Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2601,2,Mod(1,2601)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2601, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2601.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2601 = 3^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2601.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: | \(20.7690895657\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.4848615424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 16x^{4} - 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 153) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.45341\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2601.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.14144 | 1.51423 | 0.757115 | − | 0.653281i | \(-0.226608\pi\) | ||||
0.757115 | + | 0.653281i | \(0.226608\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.58579 | 1.29289 | ||||||||
\(5\) | 2.79793 | 1.25127 | 0.625637 | − | 0.780115i | \(-0.284839\pi\) | ||||
0.625637 | + | 0.780115i | \(0.284839\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.93015 | 1.10749 | 0.553747 | − | 0.832685i | \(-0.313198\pi\) | ||||
0.553747 | + | 0.832685i | \(0.313198\pi\) | |||||||
\(8\) | 1.25443 | 0.443508 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.99162 | 1.89472 | ||||||||
\(11\) | −1.15894 | −0.349434 | −0.174717 | − | 0.984619i | \(-0.555901\pi\) | ||||
−0.174717 | + | 0.984619i | \(0.555901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.41421 | 1.22428 | 0.612141 | − | 0.790748i | \(-0.290308\pi\) | ||||
0.612141 | + | 0.790748i | \(0.290308\pi\) | |||||||
\(14\) | 6.27476 | 1.67700 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.48528 | −0.621320 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.41421 | 1.47152 | 0.735761 | − | 0.677242i | \(-0.236825\pi\) | ||||
0.735761 | + | 0.677242i | \(0.236825\pi\) | |||||||
\(20\) | 7.23486 | 1.61776 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.48181 | −0.529124 | ||||||||
\(23\) | −2.79793 | −0.583409 | −0.291705 | − | 0.956508i | \(-0.594222\pi\) | ||||
−0.291705 | + | 0.956508i | \(0.594222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.82843 | 0.565685 | ||||||||
\(26\) | 9.45280 | 1.85385 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.57675 | 1.43187 | ||||||||
\(29\) | −9.55274 | −1.77390 | −0.886950 | − | 0.461866i | \(-0.847180\pi\) | ||||
−0.886950 | + | 0.461866i | \(0.847180\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.83938 | −1.40799 | −0.703997 | − | 0.710203i | \(-0.748603\pi\) | ||||
−0.703997 | + | 0.710203i | \(0.748603\pi\) | |||||||
\(32\) | −7.83095 | −1.38433 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.19837 | 1.38578 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.39942 | 0.230063 | 0.115031 | − | 0.993362i | \(-0.463303\pi\) | ||||
0.115031 | + | 0.993362i | \(0.463303\pi\) | |||||||
\(38\) | 13.7357 | 2.22822 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.50981 | 0.554950 | ||||||||
\(41\) | 0.480049 | 0.0749711 | 0.0374856 | − | 0.999297i | \(-0.488065\pi\) | ||||
0.0374856 | + | 0.999297i | \(0.488065\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.07107 | 1.23083 | 0.615413 | − | 0.788205i | \(-0.288989\pi\) | ||||
0.615413 | + | 0.788205i | \(0.288989\pi\) | |||||||
\(44\) | −2.99678 | −0.451781 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.99162 | −0.883416 | ||||||||
\(47\) | −6.05692 | −0.883493 | −0.441746 | − | 0.897140i | \(-0.645641\pi\) | ||||
−0.441746 | + | 0.897140i | \(0.645641\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.58579 | 0.226541 | ||||||||
\(50\) | 6.05692 | 0.856578 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.4142 | 1.58287 | ||||||||
\(53\) | 10.3398 | 1.42028 | 0.710141 | − | 0.704059i | \(-0.248631\pi\) | ||||
0.710141 | + | 0.704059i | \(0.248631\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.24264 | −0.437238 | ||||||||
\(56\) | 3.67567 | 0.491182 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −20.4567 | −2.68609 | ||||||||
\(59\) | −6.42433 | −0.836377 | −0.418189 | − | 0.908360i | \(-0.637335\pi\) | ||||
−0.418189 | + | 0.908360i | \(0.637335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.765367 | −0.0979952 | −0.0489976 | − | 0.998799i | \(-0.515603\pi\) | ||||
−0.0489976 | + | 0.998799i | \(0.515603\pi\) | |||||||
\(62\) | −16.7876 | −2.13203 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.7990 | −1.47487 | ||||||||
\(65\) | 12.3507 | 1.53191 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.585786 | 0.0715652 | 0.0357826 | − | 0.999360i | \(-0.488608\pi\) | ||||
0.0357826 | + | 0.999360i | \(0.488608\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 17.5563 | 2.09839 | ||||||||
\(71\) | 12.8307 | 1.52273 | 0.761363 | − | 0.648326i | \(-0.224530\pi\) | ||||
0.761363 | + | 0.648326i | \(0.224530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9832 | −1.40253 | −0.701266 | − | 0.712900i | \(-0.747381\pi\) | ||||
−0.701266 | + | 0.712900i | \(0.747381\pi\) | |||||||
\(74\) | 2.99678 | 0.348368 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.5858 | 1.90252 | ||||||||
\(77\) | −3.39587 | −0.386996 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.48181 | −0.279225 | −0.139613 | − | 0.990206i | \(-0.544586\pi\) | ||||
−0.139613 | + | 0.990206i | \(0.544586\pi\) | |||||||
\(80\) | −6.95365 | −0.777442 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.02800 | 0.113524 | ||||||||
\(83\) | 10.3398 | 1.13494 | 0.567471 | − | 0.823393i | \(-0.307922\pi\) | ||||
0.567471 | + | 0.823393i | \(0.307922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 17.2837 | 1.86375 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.45381 | −0.154977 | ||||||||
\(89\) | −11.2268 | −1.19004 | −0.595021 | − | 0.803710i | \(-0.702856\pi\) | ||||
−0.595021 | + | 0.803710i | \(0.702856\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.9343 | 1.35588 | ||||||||
\(92\) | −7.23486 | −0.754286 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.9706 | −1.33781 | ||||||||
\(95\) | 17.9465 | 1.84128 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.30864 | 0.640546 | 0.320273 | − | 0.947325i | \(-0.396225\pi\) | ||||
0.320273 | + | 0.947325i | \(0.396225\pi\) | |||||||
\(98\) | 3.39587 | 0.343035 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.31371 | 0.731371 | ||||||||
\(101\) | −1.25443 | −0.124820 | −0.0624102 | − | 0.998051i | \(-0.519879\pi\) | ||||
−0.0624102 | + | 0.998051i | \(0.519879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | 0.0985329 | 0.0492665 | − | 0.998786i | \(-0.484312\pi\) | ||||
0.0492665 | + | 0.998786i | \(0.484312\pi\) | |||||||
\(104\) | 5.53732 | 0.542979 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.1421 | 2.15063 | ||||||||
\(107\) | −5.11582 | −0.494565 | −0.247282 | − | 0.968943i | \(-0.579538\pi\) | ||||
−0.247282 | + | 0.968943i | \(0.579538\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.50981 | 0.336179 | 0.168089 | − | 0.985772i | \(-0.446240\pi\) | ||||
0.168089 | + | 0.985772i | \(0.446240\pi\) | |||||||
\(110\) | −6.94394 | −0.662078 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.28225 | −0.688108 | ||||||||
\(113\) | −2.11904 | −0.199343 | −0.0996713 | − | 0.995020i | \(-0.531779\pi\) | ||||
−0.0996713 | + | 0.995020i | \(0.531779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.82843 | −0.730005 | ||||||||
\(116\) | −24.7013 | −2.29346 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.7574 | −1.26647 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.65685 | −0.877896 | ||||||||
\(122\) | −1.63899 | −0.148387 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −20.2710 | −1.82039 | ||||||||
\(125\) | −6.07591 | −0.543446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.89949 | 0.612231 | 0.306116 | − | 0.951994i | \(-0.400971\pi\) | ||||
0.306116 | + | 0.951994i | \(0.400971\pi\) | |||||||
\(128\) | −9.60498 | −0.848969 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 26.4483 | 2.31967 | ||||||||
\(131\) | 0.198843 | 0.0173730 | 0.00868649 | − | 0.999962i | \(-0.497235\pi\) | ||||
0.00868649 | + | 0.999962i | \(0.497235\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.7946 | 1.62970 | ||||||||
\(134\) | 1.25443 | 0.108366 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.887016 | −0.0757829 | −0.0378914 | − | 0.999282i | \(-0.512064\pi\) | ||||
−0.0378914 | + | 0.999282i | \(0.512064\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.87285 | −0.837404 | −0.418702 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(140\) | 21.1992 | 1.79166 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 27.4763 | 2.30576 | ||||||||
\(143\) | −5.11582 | −0.427806 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.7279 | −2.21963 | ||||||||
\(146\) | −25.6614 | −2.12376 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.61859 | 0.297447 | ||||||||
\(149\) | 2.66105 | 0.218001 | 0.109001 | − | 0.994042i | \(-0.465235\pi\) | ||||
0.109001 | + | 0.994042i | \(0.465235\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.41421 | 0.440602 | 0.220301 | − | 0.975432i | \(-0.429296\pi\) | ||||
0.220301 | + | 0.975432i | \(0.429296\pi\) | |||||||
\(152\) | 8.04618 | 0.652631 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.27208 | −0.586001 | ||||||||
\(155\) | −21.9341 | −1.76179 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.7990 | 1.50032 | 0.750161 | − | 0.661255i | \(-0.229976\pi\) | ||||
0.750161 | + | 0.661255i | \(0.229976\pi\) | |||||||
\(158\) | −5.31466 | −0.422812 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −21.9105 | −1.73218 | ||||||||
\(161\) | −8.19837 | −0.646122 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.47343 | 0.663690 | 0.331845 | − | 0.943334i | \(-0.392329\pi\) | ||||
0.331845 | + | 0.943334i | \(0.392329\pi\) | |||||||
\(164\) | 1.24131 | 0.0969296 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.1421 | 1.71856 | ||||||||
\(167\) | 5.79471 | 0.448408 | 0.224204 | − | 0.974542i | \(-0.428022\pi\) | ||||
0.224204 | + | 0.974542i | \(0.428022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.48528 | 0.498868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 20.8701 | 1.59133 | ||||||||
\(173\) | −17.6653 | −1.34307 | −0.671535 | − | 0.740973i | \(-0.734365\pi\) | ||||
−0.671535 | + | 0.740973i | \(0.734365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.28772 | 0.626493 | ||||||||
\(176\) | 2.88030 | 0.217110 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −24.0416 | −1.80200 | ||||||||
\(179\) | 18.1708 | 1.35815 | 0.679073 | − | 0.734070i | \(-0.262382\pi\) | ||||
0.679073 | + | 0.734070i | \(0.262382\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.60474 | −0.639586 | −0.319793 | − | 0.947487i | \(-0.603613\pi\) | ||||
−0.319793 | + | 0.947487i | \(0.603613\pi\) | |||||||
\(182\) | 27.6981 | 2.05312 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.50981 | −0.258747 | ||||||||
\(185\) | 3.91548 | 0.287872 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −15.6619 | −1.14226 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 38.4315 | 2.78812 | ||||||||
\(191\) | −22.8211 | −1.65127 | −0.825637 | − | 0.564201i | \(-0.809184\pi\) | ||||
−0.825637 | + | 0.564201i | \(0.809184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.49435 | 0.467474 | 0.233737 | − | 0.972300i | \(-0.424905\pi\) | ||||
0.233737 | + | 0.972300i | \(0.424905\pi\) | |||||||
\(194\) | 13.5096 | 0.969934 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.10051 | 0.292893 | ||||||||
\(197\) | 18.6254 | 1.32701 | 0.663503 | − | 0.748173i | \(-0.269069\pi\) | ||||
0.663503 | + | 0.748173i | \(0.269069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.4370 | −0.952527 | −0.476264 | − | 0.879303i | \(-0.658009\pi\) | ||||
−0.476264 | + | 0.879303i | \(0.658009\pi\) | |||||||
\(200\) | 3.54806 | 0.250886 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.68629 | −0.189007 | ||||||||
\(203\) | −27.9910 | −1.96458 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.34315 | 0.0938094 | ||||||||
\(206\) | 2.14144 | 0.149202 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.9706 | −0.760672 | ||||||||
\(209\) | −7.43370 | −0.514200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.92177 | −0.614200 | −0.307100 | − | 0.951677i | \(-0.599359\pi\) | ||||
−0.307100 | + | 0.951677i | \(0.599359\pi\) | |||||||
\(212\) | 26.7365 | 1.83627 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.9552 | −0.748885 | ||||||||
\(215\) | 22.5823 | 1.54010 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.9706 | −1.55934 | ||||||||
\(218\) | 7.51606 | 0.509052 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.38478 | −0.565302 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.07107 | −0.406549 | −0.203274 | − | 0.979122i | \(-0.565158\pi\) | ||||
−0.203274 | + | 0.979122i | \(0.565158\pi\) | |||||||
\(224\) | −22.9459 | −1.53314 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.53781 | −0.301851 | ||||||||
\(227\) | 20.9433 | 1.39006 | 0.695028 | − | 0.718982i | \(-0.255392\pi\) | ||||
0.695028 | + | 0.718982i | \(0.255392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.5858 | 0.963856 | 0.481928 | − | 0.876211i | \(-0.339937\pi\) | ||||
0.481928 | + | 0.876211i | \(0.339937\pi\) | |||||||
\(230\) | −16.7641 | −1.10540 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.9832 | −0.786738 | ||||||||
\(233\) | −13.3108 | −0.872018 | −0.436009 | − | 0.899942i | \(-0.643608\pi\) | ||||
−0.436009 | + | 0.899942i | \(0.643608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.9469 | −1.10549 | ||||||||
\(236\) | −16.6120 | −1.08135 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.1885 | −1.49994 | −0.749969 | − | 0.661473i | \(-0.769932\pi\) | ||||
−0.749969 | + | 0.661473i | \(0.769932\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50143 | −0.612041 | −0.306020 | − | 0.952025i | \(-0.598998\pi\) | ||||
−0.306020 | + | 0.952025i | \(0.598998\pi\) | |||||||
\(242\) | −20.6796 | −1.32934 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.97908 | −0.126697 | ||||||||
\(245\) | 4.43692 | 0.283465 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.3137 | 1.80156 | ||||||||
\(248\) | −9.83395 | −0.624456 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.0112 | −0.822903 | ||||||||
\(251\) | −2.66105 | −0.167964 | −0.0839819 | − | 0.996467i | \(-0.526764\pi\) | ||||
−0.0839819 | + | 0.996467i | \(0.526764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.24264 | 0.203863 | ||||||||
\(254\) | 14.7749 | 0.927059 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.02944 | 0.189340 | ||||||||
\(257\) | −10.7072 | −0.667898 | −0.333949 | − | 0.942591i | \(-0.608381\pi\) | ||||
−0.333949 | + | 0.942591i | \(0.608381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.10051 | 0.254793 | ||||||||
\(260\) | 31.9362 | 1.98060 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.425811 | 0.0263067 | ||||||||
\(263\) | 9.97240 | 0.614924 | 0.307462 | − | 0.951560i | \(-0.400520\pi\) | ||||
0.307462 | + | 0.951560i | \(0.400520\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.9301 | 1.77716 | ||||||||
\(266\) | 40.2476 | 2.46774 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.51472 | 0.0925262 | ||||||||
\(269\) | −13.0296 | −0.794427 | −0.397213 | − | 0.917726i | \(-0.630023\pi\) | ||||
−0.397213 | + | 0.917726i | \(0.630023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.0711 | 1.94818 | 0.974089 | − | 0.226164i | \(-0.0726184\pi\) | ||||
0.974089 | + | 0.226164i | \(0.0726184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.89949 | −0.114753 | ||||||||
\(275\) | −3.27798 | −0.197670 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.7975 | 0.708845 | 0.354422 | − | 0.935085i | \(-0.384678\pi\) | ||||
0.354422 | + | 0.935085i | \(0.384678\pi\) | |||||||
\(278\) | −21.1422 | −1.26802 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.2843 | 0.614603 | ||||||||
\(281\) | −32.6413 | −1.94722 | −0.973608 | − | 0.228228i | \(-0.926707\pi\) | ||||
−0.973608 | + | 0.228228i | \(0.926707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.37849 | 0.200831 | 0.100415 | − | 0.994946i | \(-0.467983\pi\) | ||||
0.100415 | + | 0.994946i | \(0.467983\pi\) | |||||||
\(284\) | 33.1775 | 1.96872 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.9552 | −0.647797 | ||||||||
\(287\) | 1.40662 | 0.0830300 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −57.2364 | −3.36104 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −30.9861 | −1.81332 | ||||||||
\(293\) | −14.2553 | −0.832803 | −0.416401 | − | 0.909181i | \(-0.636709\pi\) | ||||
−0.416401 | + | 0.909181i | \(0.636709\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.9749 | −1.04654 | ||||||||
\(296\) | 1.75547 | 0.102035 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.69848 | 0.330104 | ||||||||
\(299\) | −12.3507 | −0.714258 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.6494 | 1.36313 | ||||||||
\(302\) | 11.5942 | 0.667174 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.9411 | −0.914286 | ||||||||
\(305\) | −2.14144 | −0.122619 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.89949 | −0.222556 | −0.111278 | − | 0.993789i | \(-0.535494\pi\) | ||||
−0.111278 | + | 0.993789i | \(0.535494\pi\) | |||||||
\(308\) | −8.78101 | −0.500344 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −46.9706 | −2.66775 | ||||||||
\(311\) | −19.7844 | −1.12187 | −0.560934 | − | 0.827860i | \(-0.689558\pi\) | ||||
−0.560934 | + | 0.827860i | \(0.689558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0279 | 1.52771 | 0.763855 | − | 0.645388i | \(-0.223304\pi\) | ||||
0.763855 | + | 0.645388i | \(0.223304\pi\) | |||||||
\(314\) | 40.2570 | 2.27183 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.41743 | −0.361009 | ||||||||
\(317\) | 9.55274 | 0.536535 | 0.268268 | − | 0.963344i | \(-0.413549\pi\) | ||||
0.268268 | + | 0.963344i | \(0.413549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.0711 | 0.619861 | ||||||||
\(320\) | −33.0128 | −1.84547 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.5563 | −0.978377 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.4853 | 0.692559 | ||||||||
\(326\) | 18.1454 | 1.00498 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.602188 | 0.0332503 | ||||||||
\(329\) | −17.7477 | −0.978462 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.1421 | 1.49187 | 0.745933 | − | 0.666021i | \(-0.232004\pi\) | ||||
0.745933 | + | 0.666021i | \(0.232004\pi\) | |||||||
\(332\) | 26.7365 | 1.46736 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4090 | 0.678993 | ||||||||
\(335\) | 1.63899 | 0.0895476 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.50143 | −0.517576 | −0.258788 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258788 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(338\) | 13.8879 | 0.755401 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.08538 | 0.492001 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8645 | −0.856601 | ||||||||
\(344\) | 10.1246 | 0.545881 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −37.8293 | −2.03372 | ||||||||
\(347\) | 29.6183 | 1.58999 | 0.794997 | − | 0.606613i | \(-0.207472\pi\) | ||||
0.794997 | + | 0.606613i | \(0.207472\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7279 | 0.841896 | 0.420948 | − | 0.907085i | \(-0.361697\pi\) | ||||
0.420948 | + | 0.907085i | \(0.361697\pi\) | |||||||
\(350\) | 17.7477 | 0.948654 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.07562 | 0.483732 | ||||||||
\(353\) | −17.2837 | −0.919921 | −0.459961 | − | 0.887939i | \(-0.652136\pi\) | ||||
−0.459961 | + | 0.887939i | \(0.652136\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 35.8995 | 1.90535 | ||||||||
\(356\) | −29.0302 | −1.53860 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 38.9117 | 2.05655 | ||||||||
\(359\) | −11.2268 | −0.592529 | −0.296265 | − | 0.955106i | \(-0.595741\pi\) | ||||
−0.296265 | + | 0.955106i | \(0.595741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.1421 | 1.16538 | ||||||||
\(362\) | −18.4266 | −0.968480 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 33.4454 | 1.75301 | ||||||||
\(365\) | −33.5283 | −1.75495 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.765367 | 0.0399518 | 0.0199759 | − | 0.999800i | \(-0.493641\pi\) | ||||
0.0199759 | + | 0.999800i | \(0.493641\pi\) | |||||||
\(368\) | 6.95365 | 0.362484 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.38478 | 0.435904 | ||||||||
\(371\) | 30.2972 | 1.57295 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.0416 | −1.65905 | −0.829526 | − | 0.558468i | \(-0.811390\pi\) | ||||
−0.829526 | + | 0.558468i | \(0.811390\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.59798 | −0.391836 | ||||||||
\(377\) | −42.1678 | −2.17175 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.2430 | −0.988444 | −0.494222 | − | 0.869336i | \(-0.664547\pi\) | ||||
−0.494222 | + | 0.869336i | \(0.664547\pi\) | |||||||
\(380\) | 46.4059 | 2.38057 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −48.8701 | −2.50041 | ||||||||
\(383\) | 14.6227 | 0.747185 | 0.373593 | − | 0.927593i | \(-0.378126\pi\) | ||||
0.373593 | + | 0.927593i | \(0.378126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.50143 | −0.484238 | ||||||||
\(386\) | 13.9073 | 0.707863 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.3128 | 0.828157 | ||||||||
\(389\) | −2.14144 | −0.108576 | −0.0542878 | − | 0.998525i | \(-0.517289\pi\) | ||||
−0.0542878 | + | 0.998525i | \(0.517289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.98926 | 0.100473 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 39.8853 | 2.00939 | ||||||||
\(395\) | −6.94394 | −0.349387 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.4567 | −1.02669 | −0.513345 | − | 0.858182i | \(-0.671594\pi\) | ||||
−0.513345 | + | 0.858182i | \(0.671594\pi\) | |||||||
\(398\) | −28.7747 | −1.44235 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.02944 | −0.351472 | ||||||||
\(401\) | −20.9433 | −1.04586 | −0.522930 | − | 0.852376i | \(-0.675161\pi\) | ||||
−0.522930 | + | 0.852376i | \(0.675161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.6047 | −1.72378 | ||||||||
\(404\) | −3.24369 | −0.161379 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −59.9411 | −2.97483 | ||||||||
\(407\) | −1.62184 | −0.0803918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.79899 | −0.138401 | −0.0692006 | − | 0.997603i | \(-0.522045\pi\) | ||||
−0.0692006 | + | 0.997603i | \(0.522045\pi\) | |||||||
\(410\) | 2.87627 | 0.142049 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.58579 | 0.127393 | ||||||||
\(413\) | −18.8243 | −0.926282 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.9301 | 1.42012 | ||||||||
\(416\) | −34.5675 | −1.69481 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.9189 | −0.778617 | ||||||||
\(419\) | −29.0559 | −1.41947 | −0.709737 | − | 0.704467i | \(-0.751186\pi\) | ||||
−0.709737 | + | 0.704467i | \(0.751186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8284 | 0.771430 | 0.385715 | − | 0.922618i | \(-0.373955\pi\) | ||||
0.385715 | + | 0.922618i | \(0.373955\pi\) | |||||||
\(422\) | −19.1055 | −0.930040 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.9706 | 0.629906 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.24264 | −0.108529 | ||||||||
\(428\) | −13.2284 | −0.639419 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 48.3588 | 2.33207 | ||||||||
\(431\) | −2.99678 | −0.144350 | −0.0721748 | − | 0.997392i | \(-0.522994\pi\) | ||||
−0.0721748 | + | 0.997392i | \(0.522994\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.20101 | −0.0577169 | −0.0288584 | − | 0.999584i | \(-0.509187\pi\) | ||||
−0.0288584 | + | 0.999584i | \(0.509187\pi\) | |||||||
\(434\) | −49.1902 | −2.36120 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.07562 | 0.434643 | ||||||||
\(437\) | −17.9465 | −0.858499 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.8226 | 0.946082 | 0.473041 | − | 0.881040i | \(-0.343156\pi\) | ||||
0.473041 | + | 0.881040i | \(0.343156\pi\) | |||||||
\(440\) | −4.06766 | −0.193918 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.1138 | 0.575546 | 0.287773 | − | 0.957699i | \(-0.407085\pi\) | ||||
0.287773 | + | 0.957699i | \(0.407085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.4119 | −1.48907 | ||||||||
\(446\) | −13.0009 | −0.615608 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −34.5728 | −1.63341 | ||||||||
\(449\) | 4.63577 | 0.218775 | 0.109388 | − | 0.993999i | \(-0.465111\pi\) | ||||
0.109388 | + | 0.993999i | \(0.465111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.556349 | −0.0261975 | ||||||||
\(452\) | −5.47939 | −0.257729 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 44.8490 | 2.10487 | ||||||||
\(455\) | 36.1893 | 1.69658 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5563 | −0.680917 | −0.340459 | − | 0.940259i | \(-0.610582\pi\) | ||||
−0.340459 | + | 0.940259i | \(0.610582\pi\) | |||||||
\(458\) | 31.2347 | 1.45950 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −20.2426 | −0.943818 | ||||||||
\(461\) | −14.2553 | −0.663935 | −0.331967 | − | 0.943291i | \(-0.607712\pi\) | ||||
−0.331967 | + | 0.943291i | \(0.607712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.5269 | −1.32576 | −0.662879 | − | 0.748727i | \(-0.730666\pi\) | ||||
−0.662879 | + | 0.748727i | \(0.730666\pi\) | |||||||
\(464\) | 23.7412 | 1.10216 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.5043 | −1.32044 | ||||||||
\(467\) | 14.9901 | 0.693660 | 0.346830 | − | 0.937928i | \(-0.387258\pi\) | ||||
0.346830 | + | 0.937928i | \(0.387258\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.71644 | 0.0792580 | ||||||||
\(470\) | −36.2908 | −1.67397 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.05887 | −0.370940 | ||||||||
\(473\) | −9.35390 | −0.430093 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.1421 | 0.832418 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −49.6569 | −2.27125 | ||||||||
\(479\) | −3.47682 | −0.158860 | −0.0794301 | − | 0.996840i | \(-0.525310\pi\) | ||||
−0.0794301 | + | 0.996840i | \(0.525310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.17733 | 0.281662 | ||||||||
\(482\) | −20.3468 | −0.926771 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24.9706 | −1.13503 | ||||||||
\(485\) | 17.6512 | 0.801498 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.5152 | −1.38278 | −0.691388 | − | 0.722483i | \(-0.743001\pi\) | ||||
−0.691388 | + | 0.722483i | \(0.743001\pi\) | |||||||
\(488\) | −0.960099 | −0.0434616 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.50143 | 0.429231 | ||||||||
\(491\) | −11.5942 | −0.523241 | −0.261620 | − | 0.965171i | \(-0.584257\pi\) | ||||
−0.261620 | + | 0.965171i | \(0.584257\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 60.6322 | 2.72797 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.4831 | 0.874815 | ||||||||
\(497\) | 37.5960 | 1.68641 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.8728 | 1.60589 | 0.802943 | − | 0.596055i | \(-0.203266\pi\) | ||||
0.802943 | + | 0.596055i | \(0.203266\pi\) | |||||||
\(500\) | −15.7110 | −0.702618 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.69848 | −0.254336 | ||||||||
\(503\) | 35.1318 | 1.56645 | 0.783225 | − | 0.621738i | \(-0.213573\pi\) | ||||
0.783225 | + | 0.621738i | \(0.213573\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.50981 | −0.156184 | ||||||||
\(506\) | 6.94394 | 0.308696 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.8406 | 0.791550 | ||||||||
\(509\) | 23.7081 | 1.05084 | 0.525421 | − | 0.850842i | \(-0.323908\pi\) | ||||
0.525421 | + | 0.850842i | \(0.323908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.1127 | −1.55329 | ||||||||
\(512\) | 25.6973 | 1.13567 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.9289 | −1.01135 | ||||||||
\(515\) | 2.79793 | 0.123292 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.01962 | 0.308722 | ||||||||
\(518\) | 8.78101 | 0.385815 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.4930 | 0.679415 | ||||||||
\(521\) | 17.6653 | 0.773932 | 0.386966 | − | 0.922094i | \(-0.373523\pi\) | ||||
0.386966 | + | 0.922094i | \(0.373523\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.443651 | 0.0193995 | 0.00969975 | − | 0.999953i | \(-0.496912\pi\) | ||||
0.00969975 | + | 0.999953i | \(0.496912\pi\) | |||||||
\(524\) | 0.514165 | 0.0224614 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.3553 | 0.931137 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.1716 | −0.659634 | ||||||||
\(530\) | 61.9522 | 2.69103 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 48.5989 | 2.10703 | ||||||||
\(533\) | 2.11904 | 0.0917858 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.3137 | −0.618836 | ||||||||
\(536\) | 0.734828 | 0.0317397 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.9021 | −1.20294 | ||||||||
\(539\) | −1.83783 | −0.0791611 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.9581 | −1.28800 | −0.644000 | − | 0.765026i | \(-0.722726\pi\) | ||||
−0.644000 | + | 0.765026i | \(0.722726\pi\) | |||||||
\(542\) | 68.6784 | 2.94999 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.82021 | 0.420652 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.8925 | 0.722270 | 0.361135 | − | 0.932514i | \(-0.382389\pi\) | ||||
0.361135 | + | 0.932514i | \(0.382389\pi\) | |||||||
\(548\) | −2.29363 | −0.0979791 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.01962 | −0.299318 | ||||||||
\(551\) | −61.2733 | −2.61033 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.27208 | −0.309240 | ||||||||
\(554\) | 25.2638 | 1.07335 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.5291 | −1.08267 | ||||||||
\(557\) | −11.7464 | −0.497712 | −0.248856 | − | 0.968540i | \(-0.580055\pi\) | ||||
−0.248856 | + | 0.968540i | \(0.580055\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.6274 | 1.50688 | ||||||||
\(560\) | −20.3752 | −0.861011 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −69.8995 | −2.94853 | ||||||||
\(563\) | 15.8771 | 0.669141 | 0.334571 | − | 0.942371i | \(-0.391409\pi\) | ||||
0.334571 | + | 0.942371i | \(0.391409\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.92893 | −0.249432 | ||||||||
\(566\) | 7.23486 | 0.304104 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.0952 | 0.675341 | ||||||||
\(569\) | −19.4252 | −0.814346 | −0.407173 | − | 0.913351i | \(-0.633485\pi\) | ||||
−0.407173 | + | 0.913351i | \(0.633485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.6858 | −1.87004 | −0.935021 | − | 0.354593i | \(-0.884619\pi\) | ||||
−0.935021 | + | 0.354593i | \(0.884619\pi\) | |||||||
\(572\) | −13.2284 | −0.553108 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.01219 | 0.125727 | ||||||||
\(575\) | −7.91375 | −0.330026 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3137 | 0.429365 | 0.214683 | − | 0.976684i | \(-0.431128\pi\) | ||||
0.214683 | + | 0.976684i | \(0.431128\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −69.1127 | −2.86975 | ||||||||
\(581\) | 30.2972 | 1.25694 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.9832 | −0.496295 | ||||||||
\(584\) | −15.0321 | −0.622034 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.5269 | −1.26106 | ||||||||
\(587\) | 3.02846 | 0.124998 | 0.0624990 | − | 0.998045i | \(-0.480093\pi\) | ||||
0.0624990 | + | 0.998045i | \(0.480093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −50.2834 | −2.07189 | ||||||||
\(590\) | −38.4922 | −1.58470 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.47795 | −0.142943 | ||||||||
\(593\) | −15.1423 | −0.621820 | −0.310910 | − | 0.950439i | \(-0.600634\pi\) | ||||
−0.310910 | + | 0.950439i | \(0.600634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.88090 | 0.281853 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26.4483 | −1.08155 | ||||||||
\(599\) | 8.93319 | 0.365000 | 0.182500 | − | 0.983206i | \(-0.441581\pi\) | ||||
0.182500 | + | 0.983206i | \(0.441581\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.43289 | −0.140030 | −0.0700152 | − | 0.997546i | \(-0.522305\pi\) | ||||
−0.0700152 | + | 0.997546i | \(0.522305\pi\) | |||||||
\(602\) | 50.6440 | 2.06410 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | −27.0192 | −1.09849 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.1033 | 1.01891 | 0.509455 | − | 0.860497i | \(-0.329847\pi\) | ||||
0.509455 | + | 0.860497i | \(0.329847\pi\) | |||||||
\(608\) | −50.2294 | −2.03707 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.58579 | −0.185673 | ||||||||
\(611\) | −26.7365 | −1.08164 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.68629 | −0.148888 | −0.0744440 | − | 0.997225i | \(-0.523718\pi\) | ||||
−0.0744440 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(614\) | −8.35055 | −0.337001 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.25988 | −0.171636 | ||||||||
\(617\) | 4.35456 | 0.175308 | 0.0876540 | − | 0.996151i | \(-0.472063\pi\) | ||||
0.0876540 | + | 0.996151i | \(0.472063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.48181 | −0.0997524 | −0.0498762 | − | 0.998755i | \(-0.515883\pi\) | ||||
−0.0498762 | + | 0.998755i | \(0.515883\pi\) | |||||||
\(620\) | −56.7168 | −2.27780 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −42.3671 | −1.69877 | ||||||||
\(623\) | −32.8963 | −1.31796 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1421 | −1.24569 | ||||||||
\(626\) | 57.8789 | 2.31330 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 48.6102 | 1.93976 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1421 | −0.443561 | −0.221781 | − | 0.975097i | \(-0.571187\pi\) | ||||
−0.221781 | + | 0.975097i | \(0.571187\pi\) | |||||||
\(632\) | −3.11326 | −0.123839 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.4567 | 0.812438 | ||||||||
\(635\) | 19.3043 | 0.766069 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00000 | 0.277350 | ||||||||
\(638\) | 23.7081 | 0.938612 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.8741 | −1.06229 | ||||||||
\(641\) | −1.15894 | −0.0457754 | −0.0228877 | − | 0.999738i | \(-0.507286\pi\) | ||||
−0.0228877 | + | 0.999738i | \(0.507286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.0740 | 1.30431 | 0.652155 | − | 0.758086i | \(-0.273865\pi\) | ||||
0.652155 | + | 0.758086i | \(0.273865\pi\) | |||||||
\(644\) | −21.1992 | −0.835366 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.5274 | 0.807017 | 0.403508 | − | 0.914976i | \(-0.367791\pi\) | ||||
0.403508 | + | 0.914976i | \(0.367791\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.44543 | 0.292259 | ||||||||
\(650\) | 26.7365 | 1.04869 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.9105 | 0.858080 | ||||||||
\(653\) | 12.7484 | 0.498882 | 0.249441 | − | 0.968390i | \(-0.419753\pi\) | ||||
0.249441 | + | 0.968390i | \(0.419753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.556349 | 0.0217384 | ||||||||
\(656\) | −1.19306 | −0.0465811 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −38.0057 | −1.48162 | ||||||||
\(659\) | −41.2071 | −1.60520 | −0.802599 | − | 0.596518i | \(-0.796550\pi\) | ||||
−0.802599 | + | 0.596518i | \(0.796550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.2132 | −1.01958 | −0.509788 | − | 0.860300i | \(-0.670276\pi\) | ||||
−0.509788 | + | 0.860300i | \(0.670276\pi\) | |||||||
\(662\) | 58.1234 | 2.25903 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.9706 | 0.503355 | ||||||||
\(665\) | 52.5861 | 2.03920 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.7279 | 1.03491 | ||||||||
\(668\) | 14.9839 | 0.579744 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.50981 | 0.135596 | ||||||||
\(671\) | 0.887016 | 0.0342429 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.0836 | 1.69930 | 0.849649 | − | 0.527349i | \(-0.176814\pi\) | ||||
0.849649 | + | 0.527349i | \(0.176814\pi\) | |||||||
\(674\) | −20.3468 | −0.783729 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.7696 | 0.644983 | ||||||||
\(677\) | 29.8172 | 1.14597 | 0.572983 | − | 0.819567i | \(-0.305786\pi\) | ||||
0.572983 | + | 0.819567i | \(0.305786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4853 | 0.709400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.4558 | 0.745003 | ||||||||
\(683\) | 33.0951 | 1.26635 | 0.633175 | − | 0.774008i | \(-0.281751\pi\) | ||||
0.633175 | + | 0.774008i | \(0.281751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.48181 | −0.0948251 | ||||||||
\(686\) | −33.9729 | −1.29709 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.0589 | −0.764737 | ||||||||
\(689\) | 45.6421 | 1.73883 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.63274 | 0.366447 | 0.183223 | − | 0.983071i | \(-0.441347\pi\) | ||||
0.183223 | + | 0.983071i | \(0.441347\pi\) | |||||||
\(692\) | −45.6788 | −1.73645 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 63.4260 | 2.40762 | ||||||||
\(695\) | −27.6236 | −1.04782 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 33.6805 | 1.27482 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.4303 | 0.809988 | ||||||||
\(701\) | 23.7081 | 0.895442 | 0.447721 | − | 0.894173i | \(-0.352236\pi\) | ||||
0.447721 | + | 0.894173i | \(0.352236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.97616 | 0.338542 | ||||||||
\(704\) | 13.6743 | 0.515371 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −37.0122 | −1.39297 | ||||||||
\(707\) | −3.67567 | −0.138238 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.6411 | 1.11319 | 0.556597 | − | 0.830783i | \(-0.312107\pi\) | ||||
0.556597 | + | 0.830783i | \(0.312107\pi\) | |||||||
\(710\) | 76.8768 | 2.88513 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.0833 | −0.527793 | ||||||||
\(713\) | 21.9341 | 0.821437 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3137 | −0.535302 | ||||||||
\(716\) | 46.9857 | 1.75594 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.0416 | −0.897226 | ||||||||
\(719\) | −3.75803 | −0.140151 | −0.0700755 | − | 0.997542i | \(-0.522324\pi\) | ||||
−0.0700755 | + | 0.997542i | \(0.522324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.93015 | 0.109125 | ||||||||
\(722\) | 47.4162 | 1.76465 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.2500 | −0.826916 | ||||||||
\(725\) | −27.0192 | −1.00347 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.85786 | 0.143080 | 0.0715401 | − | 0.997438i | \(-0.477209\pi\) | ||||
0.0715401 | + | 0.997438i | \(0.477209\pi\) | |||||||
\(728\) | 16.2252 | 0.601345 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −71.7990 | −2.65740 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.8701 | −0.770853 | −0.385427 | − | 0.922739i | \(-0.625946\pi\) | ||||
−0.385427 | + | 0.922739i | \(0.625946\pi\) | |||||||
\(734\) | 1.63899 | 0.0604963 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.9105 | 0.807631 | ||||||||
\(737\) | −0.678892 | −0.0250073 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.89949 | −0.253802 | −0.126901 | − | 0.991915i | \(-0.540503\pi\) | ||||
−0.126901 | + | 0.991915i | \(0.540503\pi\) | |||||||
\(740\) | 10.1246 | 0.372187 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 64.8798 | 2.38181 | ||||||||
\(743\) | −1.35778 | −0.0498123 | −0.0249061 | − | 0.999690i | \(-0.507929\pi\) | ||||
−0.0249061 | + | 0.999690i | \(0.507929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.44543 | 0.272779 | ||||||||
\(746\) | −68.6154 | −2.51219 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.9901 | −0.547727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.59220 | −0.167572 | −0.0837859 | − | 0.996484i | \(-0.526701\pi\) | ||||
−0.0837859 | + | 0.996484i | \(0.526701\pi\) | |||||||
\(752\) | 15.0532 | 0.548932 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −90.3001 | −3.28854 | ||||||||
\(755\) | 15.1486 | 0.551314 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.97056 | −0.362386 | −0.181193 | − | 0.983448i | \(-0.557996\pi\) | ||||
−0.181193 | + | 0.983448i | \(0.557996\pi\) | |||||||
\(758\) | −41.2077 | −1.49673 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.5127 | 0.816620 | ||||||||
\(761\) | 19.9448 | 0.722998 | 0.361499 | − | 0.932372i | \(-0.382265\pi\) | ||||
0.361499 | + | 0.932372i | \(0.382265\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.2843 | 0.372316 | ||||||||
\(764\) | −59.0104 | −2.13492 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.3137 | 1.13141 | ||||||||
\(767\) | −28.3584 | −1.02396 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.24264 | −0.261176 | −0.130588 | − | 0.991437i | \(-0.541687\pi\) | ||||
−0.130588 | + | 0.991437i | \(0.541687\pi\) | |||||||
\(770\) | −20.3468 | −0.733247 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.7930 | 0.604394 | ||||||||
\(773\) | 46.8966 | 1.68675 | 0.843376 | − | 0.537324i | \(-0.180565\pi\) | ||||
0.843376 | + | 0.537324i | \(0.180565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.1731 | −0.796482 | ||||||||
\(776\) | 7.91375 | 0.284087 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.58579 | −0.164408 | ||||||||
\(779\) | 3.07914 | 0.110322 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.8701 | −0.532092 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.94113 | −0.140754 | ||||||||
\(785\) | 52.5983 | 1.87731 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.72191 | 0.0970257 | 0.0485128 | − | 0.998823i | \(-0.484552\pi\) | ||||
0.0485128 | + | 0.998823i | \(0.484552\pi\) | |||||||
\(788\) | 48.1614 | 1.71568 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.8701 | −0.529053 | ||||||||
\(791\) | −6.20911 | −0.220770 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.37849 | −0.119974 | ||||||||
\(794\) | −43.8068 | −1.55465 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.7453 | −1.23152 | ||||||||
\(797\) | 9.30061 | 0.329444 | 0.164722 | − | 0.986340i | \(-0.447327\pi\) | ||||
0.164722 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −22.1493 | −0.783095 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −44.8490 | −1.58367 | ||||||||
\(803\) | 13.8879 | 0.490092 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.9385 | −0.808475 | ||||||||
\(806\) | −74.1040 | −2.61020 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.57359 | −0.0553588 | ||||||||
\(809\) | 11.3906 | 0.400471 | 0.200236 | − | 0.979748i | \(-0.435829\pi\) | ||||
0.200236 | + | 0.979748i | \(0.435829\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.2751 | 1.06310 | 0.531552 | − | 0.847026i | \(-0.321609\pi\) | ||||
0.531552 | + | 0.847026i | \(0.321609\pi\) | |||||||
\(812\) | −72.3787 | −2.53999 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.47309 | −0.121732 | ||||||||
\(815\) | 23.7081 | 0.830458 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.7696 | 1.81119 | ||||||||
\(818\) | −5.99388 | −0.209571 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.47309 | 0.121285 | ||||||||
\(821\) | 50.2804 | 1.75480 | 0.877399 | − | 0.479761i | \(-0.159276\pi\) | ||||
0.877399 | + | 0.479761i | \(0.159276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.2973 | 1.57896 | 0.789482 | − | 0.613773i | \(-0.210349\pi\) | ||||
0.789482 | + | 0.613773i | \(0.210349\pi\) | |||||||
\(824\) | 1.25443 | 0.0437001 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −40.3111 | −1.40260 | ||||||||
\(827\) | −7.71491 | −0.268274 | −0.134137 | − | 0.990963i | \(-0.542826\pi\) | ||||
−0.134137 | + | 0.990963i | \(0.542826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2426 | 0.425204 | 0.212602 | − | 0.977139i | \(-0.431806\pi\) | ||||
0.212602 | + | 0.977139i | \(0.431806\pi\) | |||||||
\(830\) | 61.9522 | 2.15039 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −52.0833 | −1.80566 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.2132 | 0.561081 | ||||||||
\(836\) | −19.2220 | −0.664805 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −62.2216 | −2.14941 | ||||||||
\(839\) | −4.43692 | −0.153180 | −0.0765898 | − | 0.997063i | \(-0.524403\pi\) | ||||
−0.0765898 | + | 0.997063i | \(0.524403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.2548 | 2.14672 | ||||||||
\(842\) | 33.8957 | 1.16812 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.0698 | −0.794095 | ||||||||
\(845\) | 18.1454 | 0.624220 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.2960 | −0.972264 | ||||||||
\(848\) | −25.6973 | −0.882450 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.91548 | −0.134221 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0936 | 0.482557 | 0.241278 | − | 0.970456i | \(-0.422433\pi\) | ||||
0.241278 | + | 0.970456i | \(0.422433\pi\) | |||||||
\(854\) | −4.80249 | −0.164338 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.41743 | −0.219343 | ||||||||
\(857\) | 18.4266 | 0.629440 | 0.314720 | − | 0.949185i | \(-0.398089\pi\) | ||||
0.314720 | + | 0.949185i | \(0.398089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7279 | −0.434271 | −0.217136 | − | 0.976141i | \(-0.569671\pi\) | ||||
−0.217136 | + | 0.976141i | \(0.569671\pi\) | |||||||
\(860\) | 58.3930 | 1.99119 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.41743 | −0.218579 | ||||||||
\(863\) | 27.1040 | 0.922629 | 0.461315 | − | 0.887237i | \(-0.347378\pi\) | ||||
0.461315 | + | 0.887237i | \(0.347378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.4264 | −1.68055 | ||||||||
\(866\) | −2.57190 | −0.0873966 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −59.3970 | −2.01606 | ||||||||
\(869\) | 2.87627 | 0.0975709 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.58579 | 0.0876160 | ||||||||
\(872\) | 4.40281 | 0.149098 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −38.4315 | −1.29997 | ||||||||
\(875\) | −17.8033 | −0.601863 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.9413 | 1.41626 | 0.708129 | − | 0.706083i | \(-0.249539\pi\) | ||||
0.708129 | + | 0.706083i | \(0.249539\pi\) | |||||||
\(878\) | 42.4490 | 1.43259 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.05887 | 0.271665 | ||||||||
\(881\) | −16.7876 | −0.565588 | −0.282794 | − | 0.959181i | \(-0.591261\pi\) | ||||
−0.282794 | + | 0.959181i | \(0.591261\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0000 | 0.841317 | 0.420658 | − | 0.907219i | \(-0.361799\pi\) | ||||
0.420658 | + | 0.907219i | \(0.361799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.9411 | 0.871509 | ||||||||
\(887\) | −7.31722 | −0.245688 | −0.122844 | − | 0.992426i | \(-0.539202\pi\) | ||||
−0.122844 | + | 0.992426i | \(0.539202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.2166 | 0.678042 | ||||||||
\(890\) | −67.2669 | −2.25479 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.6985 | −0.525624 | ||||||||
\(893\) | −38.8504 | −1.30008 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.8406 | 1.69941 | ||||||||
\(896\) | −28.1441 | −0.940227 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.92724 | 0.331276 | ||||||||
\(899\) | 74.8875 | 2.49764 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1.19139 | −0.0396690 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.65819 | −0.0884100 | ||||||||
\(905\) | −24.0755 | −0.800297 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.3378 | 1.67144 | 0.835720 | − | 0.549155i | \(-0.185051\pi\) | ||||
0.835720 | + | 0.549155i | \(0.185051\pi\) | |||||||
\(908\) | 54.1549 | 1.79719 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 77.4975 | 2.56902 | ||||||||
\(911\) | −28.1782 | −0.933584 | −0.466792 | − | 0.884367i | \(-0.654590\pi\) | ||||
−0.466792 | + | 0.884367i | \(0.654590\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.9832 | −0.396587 | ||||||||
\(914\) | −31.1716 | −1.03107 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37.7157 | 1.24616 | ||||||||
\(917\) | 0.582640 | 0.0192405 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.8284 | 1.44577 | 0.722883 | − | 0.690970i | \(-0.242816\pi\) | ||||
0.722883 | + | 0.690970i | \(0.242816\pi\) | |||||||
\(920\) | −9.82021 | −0.323763 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.5269 | −1.00535 | ||||||||
\(923\) | 56.6375 | 1.86425 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.95815 | 0.130143 | ||||||||
\(926\) | −61.0888 | −2.00750 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 74.8070 | 2.45566 | ||||||||
\(929\) | 20.8268 | 0.683306 | 0.341653 | − | 0.939826i | \(-0.389013\pi\) | ||||
0.341653 | + | 0.939826i | \(0.389013\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.1716 | 0.333360 | ||||||||
\(932\) | −34.4188 | −1.12743 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.1005 | 1.05036 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.28427 | −0.139961 | −0.0699805 | − | 0.997548i | \(-0.522294\pi\) | ||||
−0.0699805 | + | 0.997548i | \(0.522294\pi\) | |||||||
\(938\) | 3.67567 | 0.120015 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −43.8210 | −1.42928 | ||||||||
\(941\) | −26.7380 | −0.871635 | −0.435817 | − | 0.900035i | \(-0.643541\pi\) | ||||
−0.435817 | + | 0.900035i | \(0.643541\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.34315 | −0.0437388 | ||||||||
\(944\) | 15.9663 | 0.519658 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0309 | −0.651259 | ||||||||
\(947\) | 47.7637 | 1.55211 | 0.776056 | − | 0.630664i | \(-0.217217\pi\) | ||||
0.776056 | + | 0.630664i | \(0.217217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.8966 | −1.71710 | ||||||||
\(950\) | 38.8504 | 1.26047 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.7081 | 0.767980 | 0.383990 | − | 0.923337i | \(-0.374550\pi\) | ||||
0.383990 | + | 0.923337i | \(0.374550\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.8518 | −2.06620 | ||||||||
\(956\) | −59.9605 | −1.93926 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.44543 | −0.240551 | ||||||||
\(959\) | −2.59909 | −0.0839290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.4558 | 0.982447 | ||||||||
\(962\) | 13.2284 | 0.426501 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24.5687 | −0.791303 | ||||||||
\(965\) | 18.1708 | 0.584938 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.38478 | −0.173163 | −0.0865814 | − | 0.996245i | \(-0.527594\pi\) | ||||
−0.0865814 | + | 0.996245i | \(0.527594\pi\) | |||||||
\(968\) | −12.1138 | −0.389354 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 37.7990 | 1.21365 | ||||||||
\(971\) | 59.0104 | 1.89373 | 0.946867 | − | 0.321625i | \(-0.104229\pi\) | ||||
0.946867 | + | 0.321625i | \(0.104229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.9289 | −0.927419 | ||||||||
\(974\) | −65.3467 | −2.09384 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.90215 | 0.0608864 | ||||||||
\(977\) | 43.5007 | 1.39171 | 0.695855 | − | 0.718182i | \(-0.255026\pi\) | ||||
0.695855 | + | 0.718182i | \(0.255026\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.0112 | 0.415841 | ||||||||
\(980\) | 11.4729 | 0.366490 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.8284 | −0.792307 | ||||||||
\(983\) | −41.9690 | −1.33860 | −0.669301 | − | 0.742991i | \(-0.733407\pi\) | ||||
−0.669301 | + | 0.742991i | \(0.733407\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.1127 | 1.66045 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 73.2132 | 2.32922 | ||||||||
\(989\) | −22.5823 | −0.718075 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.8602 | 1.83799 | 0.918995 | − | 0.394270i | \(-0.129002\pi\) | ||||
0.918995 | + | 0.394270i | \(0.129002\pi\) | |||||||
\(992\) | 61.3898 | 1.94913 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 80.5097 | 2.55361 | ||||||||
\(995\) | −37.5960 | −1.19187 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.3646 | −1.08834 | −0.544169 | − | 0.838976i | \(-0.683155\pi\) | ||||
−0.544169 | + | 0.838976i | \(0.683155\pi\) | |||||||
\(998\) | 76.8196 | 2.43168 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2601.2.a.bl.1.6 | 8 | ||
3.2 | odd | 2 | inner | 2601.2.a.bl.1.3 | 8 | ||
17.10 | odd | 16 | 153.2.l.d.100.1 | ✓ | 8 | ||
17.12 | odd | 16 | 153.2.l.d.127.1 | yes | 8 | ||
17.16 | even | 2 | inner | 2601.2.a.bl.1.5 | 8 | ||
51.29 | even | 16 | 153.2.l.d.127.2 | yes | 8 | ||
51.44 | even | 16 | 153.2.l.d.100.2 | yes | 8 | ||
51.50 | odd | 2 | inner | 2601.2.a.bl.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
153.2.l.d.100.1 | ✓ | 8 | 17.10 | odd | 16 | ||
153.2.l.d.100.2 | yes | 8 | 51.44 | even | 16 | ||
153.2.l.d.127.1 | yes | 8 | 17.12 | odd | 16 | ||
153.2.l.d.127.2 | yes | 8 | 51.29 | even | 16 | ||
2601.2.a.bl.1.3 | 8 | 3.2 | odd | 2 | inner | ||
2601.2.a.bl.1.4 | 8 | 51.50 | odd | 2 | inner | ||
2601.2.a.bl.1.5 | 8 | 17.16 | even | 2 | inner | ||
2601.2.a.bl.1.6 | 8 | 1.1 | even | 1 | trivial |