.42664 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.4537 | −0.861478 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.6155 | 1.50656 | 0.753279 | − | 0.657701i | \(-0.228471\pi\) | ||||
0.753279 | + | 0.657701i | \(0.228471\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −63.0479 | −2.12655 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3973 | 1.15887 | 0.579437 | − | 0.815017i | \(-0.303272\pi\) | ||||
0.579437 | + | 0.815017i | \(0.303272\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.2057 | −1.82417 | −0.912084 | − | 0.410004i | \(-0.865527\pi\) | ||||
−0.912084 | + | 0.410004i | \(0.865527\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.69998 | 0.0570798 | 0.0285399 | − | 0.999593i | \(-0.490914\pi\) | ||||
0.0285399 | + | 0.999593i | \(0.490914\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.62377 | −0.0879984 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.0997 | −0.338353 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.85683 | −0.195991 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.29804 | −0.310453 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.6428 | 0.688477 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.8776 | −1.66166 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.37235 | 0.0456689 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.1338 | −0.436101 | −0.218050 | − | 0.975938i | \(-0.569970\pi\) | ||||
−0.218050 | + | 0.975938i | \(0.569970\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.3344 | −0.906626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7511 | 0.820040 | 0.410020 | − | 0.912076i | \(-0.365522\pi\) | ||||
0.410020 | + | 0.912076i | \(0.365522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4141 | −0.410848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.75845 | 0.0580692 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.2789 | −0.471019 | −0.235510 | − | 0.971872i | \(-0.575676\pi\) | ||||
−0.235510 | + | 0.971872i | \(0.575676\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.12707 | 0.168943 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.6621 | −0.416777 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.3624 | 0.603100 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.6484 | 0.611834 | 0.305917 | − | 0.952058i | \(-0.401037\pi\) | ||||
0.305917 | + | 0.952058i | \(0.401037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.97897 | −0.228726 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.3829 | −0.863738 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.9120 | 0.585159 | 0.292580 | − | 0.956241i | \(-0.405486\pi\) | ||||
0.292580 | + | 0.956241i | \(0.405486\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.2376 | 0.399360 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.7412 | 0.350152 | 0.175076 | − | 0.984555i | \(-0.443983\pi\) | ||||
0.175076 | + | 0.984555i | \(0.443983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.59653 | 0.117119 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −58.5220 | −1.90171 | −0.950855 | − | 0.309636i | \(-0.899793\pi\) | ||||
−0.950855 | + | 0.309636i | \(0.899793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.0315 | 1.26702 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.1285 | 0.425720 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.93656 | −0.0951244 | −0.0475622 | − | 0.998868i | \(-0.515145\pi\) | ||||
−0.0475622 | + | 0.998868i | \(0.515145\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 89.0255 | 2.87779 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.90628 | 0.0938486 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.7484 | −0.540271 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 78.4144 | 2.52687 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.5192 | −0.659852 | −0.329926 | − | 0.944007i | \(-0.607024\pi\) | ||||
−0.329926 | + | 0.944007i | \(0.607024\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.3699 | −0.654374 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.37837 | −0.0763255 | −0.0381628 | − | 0.999272i | \(-0.512151\pi\) | ||||
−0.0381628 | + | 0.999272i | \(0.512151\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.65334 | 0.0530037 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.2822 | 1.48070 | 0.740349 | − | 0.672222i | \(-0.234660\pi\) | ||||
0.740349 | + | 0.672222i | \(0.234660\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.3439 | −0.714114 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.2426 | 0.358948 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.2913 | 1.57215 | 0.786074 | − | 0.618133i | \(-0.212111\pi\) | ||||
0.786074 | + | 0.618133i | \(0.212111\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.41872 | −0.0769887 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.06949 | 0.0658059 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.92186 | 0.219880 | 0.109940 | − | 0.993938i | \(-0.464934\pi\) | ||||
0.109940 | + | 0.993938i | \(0.464934\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.66054 | −0.0844296 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1533 | 0.891624 | 0.445812 | − | 0.895127i | \(-0.352915\pi\) | ||||
0.445812 | + | 0.895127i | \(0.352915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.2225 | 0.956199 |
(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 | 3800.2.a.z.1.6 | 6 | ||
4.3 | odd | 2 | 7600.2.a.cn.1.1 | 6 | |||
5.2 | odd | 4 | 760.2.d.e.609.2 | ✓ | 12 | ||
5.3 | odd | 4 | 760.2.d.e.609.11 | yes | 12 | ||
5.4 | even | 2 | 3800.2.a.be.1.1 | 6 | |||
20.3 | even | 4 | 1520.2.d.k.609.2 | 12 | |||
20.7 | even | 4 | 1520.2.d.k.609.11 | 12 | |||
20.19 | odd | 2 | 7600.2.a.cg.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.e.609.2 | ✓ | 12 | 5.2 | odd | 4 | ||
760.2.d.e.609.11 | yes | 12 | 5.3 | odd | 4 | ||
1520.2.d.k.609.2 | 12 | 20.3 | even | 4 | |||
1520.2.d.k.609.11 | 12 | 20.7 | even | 4 | |||
3800.2.a.z.1.6 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.a.be.1.1 | 6 | 5.4 | even | 2 | |||
7600.2.a.cg.1.6 | 6 | 20.19 | odd | 2 | |||
7600.2.a.cn.1.1 | 6 | 4.3 | odd | 2 |