Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3744,2,Mod(1,3744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, 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("3744.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.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: | \(29.8959905168\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.93185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.86370 | −1.72790 | −0.863950 | − | 0.503577i | \(-0.832017\pi\) | ||||
−0.863950 | + | 0.503577i | \(0.832017\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.03528 | 0.391298 | 0.195649 | − | 0.980674i | \(-0.437319\pi\) | ||||
0.195649 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.46410 | −1.64749 | −0.823744 | − | 0.566961i | \(-0.808119\pi\) | ||||
−0.823744 | + | 0.566961i | \(0.808119\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.65685 | 1.37199 | 0.685994 | − | 0.727607i | \(-0.259367\pi\) | ||||
0.685994 | + | 0.727607i | \(0.259367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.69213 | 1.53528 | 0.767640 | − | 0.640881i | \(-0.221431\pi\) | ||||
0.767640 | + | 0.640881i | \(0.221431\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.92820 | 1.44463 | 0.722315 | − | 0.691564i | \(-0.243078\pi\) | ||||
0.722315 | + | 0.691564i | \(0.243078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.92820 | 1.98564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.72741 | −1.43494 | −0.717472 | − | 0.696588i | \(-0.754701\pi\) | ||||
−0.717472 | + | 0.696588i | \(0.754701\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.03528 | 0.185941 | 0.0929705 | − | 0.995669i | \(-0.470364\pi\) | ||||
0.0929705 | + | 0.995669i | \(0.470364\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.86370 | 0.603409 | 0.301705 | − | 0.953401i | \(-0.402444\pi\) | ||||
0.301705 | + | 0.953401i | \(0.402444\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.46410 | −1.38048 | −0.690241 | − | 0.723580i | \(-0.742495\pi\) | ||||
−0.690241 | + | 0.723580i | \(0.742495\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.92820 | −0.846886 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65685 | 0.777029 | 0.388514 | − | 0.921443i | \(-0.372988\pi\) | ||||
0.388514 | + | 0.921443i | \(0.372988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.1117 | 2.84670 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.53590 | −0.330146 | −0.165073 | − | 0.986281i | \(-0.552786\pi\) | ||||
−0.165073 | + | 0.986281i | \(0.552786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92820 | 0.630992 | 0.315496 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.86370 | 0.479233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.69213 | −0.817574 | −0.408787 | − | 0.912630i | \(-0.634048\pi\) | ||||
−0.408787 | + | 0.912630i | \(0.634048\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.46410 | −1.12318 | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||||
−0.561591 | + | 0.827415i | \(0.689811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.8564 | −1.85585 | −0.927926 | − | 0.372764i | \(-0.878410\pi\) | ||||
−0.927926 | + | 0.372764i | \(0.878410\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.65685 | −0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.4641 | −1.47788 | −0.738939 | − | 0.673773i | \(-0.764673\pi\) | ||||
−0.738939 | + | 0.673773i | \(0.764673\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.8564 | −2.37066 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.277401 | 0.0294045 | 0.0147022 | − | 0.999892i | \(-0.495320\pi\) | ||||
0.0147022 | + | 0.999892i | \(0.495320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.03528 | −0.108526 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −25.8564 | −2.65281 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.07055 | −0.206028 | −0.103014 | − | 0.994680i | \(-0.532849\pi\) | ||||
−0.103014 | + | 0.994680i | \(0.532849\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9706 | −1.67216 | −0.836080 | − | 0.548608i | \(-0.815158\pi\) | ||||
−0.836080 | + | 0.548608i | \(0.815158\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92820 | 0.669775 | 0.334887 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334887 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.00000 | −0.574696 | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.24316 | −0.869523 | −0.434761 | − | 0.900546i | \(-0.643167\pi\) | ||||
−0.434761 | + | 0.900546i | \(0.643167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.7685 | −2.49618 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.85641 | 0.536856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8564 | 1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −19.0411 | −1.70309 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.5254 | −1.55512 | −0.777562 | − | 0.628806i | \(-0.783544\pi\) | ||||
−0.777562 | + | 0.628806i | \(0.783544\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.07180 | −0.0936433 | −0.0468217 | − | 0.998903i | \(-0.514909\pi\) | ||||
−0.0468217 | + | 0.998903i | \(0.514909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.92820 | 0.600751 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.3185 | 1.65049 | 0.825246 | − | 0.564773i | \(-0.191036\pi\) | ||||
0.825246 | + | 0.564773i | \(0.191036\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.58630 | 0.304186 | 0.152093 | − | 0.988366i | \(-0.451399\pi\) | ||||
0.152093 | + | 0.988366i | \(0.451399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.46410 | 0.456931 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 29.8564 | 2.47944 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.4596 | 1.92189 | 0.960944 | − | 0.276745i | \(-0.0892556\pi\) | ||||
0.960944 | + | 0.276745i | \(0.0892556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.4901 | −1.34194 | −0.670972 | − | 0.741482i | \(-0.734123\pi\) | ||||
−0.670972 | + | 0.741482i | \(0.734123\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.9282 | −1.35102 | −0.675509 | − | 0.737352i | \(-0.736076\pi\) | ||||
−0.675509 | + | 0.737352i | \(0.736076\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.17260 | 0.565280 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.9038 | 1.01070 | 0.505351 | − | 0.862914i | \(-0.331363\pi\) | ||||
0.505351 | + | 0.862914i | \(0.331363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.46410 | −0.732354 | −0.366177 | − | 0.930545i | \(-0.619334\pi\) | ||||
−0.366177 | + | 0.930545i | \(0.619334\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.21166 | −0.472264 | −0.236132 | − | 0.971721i | \(-0.575880\pi\) | ||||
−0.236132 | + | 0.971721i | \(0.575880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.2784 | 0.776976 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.8564 | −1.33465 | −0.667325 | − | 0.744766i | \(-0.732561\pi\) | ||||
−0.667325 | + | 0.744766i | \(0.732561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.7846 | 1.69357 | 0.846783 | − | 0.531938i | \(-0.178536\pi\) | ||||
0.846783 | + | 0.531938i | \(0.178536\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.72741 | 0.568130 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.9096 | −2.26034 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0000 | −1.44715 | −0.723575 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723575 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000 | 0.719816 | 0.359908 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359908 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5911 | 0.825832 | 0.412916 | − | 0.910769i | \(-0.364510\pi\) | ||||
0.412916 | + | 0.910769i | \(0.364510\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.3843 | 0.948785 | 0.474393 | − | 0.880313i | \(-0.342668\pi\) | ||||
0.474393 | + | 0.880313i | \(0.342668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.00000 | −0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.9282 | −1.04263 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −36.5665 | −2.52936 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4548 | 1.06395 | 0.531977 | − | 0.846759i | \(-0.321449\pi\) | ||||
0.531977 | + | 0.846759i | \(0.321449\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.8564 | −1.49059 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.07180 | 0.0727583 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.65685 | −0.380521 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.5606 | −1.24291 | −0.621456 | − | 0.783449i | \(-0.713459\pi\) | ||||
−0.621456 | + | 0.783449i | \(0.713459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.53590 | −0.168313 | −0.0841567 | − | 0.996453i | \(-0.526820\pi\) | ||||
−0.0841567 | + | 0.996453i | \(0.526820\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.58630 | 0.234946 | 0.117473 | − | 0.993076i | \(-0.462521\pi\) | ||||
0.117473 | + | 0.993076i | \(0.462521\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.5665 | 2.38533 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.60770 | −0.233362 | −0.116681 | − | 0.993169i | \(-0.537226\pi\) | ||||
−0.116681 | + | 0.993169i | \(0.537226\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.9048 | 1.46334 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.69213 | −0.425810 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.7846 | 1.56439 | 0.782195 | − | 0.623033i | \(-0.214100\pi\) | ||||
0.782195 | + | 0.623033i | \(0.214100\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.8564 | −2.38001 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.8685 | −0.740337 | −0.370169 | − | 0.928965i | \(-0.620700\pi\) | ||||
−0.370169 | + | 0.928965i | \(0.620700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.07055 | −0.128658 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.92820 | −0.180561 | −0.0902804 | − | 0.995916i | \(-0.528776\pi\) | ||||
−0.0902804 | + | 0.995916i | \(0.528776\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8564 | −1.34263 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.58630 | −0.218661 | −0.109330 | − | 0.994005i | \(-0.534871\pi\) | ||||
−0.109330 | + | 0.994005i | \(0.534871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.8744 | −1.81474 | −0.907369 | − | 0.420335i | \(-0.861912\pi\) | ||||
−0.907369 | + | 0.420335i | \(0.861912\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −54.2487 | −3.27132 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.277401 | −0.0165484 | −0.00827419 | − | 0.999966i | \(-0.502634\pi\) | ||||
−0.00827419 | + | 0.999966i | \(0.502634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.6980 | −1.46814 | −0.734071 | − | 0.679073i | \(-0.762382\pi\) | ||||
−0.734071 | + | 0.679073i | \(0.762382\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.45001 | −0.435234 | −0.217617 | − | 0.976034i | \(-0.569828\pi\) | ||||
−0.217617 | + | 0.976034i | \(0.569828\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.79796 | 0.570459 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.92820 | −0.400668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.85641 | 0.337558 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.0411 | −1.09029 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.2880 | 1.50034 | 0.750169 | − | 0.661246i | \(-0.229972\pi\) | ||||
0.750169 | + | 0.661246i | \(0.229972\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.92820 | 0.392862 | 0.196431 | − | 0.980518i | \(-0.437065\pi\) | ||||
0.196431 | + | 0.980518i | \(0.437065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.8564 | −1.12235 | −0.561175 | − | 0.827697i | \(-0.689651\pi\) | ||||
−0.561175 | + | 0.827697i | \(0.689651\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.1459 | −0.682182 | −0.341091 | − | 0.940030i | \(-0.610797\pi\) | ||||
−0.341091 | + | 0.940030i | \(0.610797\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.2233 | 2.36405 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 37.8564 | 2.10639 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.92820 | −0.550718 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.79796 | −0.540179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.4607 | −1.83916 | −0.919582 | − | 0.392898i | \(-0.871472\pi\) | ||||
−0.919582 | + | 0.392898i | \(0.871472\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.8564 | 1.41269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.143594 | 0.00782204 | 0.00391102 | − | 0.999992i | \(-0.498755\pi\) | ||||
0.00391102 | + | 0.999992i | \(0.498755\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.65685 | −0.306336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.3843 | −0.722682 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0000 | −1.28839 | −0.644194 | − | 0.764862i | \(-0.722807\pi\) | ||||
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.0459 | −1.43951 | −0.719755 | − | 0.694229i | \(-0.755746\pi\) | ||||
−0.719755 | + | 0.694229i | \(0.755746\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.5665 | 1.94075 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.46410 | −0.0772723 | −0.0386362 | − | 0.999253i | \(-0.512301\pi\) | ||||
−0.0386362 | + | 0.999253i | \(0.512301\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.7846 | 1.35708 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 61.2645 | 3.20673 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.1822 | 1.21010 | 0.605051 | − | 0.796187i | \(-0.293153\pi\) | ||||
0.605051 | + | 0.796187i | \(0.293153\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.85641 | 0.304049 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.72741 | 0.397982 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.62158 | −0.237395 | −0.118697 | − | 0.992930i | \(-0.537872\pi\) | ||||
−0.118697 | + | 0.992930i | \(0.537872\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.46410 | 0.483593 | 0.241797 | − | 0.970327i | \(-0.422263\pi\) | ||||
0.241797 | + | 0.970327i | \(0.422263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.8564 | 1.11391 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.14110 | 0.209962 | 0.104981 | − | 0.994474i | \(-0.466522\pi\) | ||||
0.104981 | + | 0.994474i | \(0.466522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.1918 | 1.98202 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.14359 | −0.207961 | −0.103980 | − | 0.994579i | \(-0.533158\pi\) | ||||
−0.103980 | + | 0.994579i | \(0.533158\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.4911 | −1.32290 | −0.661452 | − | 0.749988i | \(-0.730059\pi\) | ||||
−0.661452 | + | 0.749988i | \(0.730059\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.03528 | −0.0515708 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.9282 | 0.541691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.8564 | 1.37741 | 0.688705 | − | 0.725041i | \(-0.258179\pi\) | ||||
0.688705 | + | 0.725041i | \(0.258179\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.62536 | −0.129185 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 52.0213 | 2.55362 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7846 | −0.624569 | −0.312285 | − | 0.949989i | \(-0.601094\pi\) | ||||
−0.312285 | + | 0.949989i | \(0.601094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.7128 | −0.863270 | −0.431635 | − | 0.902048i | \(-0.642063\pi\) | ||||
−0.431635 | + | 0.902048i | \(0.642063\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 56.1624 | 2.72428 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.10205 | 0.246906 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.3923 | −0.982263 | −0.491131 | − | 0.871086i | \(-0.663417\pi\) | ||||
−0.491131 | + | 0.871086i | \(0.663417\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.07180 | 0.147621 | 0.0738106 | − | 0.997272i | \(-0.476484\pi\) | ||||
0.0738106 | + | 0.997272i | \(0.476484\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 46.3644 | 2.21791 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.0802 | −0.862919 | −0.431460 | − | 0.902132i | \(-0.642001\pi\) | ||||
−0.431460 | + | 0.902132i | \(0.642001\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.6410 | −1.64584 | −0.822922 | − | 0.568154i | \(-0.807658\pi\) | ||||
−0.822922 | + | 0.568154i | \(0.807658\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.07180 | −0.0508080 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.41851 | 0.208522 | 0.104261 | − | 0.994550i | \(-0.466752\pi\) | ||||
0.104261 | + | 0.994550i | \(0.466752\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.1117 | −0.994110 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.00000 | 0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.00000 | −0.0935561 | −0.0467780 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467780 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.89520 | −0.321142 | −0.160571 | − | 0.987024i | \(-0.551333\pi\) | ||||
−0.160571 | + | 0.987024i | \(0.551333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.24693 | −0.336794 | −0.168397 | − | 0.985719i | \(-0.553859\pi\) | ||||
−0.168397 | + | 0.985719i | \(0.553859\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0718 | 0.975086 | 0.487543 | − | 0.873099i | \(-0.337893\pi\) | ||||
0.487543 | + | 0.873099i | \(0.337893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.92820 | −0.319915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.9096 | −1.42123 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 66.4408 | 3.04851 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.4641 | 1.16348 | 0.581742 | − | 0.813373i | \(-0.302371\pi\) | ||||
0.581742 | + | 0.813373i | \(0.302371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.1822 | −1.05265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.17638 | 0.234564 | 0.117282 | − | 0.993099i | \(-0.462582\pi\) | ||||
0.117282 | + | 0.993099i | \(0.462582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.7846 | −1.11851 | −0.559257 | − | 0.828994i | \(-0.688913\pi\) | ||||
−0.559257 | + | 0.828994i | \(0.688913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.7128 | −1.96873 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.79796 | −0.439499 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.4292 | −1.36220 | −0.681098 | − | 0.732192i | \(-0.738497\pi\) | ||||
−0.681098 | + | 0.732192i | \(0.738497\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.92820 | 0.130562 | 0.0652811 | − | 0.997867i | \(-0.479206\pi\) | ||||
0.0652811 | + | 0.997867i | \(0.479206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7322 | 0.697318 | 0.348659 | − | 0.937250i | \(-0.386637\pi\) | ||||
0.348659 | + | 0.937250i | \(0.386637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.4158 | −0.726190 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 65.5692 | 2.88933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.7128 | 2.27433 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.8391 | −1.26346 | −0.631731 | − | 0.775187i | \(-0.717655\pi\) | ||||
−0.631731 | + | 0.775187i | \(0.717655\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.8685 | 0.518974 | 0.259487 | − | 0.965747i | \(-0.416447\pi\) | ||||
0.259487 | + | 0.965747i | \(0.416447\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.85641 | 0.255109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.86370 | −0.167356 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.7685 | −1.15730 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.3923 | 1.39524 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.143594 | −0.00617357 | −0.00308678 | − | 0.999995i | \(-0.500983\pi\) | ||||
−0.00308678 | + | 0.999995i | \(0.500983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.1822 | 0.993017 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.7589 | 0.460018 | 0.230009 | − | 0.973189i | \(-0.426125\pi\) | ||||
0.230009 | + | 0.973189i | \(0.426125\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.7128 | −2.20304 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.30890 | −0.140203 | −0.0701013 | − | 0.997540i | \(-0.522332\pi\) | ||||
−0.0701013 | + | 0.997540i | \(0.522332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65685 | −0.239259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.8564 | 1.08972 | 0.544859 | − | 0.838528i | \(-0.316583\pi\) | ||||
0.544859 | + | 0.838528i | \(0.316583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.7128 | 1.50245 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.7781 | 1.79335 | 0.896676 | − | 0.442687i | \(-0.145975\pi\) | ||||
0.896676 | + | 0.442687i | \(0.145975\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4158 | 0.686978 | 0.343489 | − | 0.939157i | \(-0.388391\pi\) | ||||
0.343489 | + | 0.939157i | \(0.388391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 68.7846 | 2.86852 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.8564 | 0.660111 | 0.330055 | − | 0.943962i | \(-0.392933\pi\) | ||||
0.330055 | + | 0.943962i | \(0.392933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.9391 | −0.578290 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.9096 | −1.28015 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.60770 | −0.314003 | −0.157002 | − | 0.987598i | \(-0.550183\pi\) | ||||
−0.157002 | + | 0.987598i | \(0.550183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.92820 | 0.285472 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.9048 | 0.940588 | 0.470294 | − | 0.882510i | \(-0.344148\pi\) | ||||
0.470294 | + | 0.882510i | \(0.344148\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.6274 | −0.927634 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.9282 | 0.446514 | 0.223257 | − | 0.974760i | \(-0.428331\pi\) | ||||
0.223257 | + | 0.974760i | \(0.428331\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.8564 | −1.46261 | −0.731307 | − | 0.682049i | \(-0.761089\pi\) | ||||
−0.731307 | + | 0.682049i | \(0.761089\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −72.8556 | −2.96200 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.2137 | −1.06398 | −0.531991 | − | 0.846750i | \(-0.678556\pi\) | ||||
−0.531991 | + | 0.846750i | \(0.678556\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.46410 | 0.382877 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.8564 | −0.640434 | −0.320217 | − | 0.947344i | \(-0.603756\pi\) | ||||
−0.320217 | + | 0.947344i | \(0.603756\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.7322 | −0.633355 | −0.316678 | − | 0.948533i | \(-0.602567\pi\) | ||||
−0.316678 | + | 0.948533i | \(0.602567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.2490 | −1.09523 | −0.547615 | − | 0.836731i | \(-0.684464\pi\) | ||||
−0.547615 | + | 0.836731i | \(0.684464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.287187 | 0.0115059 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.3137 | −0.451107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.4510 | 0.694715 | 0.347357 | − | 0.937733i | \(-0.387079\pi\) | ||||
0.347357 | + | 0.937733i | \(0.387079\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 67.7128 | 2.68710 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.92820 | 0.234884 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.4254 | 1.28073 | 0.640363 | − | 0.768073i | \(-0.278784\pi\) | ||||
0.640363 | + | 0.768073i | \(0.278784\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.69213 | −0.263912 | −0.131956 | − | 0.991256i | \(-0.542126\pi\) | ||||
−0.131956 | + | 0.991256i | \(0.542126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.1436 | 0.713298 | 0.356649 | − | 0.934238i | \(-0.383919\pi\) | ||||
0.356649 | + | 0.934238i | \(0.383919\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.8564 | 0.543912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.8096 | 1.79267 | 0.896335 | − | 0.443378i | \(-0.146220\pi\) | ||||
0.896335 | + | 0.443378i | \(0.146220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.14110 | 0.161806 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.8564 | −1.47468 | −0.737338 | − | 0.675524i | \(-0.763918\pi\) | ||||
−0.737338 | + | 0.675524i | \(0.763918\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.8564 | −0.616743 | −0.308371 | − | 0.951266i | \(-0.599784\pi\) | ||||
−0.308371 | + | 0.951266i | \(0.599784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.7685 | −1.03804 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −53.5370 | −2.07296 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.9282 | −1.03955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.9282 | −1.11510 | −0.557550 | − | 0.830143i | \(-0.688259\pi\) | ||||
−0.557550 | + | 0.830143i | \(0.688259\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.9706 | −0.652232 | −0.326116 | − | 0.945330i | \(-0.605740\pi\) | ||||
−0.326116 | + | 0.945330i | \(0.605740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.21166 | 0.238382 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.1769 | −0.657256 | −0.328628 | − | 0.944459i | \(-0.606586\pi\) | ||||
−0.328628 | + | 0.944459i | \(0.606586\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −74.6410 | −2.85189 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.65685 | −0.215509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9743 | −0.569651 | −0.284825 | − | 0.958579i | \(-0.591936\pi\) | ||||
−0.284825 | + | 0.958579i | \(0.591936\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.8564 | −0.525603 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.8564 | 0.827870 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.5959 | −0.740128 | −0.370064 | − | 0.929006i | \(-0.620664\pi\) | ||||
−0.370064 | + | 0.929006i | \(0.620664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.3843 | −0.504797 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.14359 | −0.0806181 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.7128 | 1.41633 | 0.708167 | − | 0.706045i | \(-0.249522\pi\) | ||||
0.708167 | + | 0.706045i | \(0.249522\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.17260 | 0.268616 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.1117 | −0.789532 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.21539 | 0.119914 | 0.0599569 | − | 0.998201i | \(-0.480904\pi\) | ||||
0.0599569 | + | 0.998201i | \(0.480904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5692 | −0.654312 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −76.7193 | −2.84928 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.07055 | −0.0767925 | −0.0383963 | − | 0.999263i | \(-0.512225\pi\) | ||||
−0.0383963 | + | 0.999263i | \(0.512225\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.0000 | 1.18356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.7128 | 1.39295 | 0.696477 | − | 0.717579i | \(-0.254750\pi\) | ||||
0.696477 | + | 0.717579i | \(0.254750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.5665 | 1.34694 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.6723 | −1.45937 | −0.729685 | − | 0.683784i | \(-0.760333\pi\) | ||||
−0.729685 | + | 0.683784i | \(0.760333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.2487 | 0.669480 | 0.334740 | − | 0.942310i | \(-0.391351\pi\) | ||||
0.334740 | + | 0.942310i | \(0.391351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −90.6410 | −3.32083 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.17260 | 0.262081 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.0213 | −1.89828 | −0.949142 | − | 0.314848i | \(-0.898046\pi\) | ||||
−0.949142 | + | 0.314848i | \(0.898046\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.7128 | 2.31875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.6410 | −1.47712 | −0.738561 | − | 0.674186i | \(-0.764495\pi\) | ||||
−0.738561 | + | 0.674186i | \(0.764495\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.9459 | 1.52054 | 0.760269 | − | 0.649608i | \(-0.225067\pi\) | ||||
0.760269 | + | 0.649608i | \(0.225067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.21166 | −0.224877 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.53590 | 0.0915660 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.7128 | −1.21572 | −0.607858 | − | 0.794046i | \(-0.707971\pi\) | ||||
−0.607858 | + | 0.794046i | \(0.707971\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.1185 | 1.76667 | 0.883335 | − | 0.468741i | \(-0.155292\pi\) | ||||
0.883335 | + | 0.468741i | \(0.155292\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.2784 | 0.369212 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.8564 | 0.926402 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.7128 | 1.85043 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 65.4056 | 2.33442 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.9743 | 0.533778 | 0.266889 | − | 0.963727i | \(-0.414004\pi\) | ||||
0.266889 | + | 0.963727i | \(0.414004\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.56922 | −0.340242 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.92820 | −0.175006 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.3644 | −1.64231 | −0.821156 | − | 0.570703i | \(-0.806671\pi\) | ||||
−0.821156 | + | 0.570703i | \(0.806671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53.5370 | −1.89400 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 86.6410 | 3.05750 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.7128 | −0.976748 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.8391 | 1.01393 | 0.506964 | − | 0.861967i | \(-0.330768\pi\) | ||||
0.506964 | + | 0.861967i | \(0.330768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.7744 | 1.57224 | 0.786120 | − | 0.618074i | \(-0.212087\pi\) | ||||
0.786120 | + | 0.618074i | \(0.212087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49.8564 | −1.74639 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.8564 | 1.32443 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.1774 | 0.529695 | 0.264848 | − | 0.964290i | \(-0.414678\pi\) | ||||
0.264848 | + | 0.964290i | \(0.414678\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.1432 | 0.841578 | 0.420789 | − | 0.907159i | \(-0.361753\pi\) | ||||
0.420789 | + | 0.907159i | \(0.361753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.0333 | −1.35732 | −0.678661 | − | 0.734452i | \(-0.737439\pi\) | ||||
−0.678661 | + | 0.734452i | \(0.737439\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.7846 | −1.20812 | −0.604060 | − | 0.796939i | \(-0.706451\pi\) | ||||
−0.604060 | + | 0.796939i | \(0.706451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.5350 | −1.16192 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.5665 | 1.26544 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.3205 | 0.528923 | 0.264461 | − | 0.964396i | \(-0.414806\pi\) | ||||
0.264461 | + | 0.964396i | \(0.414806\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.7128 | 1.05906 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.86370 | −0.132915 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.5216 | 0.670770 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8564 | −0.474991 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.7128 | −0.469518 | −0.234759 | − | 0.972054i | \(-0.575430\pi\) | ||||
−0.234759 | + | 0.972054i | \(0.575430\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.9000 | −0.508975 | −0.254487 | − | 0.967076i | \(-0.581907\pi\) | ||||
−0.254487 | + | 0.967076i | \(0.581907\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.9411 | −1.15806 | −0.579028 | − | 0.815308i | \(-0.696568\pi\) | ||||
−0.579028 | + | 0.815308i | \(0.696568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.1769 | 1.53784 | 0.768920 | − | 0.639345i | \(-0.220794\pi\) | ||||
0.768920 | + | 0.639345i | \(0.220794\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | 0.816024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.69213 | 0.226754 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.7128 | −0.666415 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.0000 | −0.877958 | −0.438979 | − | 0.898497i | \(-0.644660\pi\) | ||||
−0.438979 | + | 0.898497i | \(0.644660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.8096 | 1.54337 | 0.771683 | − | 0.636007i | \(-0.219415\pi\) | ||||
0.771683 | + | 0.636007i | \(0.219415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.5254 | −0.589776 | −0.294888 | − | 0.955532i | \(-0.595282\pi\) | ||||
−0.294888 | + | 0.955532i | \(0.595282\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.8564 | 1.67401 | 0.837007 | − | 0.547192i | \(-0.184303\pi\) | ||||
0.837007 | + | 0.547192i | \(0.184303\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.1436 | −0.608517 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −63.3350 | −2.11943 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 68.9919 | 2.30614 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0000 | 1.06607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −88.0330 | −2.92631 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.9802 | 1.09509 | 0.547544 | − | 0.836777i | \(-0.315563\pi\) | ||||
0.547544 | + | 0.836777i | \(0.315563\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7128 | 1.31574 | 0.657872 | − | 0.753130i | \(-0.271457\pi\) | ||||
0.657872 | + | 0.753130i | \(0.271457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73.5692 | 2.43479 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.10961 | −0.0366424 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.28221 | −0.273205 | −0.136602 | − | 0.990626i | \(-0.543618\pi\) | ||||
−0.136602 | + | 0.990626i | \(0.543618\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.46410 | 0.311515 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.8564 | −0.652875 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.6226 | −0.479752 | −0.239876 | − | 0.970804i | \(-0.577107\pi\) | ||||
−0.239876 | + | 0.970804i | \(0.577107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.6723 | −1.30021 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 119.426 | 3.90564 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6410 | 0.674313 | 0.337156 | − | 0.941449i | \(-0.390535\pi\) | ||||
0.337156 | + | 0.941449i | \(0.390535\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.7733 | 1.13358 | 0.566789 | − | 0.823863i | \(-0.308185\pi\) | ||||
0.566789 | + | 0.823863i | \(0.308185\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.7685 | 0.871703 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.2487 | −0.463021 | −0.231510 | − | 0.972832i | \(-0.574367\pi\) | ||||
−0.231510 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.8564 | 0.514721 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.0726 | −0.715002 | −0.357501 | − | 0.933913i | \(-0.616371\pi\) | ||||
−0.357501 | + | 0.933913i | \(0.616371\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 77.2741 | 2.50053 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.0000 | 0.645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9282 | −0.965426 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.6370 | −1.24377 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.2784 | −0.330532 | −0.165266 | − | 0.986249i | \(-0.552848\pi\) | ||||
−0.165266 | + | 0.986249i | \(0.552848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.7128 | 0.375882 | 0.187941 | − | 0.982180i | \(-0.439819\pi\) | ||||
0.187941 | + | 0.982180i | \(0.439819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.71281 | 0.119027 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.2281 | −1.60694 | −0.803470 | − | 0.595345i | \(-0.797015\pi\) | ||||
−0.803470 | + | 0.595345i | \(0.797015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.51575 | −0.0484436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.6077 | 0.370228 | 0.185114 | − | 0.982717i | \(-0.440735\pi\) | ||||
0.185114 | + | 0.982717i | \(0.440735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.7846 | −1.42696 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39.1918 | 1.24623 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.58630 | −0.113923 | −0.0569613 | − | 0.998376i | \(-0.518141\pi\) | ||||
−0.0569613 | + | 0.998376i | \(0.518141\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.7128 | −1.63941 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.7128 | 1.32106 | 0.660529 | − | 0.750801i | \(-0.270332\pi\) | ||||
0.660529 | + | 0.750801i | \(0.270332\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3744.2.a.bc.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 3744.2.a.bd.1.4 | yes | 4 | ||
4.3 | odd | 2 | 3744.2.a.bd.1.1 | yes | 4 | ||
8.3 | odd | 2 | 7488.2.a.db.1.4 | 4 | |||
8.5 | even | 2 | 7488.2.a.dc.1.4 | 4 | |||
12.11 | even | 2 | inner | 3744.2.a.bc.1.4 | yes | 4 | |
24.5 | odd | 2 | 7488.2.a.db.1.1 | 4 | |||
24.11 | even | 2 | 7488.2.a.dc.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3744.2.a.bc.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3744.2.a.bc.1.4 | yes | 4 | 12.11 | even | 2 | inner | |
3744.2.a.bd.1.1 | yes | 4 | 4.3 | odd | 2 | ||
3744.2.a.bd.1.4 | yes | 4 | 3.2 | odd | 2 | ||
7488.2.a.db.1.1 | 4 | 24.5 | odd | 2 | |||
7488.2.a.db.1.4 | 4 | 8.3 | odd | 2 | |||
7488.2.a.dc.1.1 | 4 | 24.11 | even | 2 | |||
7488.2.a.dc.1.4 | 4 | 8.5 | even | 2 |