Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | −1.22474 | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | −2.73205 | −1.57735 | −0.788675 | − | 0.614810i | \(-0.789233\pi\) | ||||
−0.788675 | + | 0.614810i | \(0.789233\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.73205 | 0.774597 | 0.387298 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387298 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(6\) | 4.73205 | 1.93185 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | −3.00000 | −0.948683 | ||||||||
\(11\) | −1.26795 | −0.382301 | −0.191151 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191151 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(12\) | −2.73205 | −0.788675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.73205 | −1.22181 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 7.73205 | 1.87530 | 0.937649 | − | 0.347584i | \(-0.112998\pi\) | ||||
0.937649 | + | 0.347584i | \(0.112998\pi\) | |||||||
\(18\) | −7.73205 | −1.82246 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.19615 | 0.468221 | ||||||||
\(23\) | 4.73205 | 0.986701 | 0.493350 | − | 0.869831i | \(-0.335772\pi\) | ||||
0.493350 | + | 0.869831i | \(0.335772\pi\) | |||||||
\(24\) | −4.73205 | −0.965926 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 8.19615 | 1.49641 | ||||||||
\(31\) | 4.19615 | 0.753651 | 0.376826 | − | 0.926284i | \(-0.377016\pi\) | ||||
0.376826 | + | 0.926284i | \(0.377016\pi\) | |||||||
\(32\) | 5.19615 | 0.918559 | ||||||||
\(33\) | 3.46410 | 0.603023 | ||||||||
\(34\) | −13.3923 | −2.29676 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.46410 | 0.744017 | ||||||||
\(37\) | 7.00000 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(38\) | −3.46410 | −0.561951 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | −5.19615 | −0.811503 | −0.405751 | − | 0.913984i | \(-0.632990\pi\) | ||||
−0.405751 | + | 0.913984i | \(0.632990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.196152 | −0.0299130 | −0.0149565 | − | 0.999888i | \(-0.504761\pi\) | ||||
−0.0149565 | + | 0.999888i | \(0.504761\pi\) | |||||||
\(44\) | −1.26795 | −0.191151 | ||||||||
\(45\) | 7.73205 | 1.15263 | ||||||||
\(46\) | −8.19615 | −1.20846 | ||||||||
\(47\) | 12.9282 | 1.88577 | 0.942886 | − | 0.333115i | \(-0.108100\pi\) | ||||
0.942886 | + | 0.333115i | \(0.108100\pi\) | |||||||
\(48\) | 13.6603 | 1.97169 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.46410 | 0.489898 | ||||||||
\(51\) | −21.1244 | −2.95800 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.92820 | −1.36374 | −0.681872 | − | 0.731472i | \(-0.738834\pi\) | ||||
−0.681872 | + | 0.731472i | \(0.738834\pi\) | |||||||
\(54\) | 6.92820 | 0.942809 | ||||||||
\(55\) | −2.19615 | −0.296129 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.46410 | −0.723738 | ||||||||
\(58\) | 5.19615 | 0.682288 | ||||||||
\(59\) | 7.26795 | 0.946206 | 0.473103 | − | 0.881007i | \(-0.343134\pi\) | ||||
0.473103 | + | 0.881007i | \(0.343134\pi\) | |||||||
\(60\) | −4.73205 | −0.610905 | ||||||||
\(61\) | 4.80385 | 0.615070 | 0.307535 | − | 0.951537i | \(-0.400496\pi\) | ||||
0.307535 | + | 0.951537i | \(0.400496\pi\) | |||||||
\(62\) | −7.26795 | −0.923030 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | −0.738549 | ||||||||
\(67\) | 6.19615 | 0.756980 | 0.378490 | − | 0.925605i | \(-0.376443\pi\) | ||||
0.378490 | + | 0.925605i | \(0.376443\pi\) | |||||||
\(68\) | 7.73205 | 0.937649 | ||||||||
\(69\) | −12.9282 | −1.55637 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 7.73205 | 0.911231 | ||||||||
\(73\) | −3.19615 | −0.374081 | −0.187041 | − | 0.982352i | \(-0.559890\pi\) | ||||
−0.187041 | + | 0.982352i | \(0.559890\pi\) | |||||||
\(74\) | −12.1244 | −1.40943 | ||||||||
\(75\) | 5.46410 | 0.630940 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.1962 | 1.82221 | 0.911105 | − | 0.412175i | \(-0.135231\pi\) | ||||
0.911105 | + | 0.412175i | \(0.135231\pi\) | |||||||
\(80\) | −8.66025 | −0.968246 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 9.00000 | 0.993884 | ||||||||
\(83\) | −2.19615 | −0.241059 | −0.120530 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120530 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3923 | 1.45260 | ||||||||
\(86\) | 0.339746 | 0.0366357 | ||||||||
\(87\) | 8.19615 | 0.878720 | ||||||||
\(88\) | −2.19615 | −0.234111 | ||||||||
\(89\) | 12.9282 | 1.37039 | 0.685193 | − | 0.728361i | \(-0.259718\pi\) | ||||
0.685193 | + | 0.728361i | \(0.259718\pi\) | |||||||
\(90\) | −13.3923 | −1.41167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.73205 | 0.493350 | ||||||||
\(93\) | −11.4641 | −1.18877 | ||||||||
\(94\) | −22.3923 | −2.30959 | ||||||||
\(95\) | 3.46410 | 0.355409 | ||||||||
\(96\) | −14.1962 | −1.44889 | ||||||||
\(97\) | 6.39230 | 0.649040 | 0.324520 | − | 0.945879i | \(-0.394797\pi\) | ||||
0.324520 | + | 0.945879i | \(0.394797\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.66025 | −0.568877 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 7.73205 | 0.769368 | 0.384684 | − | 0.923048i | \(-0.374310\pi\) | ||||
0.384684 | + | 0.923048i | \(0.374310\pi\) | |||||||
\(102\) | 36.5885 | 3.62280 | ||||||||
\(103\) | 14.3923 | 1.41812 | 0.709058 | − | 0.705150i | \(-0.249120\pi\) | ||||
0.709058 | + | 0.705150i | \(0.249120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.1962 | 1.67024 | ||||||||
\(107\) | −7.85641 | −0.759507 | −0.379754 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379754 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(108\) | −4.00000 | −0.384900 | ||||||||
\(109\) | 8.39230 | 0.803837 | 0.401919 | − | 0.915675i | \(-0.368344\pi\) | ||||
0.401919 | + | 0.915675i | \(0.368344\pi\) | |||||||
\(110\) | 3.80385 | 0.362683 | ||||||||
\(111\) | −19.1244 | −1.81520 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3923 | 1.25984 | 0.629921 | − | 0.776659i | \(-0.283087\pi\) | ||||
0.629921 | + | 0.776659i | \(0.283087\pi\) | |||||||
\(114\) | 9.46410 | 0.886394 | ||||||||
\(115\) | 8.19615 | 0.764295 | ||||||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.5885 | −1.15886 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −8.19615 | −0.748203 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | −8.32051 | −0.753303 | ||||||||
\(123\) | 14.1962 | 1.28002 | ||||||||
\(124\) | 4.19615 | 0.376826 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.3923 | 1.63205 | 0.816027 | − | 0.578014i | \(-0.196172\pi\) | ||||
0.816027 | + | 0.578014i | \(0.196172\pi\) | |||||||
\(128\) | −12.1244 | −1.07165 | ||||||||
\(129\) | 0.535898 | 0.0471832 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.46410 | 0.302660 | 0.151330 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151330 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(132\) | 3.46410 | 0.301511 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.7321 | −0.927108 | ||||||||
\(135\) | −6.92820 | −0.596285 | ||||||||
\(136\) | 13.3923 | 1.14838 | ||||||||
\(137\) | −8.07180 | −0.689620 | −0.344810 | − | 0.938672i | \(-0.612057\pi\) | ||||
−0.344810 | + | 0.938672i | \(0.612057\pi\) | |||||||
\(138\) | 22.3923 | 1.90616 | ||||||||
\(139\) | 10.5885 | 0.898101 | 0.449051 | − | 0.893506i | \(-0.351762\pi\) | ||||
0.449051 | + | 0.893506i | \(0.351762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −35.3205 | −2.97452 | ||||||||
\(142\) | 10.3923 | 0.872103 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −22.3205 | −1.86004 | ||||||||
\(145\) | −5.19615 | −0.431517 | ||||||||
\(146\) | 5.53590 | 0.458154 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.00000 | 0.575396 | ||||||||
\(149\) | 6.46410 | 0.529560 | 0.264780 | − | 0.964309i | \(-0.414701\pi\) | ||||
0.264780 | + | 0.964309i | \(0.414701\pi\) | |||||||
\(150\) | −9.46410 | −0.772741 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 3.46410 | 0.280976 | ||||||||
\(153\) | 34.5167 | 2.79051 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.26795 | 0.583776 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.19615 | −0.0954634 | −0.0477317 | − | 0.998860i | \(-0.515199\pi\) | ||||
−0.0477317 | + | 0.998860i | \(0.515199\pi\) | |||||||
\(158\) | −28.0526 | −2.23174 | ||||||||
\(159\) | 27.1244 | 2.15110 | ||||||||
\(160\) | 9.00000 | 0.711512 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.26795 | 0.335322 | ||||||||
\(163\) | −16.1962 | −1.26858 | −0.634290 | − | 0.773095i | \(-0.718708\pi\) | ||||
−0.634290 | + | 0.773095i | \(0.718708\pi\) | |||||||
\(164\) | −5.19615 | −0.405751 | ||||||||
\(165\) | 6.00000 | 0.467099 | ||||||||
\(166\) | 3.80385 | 0.295236 | ||||||||
\(167\) | −6.58846 | −0.509830 | −0.254915 | − | 0.966963i | \(-0.582048\pi\) | ||||
−0.254915 | + | 0.966963i | \(0.582048\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −23.1962 | −1.77906 | ||||||||
\(171\) | 8.92820 | 0.682757 | ||||||||
\(172\) | −0.196152 | −0.0149565 | ||||||||
\(173\) | −8.53590 | −0.648972 | −0.324486 | − | 0.945890i | \(-0.605191\pi\) | ||||
−0.324486 | + | 0.945890i | \(0.605191\pi\) | |||||||
\(174\) | −14.1962 | −1.07621 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.33975 | 0.477876 | ||||||||
\(177\) | −19.8564 | −1.49250 | ||||||||
\(178\) | −22.3923 | −1.67837 | ||||||||
\(179\) | −6.92820 | −0.517838 | −0.258919 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(180\) | 7.73205 | 0.576313 | ||||||||
\(181\) | −5.58846 | −0.415387 | −0.207693 | − | 0.978194i | \(-0.566596\pi\) | ||||
−0.207693 | + | 0.978194i | \(0.566596\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.1244 | −0.970180 | ||||||||
\(184\) | 8.19615 | 0.604228 | ||||||||
\(185\) | 12.1244 | 0.891400 | ||||||||
\(186\) | 19.8564 | 1.45594 | ||||||||
\(187\) | −9.80385 | −0.716928 | ||||||||
\(188\) | 12.9282 | 0.942886 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | 4.73205 | 0.342399 | 0.171200 | − | 0.985236i | \(-0.445236\pi\) | ||||
0.171200 | + | 0.985236i | \(0.445236\pi\) | |||||||
\(192\) | −2.73205 | −0.197169 | ||||||||
\(193\) | −5.00000 | −0.359908 | −0.179954 | − | 0.983675i | \(-0.557595\pi\) | ||||
−0.179954 | + | 0.983675i | \(0.557595\pi\) | |||||||
\(194\) | −11.0718 | −0.794909 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 9.80385 | 0.696729 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | −3.46410 | −0.244949 | ||||||||
\(201\) | −16.9282 | −1.19402 | ||||||||
\(202\) | −13.3923 | −0.942279 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −21.1244 | −1.47900 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | −24.9282 | −1.73683 | ||||||||
\(207\) | 21.1244 | 1.46824 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.53590 | −0.175412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.80385 | −0.124182 | −0.0620910 | − | 0.998070i | \(-0.519777\pi\) | ||||
−0.0620910 | + | 0.998070i | \(0.519777\pi\) | |||||||
\(212\) | −9.92820 | −0.681872 | ||||||||
\(213\) | 16.3923 | 1.12318 | ||||||||
\(214\) | 13.6077 | 0.930203 | ||||||||
\(215\) | −0.339746 | −0.0231705 | ||||||||
\(216\) | −6.92820 | −0.471405 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.5359 | −0.984495 | ||||||||
\(219\) | 8.73205 | 0.590057 | ||||||||
\(220\) | −2.19615 | −0.148065 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 33.1244 | 2.22316 | ||||||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.92820 | −0.595214 | ||||||||
\(226\) | −23.1962 | −1.54299 | ||||||||
\(227\) | 5.66025 | 0.375684 | 0.187842 | − | 0.982199i | \(-0.439851\pi\) | ||||
0.187842 | + | 0.982199i | \(0.439851\pi\) | |||||||
\(228\) | −5.46410 | −0.361869 | ||||||||
\(229\) | −14.3923 | −0.951070 | −0.475535 | − | 0.879697i | \(-0.657746\pi\) | ||||
−0.475535 | + | 0.879697i | \(0.657746\pi\) | |||||||
\(230\) | −14.1962 | −0.936067 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.19615 | −0.341144 | ||||||||
\(233\) | −1.85641 | −0.121617 | −0.0608086 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608086 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.3923 | 1.46071 | ||||||||
\(236\) | 7.26795 | 0.473103 | ||||||||
\(237\) | −44.2487 | −2.87426 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.8038 | 1.02227 | 0.511133 | − | 0.859502i | \(-0.329226\pi\) | ||||
0.511133 | + | 0.859502i | \(0.329226\pi\) | |||||||
\(240\) | 23.6603 | 1.52726 | ||||||||
\(241\) | −21.1962 | −1.36536 | −0.682682 | − | 0.730716i | \(-0.739187\pi\) | ||||
−0.682682 | + | 0.730716i | \(0.739187\pi\) | |||||||
\(242\) | 16.2679 | 1.04574 | ||||||||
\(243\) | 18.7321 | 1.20166 | ||||||||
\(244\) | 4.80385 | 0.307535 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.5885 | −1.56770 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.26795 | 0.461515 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 21.0000 | 1.32816 | ||||||||
\(251\) | 1.60770 | 0.101477 | 0.0507384 | − | 0.998712i | \(-0.483843\pi\) | ||||
0.0507384 | + | 0.998712i | \(0.483843\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | −31.8564 | −1.99885 | ||||||||
\(255\) | −36.5885 | −2.29126 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −6.12436 | −0.382027 | −0.191013 | − | 0.981587i | \(-0.561177\pi\) | ||||
−0.191013 | + | 0.981587i | \(0.561177\pi\) | |||||||
\(258\) | −0.928203 | −0.0577874 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.3923 | −0.828963 | ||||||||
\(262\) | −6.00000 | −0.370681 | ||||||||
\(263\) | 1.26795 | 0.0781851 | 0.0390925 | − | 0.999236i | \(-0.487553\pi\) | ||||
0.0390925 | + | 0.999236i | \(0.487553\pi\) | |||||||
\(264\) | 6.00000 | 0.369274 | ||||||||
\(265\) | −17.1962 | −1.05635 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.3205 | −2.16158 | ||||||||
\(268\) | 6.19615 | 0.378490 | ||||||||
\(269\) | −5.07180 | −0.309233 | −0.154616 | − | 0.987975i | \(-0.549414\pi\) | ||||
−0.154616 | + | 0.987975i | \(0.549414\pi\) | |||||||
\(270\) | 12.0000 | 0.730297 | ||||||||
\(271\) | 5.80385 | 0.352559 | 0.176279 | − | 0.984340i | \(-0.443594\pi\) | ||||
0.176279 | + | 0.984340i | \(0.443594\pi\) | |||||||
\(272\) | −38.6603 | −2.34412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.9808 | 0.844609 | ||||||||
\(275\) | 2.53590 | 0.152920 | ||||||||
\(276\) | −12.9282 | −0.778186 | ||||||||
\(277\) | 17.0000 | 1.02143 | 0.510716 | − | 0.859750i | \(-0.329381\pi\) | ||||
0.510716 | + | 0.859750i | \(0.329381\pi\) | |||||||
\(278\) | −18.3397 | −1.09994 | ||||||||
\(279\) | 18.7321 | 1.12146 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.3923 | −0.798918 | −0.399459 | − | 0.916751i | \(-0.630802\pi\) | ||||
−0.399459 | + | 0.916751i | \(0.630802\pi\) | |||||||
\(282\) | 61.1769 | 3.64303 | ||||||||
\(283\) | −10.1962 | −0.606098 | −0.303049 | − | 0.952975i | \(-0.598005\pi\) | ||||
−0.303049 | + | 0.952975i | \(0.598005\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | −9.46410 | −0.560605 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 23.1962 | 1.36685 | ||||||||
\(289\) | 42.7846 | 2.51674 | ||||||||
\(290\) | 9.00000 | 0.528498 | ||||||||
\(291\) | −17.4641 | −1.02376 | ||||||||
\(292\) | −3.19615 | −0.187041 | ||||||||
\(293\) | −0.803848 | −0.0469613 | −0.0234806 | − | 0.999724i | \(-0.507475\pi\) | ||||
−0.0234806 | + | 0.999724i | \(0.507475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.5885 | 0.732928 | ||||||||
\(296\) | 12.1244 | 0.704714 | ||||||||
\(297\) | 5.07180 | 0.294295 | ||||||||
\(298\) | −11.1962 | −0.648576 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.46410 | 0.315470 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.46410 | 0.199337 | ||||||||
\(303\) | −21.1244 | −1.21356 | ||||||||
\(304\) | −10.0000 | −0.573539 | ||||||||
\(305\) | 8.32051 | 0.476431 | ||||||||
\(306\) | −59.7846 | −3.41766 | ||||||||
\(307\) | −4.58846 | −0.261877 | −0.130939 | − | 0.991390i | \(-0.541799\pi\) | ||||
−0.130939 | + | 0.991390i | \(0.541799\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −39.3205 | −2.23687 | ||||||||
\(310\) | −12.5885 | −0.714976 | ||||||||
\(311\) | −1.26795 | −0.0718988 | −0.0359494 | − | 0.999354i | \(-0.511446\pi\) | ||||
−0.0359494 | + | 0.999354i | \(0.511446\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.7846 | −1.62700 | −0.813501 | − | 0.581563i | \(-0.802441\pi\) | ||||
−0.813501 | + | 0.581563i | \(0.802441\pi\) | |||||||
\(314\) | 2.07180 | 0.116918 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.1962 | 0.911105 | ||||||||
\(317\) | 6.46410 | 0.363060 | 0.181530 | − | 0.983385i | \(-0.441895\pi\) | ||||
0.181530 | + | 0.983385i | \(0.441895\pi\) | |||||||
\(318\) | −46.9808 | −2.63455 | ||||||||
\(319\) | 3.80385 | 0.212975 | ||||||||
\(320\) | 1.73205 | 0.0968246 | ||||||||
\(321\) | 21.4641 | 1.19801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.4641 | 0.860446 | ||||||||
\(324\) | −2.46410 | −0.136895 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 28.0526 | 1.55369 | ||||||||
\(327\) | −22.9282 | −1.26793 | ||||||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.3923 | −0.572078 | ||||||||
\(331\) | −24.9808 | −1.37307 | −0.686533 | − | 0.727098i | \(-0.740868\pi\) | ||||
−0.686533 | + | 0.727098i | \(0.740868\pi\) | |||||||
\(332\) | −2.19615 | −0.120530 | ||||||||
\(333\) | 31.2487 | 1.71242 | ||||||||
\(334\) | 11.4115 | 0.624412 | ||||||||
\(335\) | 10.7321 | 0.586355 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | 0.599208 | 0.299604 | − | 0.954064i | \(-0.403145\pi\) | ||||
0.299604 | + | 0.954064i | \(0.403145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.5885 | −1.98721 | ||||||||
\(340\) | 13.3923 | 0.726300 | ||||||||
\(341\) | −5.32051 | −0.288122 | ||||||||
\(342\) | −15.4641 | −0.836203 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.339746 | −0.0183179 | ||||||||
\(345\) | −22.3923 | −1.20556 | ||||||||
\(346\) | 14.7846 | 0.794826 | ||||||||
\(347\) | 7.26795 | 0.390164 | 0.195082 | − | 0.980787i | \(-0.437503\pi\) | ||||
0.195082 | + | 0.980787i | \(0.437503\pi\) | |||||||
\(348\) | 8.19615 | 0.439360 | ||||||||
\(349\) | −24.7846 | −1.32669 | −0.663345 | − | 0.748314i | \(-0.730864\pi\) | ||||
−0.663345 | + | 0.748314i | \(0.730864\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.58846 | −0.351166 | ||||||||
\(353\) | 20.6603 | 1.09963 | 0.549817 | − | 0.835285i | \(-0.314697\pi\) | ||||
0.549817 | + | 0.835285i | \(0.314697\pi\) | |||||||
\(354\) | 34.3923 | 1.82793 | ||||||||
\(355\) | −10.3923 | −0.551566 | ||||||||
\(356\) | 12.9282 | 0.685193 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | −18.9282 | −0.998992 | −0.499496 | − | 0.866316i | \(-0.666482\pi\) | ||||
−0.499496 | + | 0.866316i | \(0.666482\pi\) | |||||||
\(360\) | 13.3923 | 0.705836 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 9.67949 | 0.508743 | ||||||||
\(363\) | 25.6603 | 1.34681 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.53590 | −0.289762 | ||||||||
\(366\) | 22.7321 | 1.18822 | ||||||||
\(367\) | −4.19615 | −0.219037 | −0.109519 | − | 0.993985i | \(-0.534931\pi\) | ||||
−0.109519 | + | 0.993985i | \(0.534931\pi\) | |||||||
\(368\) | −23.6603 | −1.23338 | ||||||||
\(369\) | −23.1962 | −1.20754 | ||||||||
\(370\) | −21.0000 | −1.09174 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.4641 | −0.594386 | ||||||||
\(373\) | −11.3923 | −0.589871 | −0.294936 | − | 0.955517i | \(-0.595298\pi\) | ||||
−0.294936 | + | 0.955517i | \(0.595298\pi\) | |||||||
\(374\) | 16.9808 | 0.878054 | ||||||||
\(375\) | 33.1244 | 1.71053 | ||||||||
\(376\) | 22.3923 | 1.15479 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.5885 | −1.36576 | −0.682879 | − | 0.730532i | \(-0.739272\pi\) | ||||
−0.682879 | + | 0.730532i | \(0.739272\pi\) | |||||||
\(380\) | 3.46410 | 0.177705 | ||||||||
\(381\) | −50.2487 | −2.57432 | ||||||||
\(382\) | −8.19615 | −0.419352 | ||||||||
\(383\) | −11.6603 | −0.595811 | −0.297906 | − | 0.954595i | \(-0.596288\pi\) | ||||
−0.297906 | + | 0.954595i | \(0.596288\pi\) | |||||||
\(384\) | 33.1244 | 1.69037 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.66025 | 0.440795 | ||||||||
\(387\) | −0.875644 | −0.0445115 | ||||||||
\(388\) | 6.39230 | 0.324520 | ||||||||
\(389\) | −23.5359 | −1.19332 | −0.596659 | − | 0.802495i | \(-0.703505\pi\) | ||||
−0.596659 | + | 0.802495i | \(0.703505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.5885 | 1.85036 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.46410 | −0.477401 | ||||||||
\(394\) | 20.7846 | 1.04711 | ||||||||
\(395\) | 28.0526 | 1.41148 | ||||||||
\(396\) | −5.66025 | −0.284438 | ||||||||
\(397\) | −18.7846 | −0.942773 | −0.471386 | − | 0.881927i | \(-0.656246\pi\) | ||||
−0.471386 | + | 0.881927i | \(0.656246\pi\) | |||||||
\(398\) | 3.46410 | 0.173640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.0000 | 0.500000 | ||||||||
\(401\) | 10.8564 | 0.542143 | 0.271072 | − | 0.962559i | \(-0.412622\pi\) | ||||
0.271072 | + | 0.962559i | \(0.412622\pi\) | |||||||
\(402\) | 29.3205 | 1.46237 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7.73205 | 0.384684 | ||||||||
\(405\) | −4.26795 | −0.212076 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.87564 | −0.439949 | ||||||||
\(408\) | −36.5885 | −1.81140 | ||||||||
\(409\) | −16.8038 | −0.830897 | −0.415448 | − | 0.909617i | \(-0.636375\pi\) | ||||
−0.415448 | + | 0.909617i | \(0.636375\pi\) | |||||||
\(410\) | 15.5885 | 0.769859 | ||||||||
\(411\) | 22.0526 | 1.08777 | ||||||||
\(412\) | 14.3923 | 0.709058 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −36.5885 | −1.79822 | ||||||||
\(415\) | −3.80385 | −0.186724 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.9282 | −1.41662 | ||||||||
\(418\) | 4.39230 | 0.214835 | ||||||||
\(419\) | 32.1962 | 1.57288 | 0.786442 | − | 0.617664i | \(-0.211921\pi\) | ||||
0.786442 | + | 0.617664i | \(0.211921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.1769 | 1.56821 | 0.784103 | − | 0.620630i | \(-0.213123\pi\) | ||||
0.784103 | + | 0.620630i | \(0.213123\pi\) | |||||||
\(422\) | 3.12436 | 0.152091 | ||||||||
\(423\) | 57.7128 | 2.80609 | ||||||||
\(424\) | −17.1962 | −0.835119 | ||||||||
\(425\) | −15.4641 | −0.750119 | ||||||||
\(426\) | −28.3923 | −1.37561 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.85641 | −0.379754 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.588457 | 0.0283779 | ||||||||
\(431\) | −0.679492 | −0.0327300 | −0.0163650 | − | 0.999866i | \(-0.505209\pi\) | ||||
−0.0163650 | + | 0.999866i | \(0.505209\pi\) | |||||||
\(432\) | 20.0000 | 0.962250 | ||||||||
\(433\) | 13.5885 | 0.653020 | 0.326510 | − | 0.945194i | \(-0.394127\pi\) | ||||
0.326510 | + | 0.945194i | \(0.394127\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.1962 | 0.680653 | ||||||||
\(436\) | 8.39230 | 0.401919 | ||||||||
\(437\) | 9.46410 | 0.452729 | ||||||||
\(438\) | −15.1244 | −0.722670 | ||||||||
\(439\) | −14.5885 | −0.696269 | −0.348135 | − | 0.937445i | \(-0.613185\pi\) | ||||
−0.348135 | + | 0.937445i | \(0.613185\pi\) | |||||||
\(440\) | −3.80385 | −0.181341 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.3205 | 1.10799 | 0.553995 | − | 0.832520i | \(-0.313103\pi\) | ||||
0.553995 | + | 0.832520i | \(0.313103\pi\) | |||||||
\(444\) | −19.1244 | −0.907602 | ||||||||
\(445\) | 22.3923 | 1.06150 | ||||||||
\(446\) | 17.3205 | 0.820150 | ||||||||
\(447\) | −17.6603 | −0.835301 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 15.4641 | 0.728985 | ||||||||
\(451\) | 6.58846 | 0.310238 | ||||||||
\(452\) | 13.3923 | 0.629921 | ||||||||
\(453\) | 5.46410 | 0.256726 | ||||||||
\(454\) | −9.80385 | −0.460117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.46410 | −0.443197 | ||||||||
\(457\) | −11.0000 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(458\) | 24.9282 | 1.16482 | ||||||||
\(459\) | −30.9282 | −1.44360 | ||||||||
\(460\) | 8.19615 | 0.382148 | ||||||||
\(461\) | −15.5885 | −0.726027 | −0.363013 | − | 0.931784i | \(-0.618252\pi\) | ||||
−0.363013 | + | 0.931784i | \(0.618252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.58846 | 0.213244 | 0.106622 | − | 0.994300i | \(-0.465997\pi\) | ||||
0.106622 | + | 0.994300i | \(0.465997\pi\) | |||||||
\(464\) | 15.0000 | 0.696358 | ||||||||
\(465\) | −19.8564 | −0.920819 | ||||||||
\(466\) | 3.21539 | 0.148950 | ||||||||
\(467\) | −25.5167 | −1.18077 | −0.590385 | − | 0.807122i | \(-0.701024\pi\) | ||||
−0.590385 | + | 0.807122i | \(0.701024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −38.7846 | −1.78900 | ||||||||
\(471\) | 3.26795 | 0.150579 | ||||||||
\(472\) | 12.5885 | 0.579431 | ||||||||
\(473\) | 0.248711 | 0.0114358 | ||||||||
\(474\) | 76.6410 | 3.52024 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −44.3205 | −2.02930 | ||||||||
\(478\) | −27.3731 | −1.25201 | ||||||||
\(479\) | 1.26795 | 0.0579341 | 0.0289670 | − | 0.999580i | \(-0.490778\pi\) | ||||
0.0289670 | + | 0.999580i | \(0.490778\pi\) | |||||||
\(480\) | −24.5885 | −1.12230 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 36.7128 | 1.67222 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.39230 | −0.426923 | ||||||||
\(485\) | 11.0718 | 0.502744 | ||||||||
\(486\) | −32.4449 | −1.47173 | ||||||||
\(487\) | −40.7846 | −1.84813 | −0.924064 | − | 0.382239i | \(-0.875153\pi\) | ||||
−0.924064 | + | 0.382239i | \(0.875153\pi\) | |||||||
\(488\) | 8.32051 | 0.376652 | ||||||||
\(489\) | 44.2487 | 2.00100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.60770 | 0.343330 | 0.171665 | − | 0.985155i | \(-0.445085\pi\) | ||||
0.171665 | + | 0.985155i | \(0.445085\pi\) | |||||||
\(492\) | 14.1962 | 0.640012 | ||||||||
\(493\) | −23.1962 | −1.04470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.80385 | −0.440650 | ||||||||
\(496\) | −20.9808 | −0.942064 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10.3923 | −0.465690 | ||||||||
\(499\) | 38.9808 | 1.74502 | 0.872509 | − | 0.488598i | \(-0.162491\pi\) | ||||
0.872509 | + | 0.488598i | \(0.162491\pi\) | |||||||
\(500\) | −12.1244 | −0.542218 | ||||||||
\(501\) | 18.0000 | 0.804181 | ||||||||
\(502\) | −2.78461 | −0.124283 | ||||||||
\(503\) | 18.5885 | 0.828818 | 0.414409 | − | 0.910091i | \(-0.363988\pi\) | ||||
0.414409 | + | 0.910091i | \(0.363988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3923 | 0.595950 | ||||||||
\(506\) | 10.3923 | 0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.3923 | 0.816027 | ||||||||
\(509\) | 13.7321 | 0.608662 | 0.304331 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304331 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(510\) | 63.3731 | 2.80621 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8.66025 | −0.382733 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 10.6077 | 0.467885 | ||||||||
\(515\) | 24.9282 | 1.09847 | ||||||||
\(516\) | 0.535898 | 0.0235916 | ||||||||
\(517\) | −16.3923 | −0.720933 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.3205 | 1.02366 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.1244 | 1.05691 | 0.528454 | − | 0.848962i | \(-0.322772\pi\) | ||||
0.528454 | + | 0.848962i | \(0.322772\pi\) | |||||||
\(522\) | 23.1962 | 1.01527 | ||||||||
\(523\) | 29.1769 | 1.27582 | 0.637909 | − | 0.770112i | \(-0.279800\pi\) | ||||
0.637909 | + | 0.770112i | \(0.279800\pi\) | |||||||
\(524\) | 3.46410 | 0.151330 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.19615 | −0.0957568 | ||||||||
\(527\) | 32.4449 | 1.41332 | ||||||||
\(528\) | −17.3205 | −0.753778 | ||||||||
\(529\) | −0.607695 | −0.0264215 | ||||||||
\(530\) | 29.7846 | 1.29376 | ||||||||
\(531\) | 32.4449 | 1.40799 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 61.1769 | 2.64738 | ||||||||
\(535\) | −13.6077 | −0.588312 | ||||||||
\(536\) | 10.7321 | 0.463554 | ||||||||
\(537\) | 18.9282 | 0.816812 | ||||||||
\(538\) | 8.78461 | 0.378731 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.92820 | −0.298142 | ||||||||
\(541\) | 14.6077 | 0.628034 | 0.314017 | − | 0.949417i | \(-0.398325\pi\) | ||||
0.314017 | + | 0.949417i | \(0.398325\pi\) | |||||||
\(542\) | −10.0526 | −0.431794 | ||||||||
\(543\) | 15.2679 | 0.655210 | ||||||||
\(544\) | 40.1769 | 1.72257 | ||||||||
\(545\) | 14.5359 | 0.622649 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8038 | 0.761238 | 0.380619 | − | 0.924732i | \(-0.375711\pi\) | ||||
0.380619 | + | 0.924732i | \(0.375711\pi\) | |||||||
\(548\) | −8.07180 | −0.344810 | ||||||||
\(549\) | 21.4449 | 0.915244 | ||||||||
\(550\) | −4.39230 | −0.187289 | ||||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | −22.3923 | −0.953080 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −29.4449 | −1.25099 | ||||||||
\(555\) | −33.1244 | −1.40605 | ||||||||
\(556\) | 10.5885 | 0.449051 | ||||||||
\(557\) | −43.6410 | −1.84913 | −0.924565 | − | 0.381025i | \(-0.875571\pi\) | ||||
−0.924565 | + | 0.381025i | \(0.875571\pi\) | |||||||
\(558\) | −32.4449 | −1.37350 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.7846 | 1.13085 | ||||||||
\(562\) | 23.1962 | 0.978471 | ||||||||
\(563\) | −28.0526 | −1.18227 | −0.591137 | − | 0.806571i | \(-0.701321\pi\) | ||||
−0.591137 | + | 0.806571i | \(0.701321\pi\) | |||||||
\(564\) | −35.3205 | −1.48726 | ||||||||
\(565\) | 23.1962 | 0.975869 | ||||||||
\(566\) | 17.6603 | 0.742316 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.3923 | −0.436051 | ||||||||
\(569\) | 42.9282 | 1.79964 | 0.899822 | − | 0.436257i | \(-0.143696\pi\) | ||||
0.899822 | + | 0.436257i | \(0.143696\pi\) | |||||||
\(570\) | 16.3923 | 0.686598 | ||||||||
\(571\) | 16.7846 | 0.702414 | 0.351207 | − | 0.936298i | \(-0.385771\pi\) | ||||
0.351207 | + | 0.936298i | \(0.385771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.9282 | −0.540083 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.46410 | −0.394680 | ||||||||
\(576\) | 4.46410 | 0.186004 | ||||||||
\(577\) | 43.1962 | 1.79828 | 0.899140 | − | 0.437662i | \(-0.144193\pi\) | ||||
0.899140 | + | 0.437662i | \(0.144193\pi\) | |||||||
\(578\) | −74.1051 | −3.08237 | ||||||||
\(579\) | 13.6603 | 0.567701 | ||||||||
\(580\) | −5.19615 | −0.215758 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 30.2487 | 1.25385 | ||||||||
\(583\) | 12.5885 | 0.521361 | ||||||||
\(584\) | −5.53590 | −0.229077 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.39230 | 0.0575156 | ||||||||
\(587\) | 16.3923 | 0.676583 | 0.338291 | − | 0.941041i | \(-0.390151\pi\) | ||||
0.338291 | + | 0.941041i | \(0.390151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.39230 | 0.345799 | ||||||||
\(590\) | −21.8038 | −0.897650 | ||||||||
\(591\) | 32.7846 | 1.34858 | ||||||||
\(592\) | −35.0000 | −1.43849 | ||||||||
\(593\) | −17.4449 | −0.716375 | −0.358187 | − | 0.933650i | \(-0.616605\pi\) | ||||
−0.358187 | + | 0.933650i | \(0.616605\pi\) | |||||||
\(594\) | −8.78461 | −0.360437 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.46410 | 0.264780 | ||||||||
\(597\) | 5.46410 | 0.223631 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.8564 | 1.79192 | 0.895962 | − | 0.444131i | \(-0.146487\pi\) | ||||
0.895962 | + | 0.444131i | \(0.146487\pi\) | |||||||
\(600\) | 9.46410 | 0.386370 | ||||||||
\(601\) | 29.9808 | 1.22294 | 0.611470 | − | 0.791267i | \(-0.290578\pi\) | ||||
0.611470 | + | 0.791267i | \(0.290578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.6603 | 1.12641 | ||||||||
\(604\) | −2.00000 | −0.0813788 | ||||||||
\(605\) | −16.2679 | −0.661386 | ||||||||
\(606\) | 36.5885 | 1.48630 | ||||||||
\(607\) | 14.3923 | 0.584166 | 0.292083 | − | 0.956393i | \(-0.405652\pi\) | ||||
0.292083 | + | 0.956393i | \(0.405652\pi\) | |||||||
\(608\) | 10.3923 | 0.421464 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.4115 | −0.583506 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 34.5167 | 1.39525 | ||||||||
\(613\) | −3.39230 | −0.137014 | −0.0685070 | − | 0.997651i | \(-0.521824\pi\) | ||||
−0.0685070 | + | 0.997651i | \(0.521824\pi\) | |||||||
\(614\) | 7.94744 | 0.320733 | ||||||||
\(615\) | 24.5885 | 0.991502 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −49.3923 | −1.98846 | −0.994230 | − | 0.107272i | \(-0.965788\pi\) | ||||
−0.994230 | + | 0.107272i | \(0.965788\pi\) | |||||||
\(618\) | 68.1051 | 2.73959 | ||||||||
\(619\) | 35.3731 | 1.42176 | 0.710882 | − | 0.703311i | \(-0.248296\pi\) | ||||
0.710882 | + | 0.703311i | \(0.248296\pi\) | |||||||
\(620\) | 7.26795 | 0.291888 | ||||||||
\(621\) | −18.9282 | −0.759563 | ||||||||
\(622\) | 2.19615 | 0.0880577 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 49.8564 | 1.99266 | ||||||||
\(627\) | 6.92820 | 0.276686 | ||||||||
\(628\) | −1.19615 | −0.0477317 | ||||||||
\(629\) | 54.1244 | 2.15808 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7846 | 0.508947 | 0.254474 | − | 0.967080i | \(-0.418098\pi\) | ||||
0.254474 | + | 0.967080i | \(0.418098\pi\) | |||||||
\(632\) | 28.0526 | 1.11587 | ||||||||
\(633\) | 4.92820 | 0.195878 | ||||||||
\(634\) | −11.1962 | −0.444656 | ||||||||
\(635\) | 31.8564 | 1.26418 | ||||||||
\(636\) | 27.1244 | 1.07555 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.58846 | −0.260840 | ||||||||
\(639\) | −26.7846 | −1.05958 | ||||||||
\(640\) | −21.0000 | −0.830098 | ||||||||
\(641\) | 28.8564 | 1.13976 | 0.569880 | − | 0.821728i | \(-0.306990\pi\) | ||||
0.569880 | + | 0.821728i | \(0.306990\pi\) | |||||||
\(642\) | −37.1769 | −1.46726 | ||||||||
\(643\) | −0.784610 | −0.0309420 | −0.0154710 | − | 0.999880i | \(-0.504925\pi\) | ||||
−0.0154710 | + | 0.999880i | \(0.504925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.928203 | 0.0365480 | ||||||||
\(646\) | −26.7846 | −1.05383 | ||||||||
\(647\) | −45.0333 | −1.77044 | −0.885221 | − | 0.465170i | \(-0.845993\pi\) | ||||
−0.885221 | + | 0.465170i | \(0.845993\pi\) | |||||||
\(648\) | −4.26795 | −0.167661 | ||||||||
\(649\) | −9.21539 | −0.361736 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.1962 | −0.634290 | ||||||||
\(653\) | −37.8564 | −1.48144 | −0.740718 | − | 0.671816i | \(-0.765514\pi\) | ||||
−0.740718 | + | 0.671816i | \(0.765514\pi\) | |||||||
\(654\) | 39.7128 | 1.55289 | ||||||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | 25.9808 | 1.01438 | ||||||||
\(657\) | −14.2679 | −0.556646 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.3923 | 1.10601 | 0.553004 | − | 0.833179i | \(-0.313482\pi\) | ||||
0.553004 | + | 0.833179i | \(0.313482\pi\) | |||||||
\(660\) | 6.00000 | 0.233550 | ||||||||
\(661\) | −33.1962 | −1.29118 | −0.645590 | − | 0.763684i | \(-0.723389\pi\) | ||||
−0.645590 | + | 0.763684i | \(0.723389\pi\) | |||||||
\(662\) | 43.2679 | 1.68166 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.80385 | −0.147618 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −54.1244 | −2.09728 | ||||||||
\(667\) | −14.1962 | −0.549677 | ||||||||
\(668\) | −6.58846 | −0.254915 | ||||||||
\(669\) | 27.3205 | 1.05627 | ||||||||
\(670\) | −18.5885 | −0.718135 | ||||||||
\(671\) | −6.09103 | −0.235142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.1769 | −1.70289 | −0.851447 | − | 0.524440i | \(-0.824275\pi\) | ||||
−0.851447 | + | 0.524440i | \(0.824275\pi\) | |||||||
\(674\) | −19.0526 | −0.733877 | ||||||||
\(675\) | 8.00000 | 0.307920 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.0718 | 0.886721 | 0.443361 | − | 0.896343i | \(-0.353786\pi\) | ||||
0.443361 | + | 0.896343i | \(0.353786\pi\) | |||||||
\(678\) | 63.3731 | 2.43383 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 23.1962 | 0.889532 | ||||||||
\(681\) | −15.4641 | −0.592586 | ||||||||
\(682\) | 9.21539 | 0.352876 | ||||||||
\(683\) | −15.4641 | −0.591717 | −0.295859 | − | 0.955232i | \(-0.595606\pi\) | ||||
−0.295859 | + | 0.955232i | \(0.595606\pi\) | |||||||
\(684\) | 8.92820 | 0.341378 | ||||||||
\(685\) | −13.9808 | −0.534177 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.3205 | 1.50017 | ||||||||
\(688\) | 0.980762 | 0.0373912 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 38.7846 | 1.47650 | ||||||||
\(691\) | 0.392305 | 0.0149240 | 0.00746199 | − | 0.999972i | \(-0.497625\pi\) | ||||
0.00746199 | + | 0.999972i | \(0.497625\pi\) | |||||||
\(692\) | −8.53590 | −0.324486 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.5885 | −0.477851 | ||||||||
\(695\) | 18.3397 | 0.695666 | ||||||||
\(696\) | 14.1962 | 0.538104 | ||||||||
\(697\) | −40.1769 | −1.52181 | ||||||||
\(698\) | 42.9282 | 1.62486 | ||||||||
\(699\) | 5.07180 | 0.191833 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7846 | 0.785024 | 0.392512 | − | 0.919747i | \(-0.371606\pi\) | ||||
0.392512 | + | 0.919747i | \(0.371606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0000 | 0.528020 | ||||||||
\(704\) | −1.26795 | −0.0477876 | ||||||||
\(705\) | −61.1769 | −2.30406 | ||||||||
\(706\) | −35.7846 | −1.34677 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −19.8564 | −0.746249 | ||||||||
\(709\) | −30.1769 | −1.13332 | −0.566659 | − | 0.823952i | \(-0.691764\pi\) | ||||
−0.566659 | + | 0.823952i | \(0.691764\pi\) | |||||||
\(710\) | 18.0000 | 0.675528 | ||||||||
\(711\) | 72.3013 | 2.71151 | ||||||||
\(712\) | 22.3923 | 0.839187 | ||||||||
\(713\) | 19.8564 | 0.743628 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.92820 | −0.258919 | ||||||||
\(717\) | −43.1769 | −1.61247 | ||||||||
\(718\) | 32.7846 | 1.22351 | ||||||||
\(719\) | 7.26795 | 0.271049 | 0.135524 | − | 0.990774i | \(-0.456728\pi\) | ||||
0.135524 | + | 0.990774i | \(0.456728\pi\) | |||||||
\(720\) | −38.6603 | −1.44078 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.9808 | 0.966904 | ||||||||
\(723\) | 57.9090 | 2.15366 | ||||||||
\(724\) | −5.58846 | −0.207693 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | −44.4449 | −1.64950 | ||||||||
\(727\) | 41.1769 | 1.52717 | 0.763584 | − | 0.645709i | \(-0.223438\pi\) | ||||
0.763584 | + | 0.645709i | \(0.223438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 9.58846 | 0.354885 | ||||||||
\(731\) | −1.51666 | −0.0560957 | ||||||||
\(732\) | −13.1244 | −0.485090 | ||||||||
\(733\) | 23.5885 | 0.871260 | 0.435630 | − | 0.900126i | \(-0.356526\pi\) | ||||
0.435630 | + | 0.900126i | \(0.356526\pi\) | |||||||
\(734\) | 7.26795 | 0.268265 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.5885 | 0.906343 | ||||||||
\(737\) | −7.85641 | −0.289394 | ||||||||
\(738\) | 40.1769 | 1.47893 | ||||||||
\(739\) | −40.7846 | −1.50029 | −0.750143 | − | 0.661276i | \(-0.770015\pi\) | ||||
−0.750143 | + | 0.661276i | \(0.770015\pi\) | |||||||
\(740\) | 12.1244 | 0.445700 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.60770 | 0.279099 | 0.139550 | − | 0.990215i | \(-0.455435\pi\) | ||||
0.139550 | + | 0.990215i | \(0.455435\pi\) | |||||||
\(744\) | −19.8564 | −0.727971 | ||||||||
\(745\) | 11.1962 | 0.410195 | ||||||||
\(746\) | 19.7321 | 0.722442 | ||||||||
\(747\) | −9.80385 | −0.358704 | ||||||||
\(748\) | −9.80385 | −0.358464 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −57.3731 | −2.09497 | ||||||||
\(751\) | 35.8038 | 1.30650 | 0.653250 | − | 0.757142i | \(-0.273405\pi\) | ||||
0.653250 | + | 0.757142i | \(0.273405\pi\) | |||||||
\(752\) | −64.6410 | −2.35722 | ||||||||
\(753\) | −4.39230 | −0.160064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.46410 | −0.126072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | −0.581530 | −0.290765 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290765 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(758\) | 46.0526 | 1.67270 | ||||||||
\(759\) | 16.3923 | 0.595003 | ||||||||
\(760\) | 6.00000 | 0.217643 | ||||||||
\(761\) | 41.3205 | 1.49787 | 0.748934 | − | 0.662645i | \(-0.230566\pi\) | ||||
0.748934 | + | 0.662645i | \(0.230566\pi\) | |||||||
\(762\) | 87.0333 | 3.15288 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.73205 | 0.171200 | ||||||||
\(765\) | 59.7846 | 2.16152 | ||||||||
\(766\) | 20.1962 | 0.729717 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −51.9090 | −1.87310 | ||||||||
\(769\) | 15.1769 | 0.547294 | 0.273647 | − | 0.961830i | \(-0.411770\pi\) | ||||
0.273647 | + | 0.961830i | \(0.411770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.7321 | 0.602590 | ||||||||
\(772\) | −5.00000 | −0.179954 | ||||||||
\(773\) | −12.9282 | −0.464995 | −0.232498 | − | 0.972597i | \(-0.574690\pi\) | ||||
−0.232498 | + | 0.972597i | \(0.574690\pi\) | |||||||
\(774\) | 1.51666 | 0.0545152 | ||||||||
\(775\) | −8.39230 | −0.301460 | ||||||||
\(776\) | 11.0718 | 0.397454 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 40.7654 | 1.46151 | ||||||||
\(779\) | −10.3923 | −0.372343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.60770 | 0.272225 | ||||||||
\(782\) | −63.3731 | −2.26622 | ||||||||
\(783\) | 12.0000 | 0.428845 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.07180 | −0.0739456 | ||||||||
\(786\) | 16.3923 | 0.584694 | ||||||||
\(787\) | 12.9808 | 0.462714 | 0.231357 | − | 0.972869i | \(-0.425683\pi\) | ||||
0.231357 | + | 0.972869i | \(0.425683\pi\) | |||||||
\(788\) | −12.0000 | −0.427482 | ||||||||
\(789\) | −3.46410 | −0.123325 | ||||||||
\(790\) | −48.5885 | −1.72870 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9.80385 | −0.348365 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 32.5359 | 1.15466 | ||||||||
\(795\) | 46.9808 | 1.66624 | ||||||||
\(796\) | −2.00000 | −0.0708881 | ||||||||
\(797\) | 34.3923 | 1.21824 | 0.609119 | − | 0.793079i | \(-0.291523\pi\) | ||||
0.609119 | + | 0.793079i | \(0.291523\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 99.9615 | 3.53638 | ||||||||
\(800\) | −10.3923 | −0.367423 | ||||||||
\(801\) | 57.7128 | 2.03918 | ||||||||
\(802\) | −18.8038 | −0.663987 | ||||||||
\(803\) | 4.05256 | 0.143012 | ||||||||
\(804\) | −16.9282 | −0.597012 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.8564 | 0.487769 | ||||||||
\(808\) | 13.3923 | 0.471140 | ||||||||
\(809\) | 2.07180 | 0.0728405 | 0.0364202 | − | 0.999337i | \(-0.488405\pi\) | ||||
0.0364202 | + | 0.999337i | \(0.488405\pi\) | |||||||
\(810\) | 7.39230 | 0.259739 | ||||||||
\(811\) | −16.5885 | −0.582500 | −0.291250 | − | 0.956647i | \(-0.594071\pi\) | ||||
−0.291250 | + | 0.956647i | \(0.594071\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.8564 | −0.556108 | ||||||||
\(814\) | 15.3731 | 0.538826 | ||||||||
\(815\) | −28.0526 | −0.982638 | ||||||||
\(816\) | 105.622 | 3.69750 | ||||||||
\(817\) | −0.392305 | −0.0137250 | ||||||||
\(818\) | 29.1051 | 1.01764 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −4.14359 | −0.144612 | −0.0723062 | − | 0.997382i | \(-0.523036\pi\) | ||||
−0.0723062 | + | 0.997382i | \(0.523036\pi\) | |||||||
\(822\) | −38.1962 | −1.33224 | ||||||||
\(823\) | −41.1769 | −1.43534 | −0.717669 | − | 0.696385i | \(-0.754791\pi\) | ||||
−0.717669 | + | 0.696385i | \(0.754791\pi\) | |||||||
\(824\) | 24.9282 | 0.868415 | ||||||||
\(825\) | −6.92820 | −0.241209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9808 | 0.590479 | 0.295239 | − | 0.955423i | \(-0.404601\pi\) | ||||
0.295239 | + | 0.955423i | \(0.404601\pi\) | |||||||
\(828\) | 21.1244 | 0.734122 | ||||||||
\(829\) | 0.411543 | 0.0142935 | 0.00714673 | − | 0.999974i | \(-0.497725\pi\) | ||||
0.00714673 | + | 0.999974i | \(0.497725\pi\) | |||||||
\(830\) | 6.58846 | 0.228689 | ||||||||
\(831\) | −46.4449 | −1.61115 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 50.1051 | 1.73500 | ||||||||
\(835\) | −11.4115 | −0.394913 | ||||||||
\(836\) | −2.53590 | −0.0877059 | ||||||||
\(837\) | −16.7846 | −0.580161 | ||||||||
\(838\) | −55.7654 | −1.92638 | ||||||||
\(839\) | −18.0000 | −0.621429 | −0.310715 | − | 0.950503i | \(-0.600568\pi\) | ||||
−0.310715 | + | 0.950503i | \(0.600568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −55.7321 | −1.92065 | ||||||||
\(843\) | 36.5885 | 1.26017 | ||||||||
\(844\) | −1.80385 | −0.0620910 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −99.9615 | −3.43675 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 49.6410 | 1.70468 | ||||||||
\(849\) | 27.8564 | 0.956029 | ||||||||
\(850\) | 26.7846 | 0.918705 | ||||||||
\(851\) | 33.1244 | 1.13549 | ||||||||
\(852\) | 16.3923 | 0.561591 | ||||||||
\(853\) | 5.58846 | 0.191345 | 0.0956726 | − | 0.995413i | \(-0.469500\pi\) | ||||
0.0956726 | + | 0.995413i | \(0.469500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.4641 | 0.528861 | ||||||||
\(856\) | −13.6077 | −0.465101 | ||||||||
\(857\) | 30.1244 | 1.02903 | 0.514514 | − | 0.857482i | \(-0.327972\pi\) | ||||
0.514514 | + | 0.857482i | \(0.327972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.80385 | 0.266264 | 0.133132 | − | 0.991098i | \(-0.457497\pi\) | ||||
0.133132 | + | 0.991098i | \(0.457497\pi\) | |||||||
\(860\) | −0.339746 | −0.0115852 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.17691 | 0.0400859 | ||||||||
\(863\) | −7.51666 | −0.255870 | −0.127935 | − | 0.991783i | \(-0.540835\pi\) | ||||
−0.127935 | + | 0.991783i | \(0.540835\pi\) | |||||||
\(864\) | −20.7846 | −0.707107 | ||||||||
\(865\) | −14.7846 | −0.502692 | ||||||||
\(866\) | −23.5359 | −0.799782 | ||||||||
\(867\) | −116.890 | −3.96978 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.5359 | −0.696633 | ||||||||
\(870\) | −24.5885 | −0.833627 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.5359 | 0.492248 | ||||||||
\(873\) | 28.5359 | 0.965794 | ||||||||
\(874\) | −16.3923 | −0.554478 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.73205 | 0.295029 | ||||||||
\(877\) | −19.7846 | −0.668079 | −0.334039 | − | 0.942559i | \(-0.608412\pi\) | ||||
−0.334039 | + | 0.942559i | \(0.608412\pi\) | |||||||
\(878\) | 25.2679 | 0.852752 | ||||||||
\(879\) | 2.19615 | 0.0740744 | ||||||||
\(880\) | 10.9808 | 0.370161 | ||||||||
\(881\) | 8.41154 | 0.283392 | 0.141696 | − | 0.989910i | \(-0.454744\pi\) | ||||
0.141696 | + | 0.989910i | \(0.454744\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7654 | −1.60743 | −0.803716 | − | 0.595013i | \(-0.797147\pi\) | ||||
−0.803716 | + | 0.595013i | \(0.797147\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.3923 | −1.15608 | ||||||||
\(886\) | −40.3923 | −1.35701 | ||||||||
\(887\) | −11.3205 | −0.380105 | −0.190053 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190053 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(888\) | −33.1244 | −1.11158 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −38.7846 | −1.30006 | ||||||||
\(891\) | 3.12436 | 0.104670 | ||||||||
\(892\) | −10.0000 | −0.334825 | ||||||||
\(893\) | 25.8564 | 0.865252 | ||||||||
\(894\) | 30.5885 | 1.02303 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.7846 | −0.693591 | ||||||||
\(899\) | −12.5885 | −0.419849 | ||||||||
\(900\) | −8.92820 | −0.297607 | ||||||||
\(901\) | −76.7654 | −2.55743 | ||||||||
\(902\) | −11.4115 | −0.379963 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23.1962 | 0.771493 | ||||||||
\(905\) | −9.67949 | −0.321757 | ||||||||
\(906\) | −9.46410 | −0.314424 | ||||||||
\(907\) | −16.5885 | −0.550811 | −0.275405 | − | 0.961328i | \(-0.588812\pi\) | ||||
−0.275405 | + | 0.961328i | \(0.588812\pi\) | |||||||
\(908\) | 5.66025 | 0.187842 | ||||||||
\(909\) | 34.5167 | 1.14485 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 27.3205 | 0.904672 | ||||||||
\(913\) | 2.78461 | 0.0921571 | ||||||||
\(914\) | 19.0526 | 0.630203 | ||||||||
\(915\) | −22.7321 | −0.751498 | ||||||||
\(916\) | −14.3923 | −0.475535 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 53.5692 | 1.76805 | ||||||||
\(919\) | −39.5692 | −1.30527 | −0.652634 | − | 0.757673i | \(-0.726336\pi\) | ||||
−0.652634 | + | 0.757673i | \(0.726336\pi\) | |||||||
\(920\) | 14.1962 | 0.468033 | ||||||||
\(921\) | 12.5359 | 0.413072 | ||||||||
\(922\) | 27.0000 | 0.889198 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0000 | −0.460317 | ||||||||
\(926\) | −7.94744 | −0.261169 | ||||||||
\(927\) | 64.2487 | 2.11020 | ||||||||
\(928\) | −15.5885 | −0.511716 | ||||||||
\(929\) | 52.5167 | 1.72302 | 0.861508 | − | 0.507744i | \(-0.169520\pi\) | ||||
0.861508 | + | 0.507744i | \(0.169520\pi\) | |||||||
\(930\) | 34.3923 | 1.12777 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.85641 | −0.0608086 | ||||||||
\(933\) | 3.46410 | 0.113410 | ||||||||
\(934\) | 44.1962 | 1.44614 | ||||||||
\(935\) | −16.9808 | −0.555330 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.1962 | 1.67251 | 0.836253 | − | 0.548344i | \(-0.184742\pi\) | ||||
0.836253 | + | 0.548344i | \(0.184742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 78.6410 | 2.56635 | ||||||||
\(940\) | 22.3923 | 0.730356 | ||||||||
\(941\) | −28.1436 | −0.917455 | −0.458727 | − | 0.888577i | \(-0.651695\pi\) | ||||
−0.458727 | + | 0.888577i | \(0.651695\pi\) | |||||||
\(942\) | −5.66025 | −0.184421 | ||||||||
\(943\) | −24.5885 | −0.800710 | ||||||||
\(944\) | −36.3397 | −1.18276 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.430781 | −0.0140059 | ||||||||
\(947\) | 7.26795 | 0.236177 | 0.118088 | − | 0.993003i | \(-0.462323\pi\) | ||||
0.118088 | + | 0.993003i | \(0.462323\pi\) | |||||||
\(948\) | −44.2487 | −1.43713 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.92820 | 0.224781 | ||||||||
\(951\) | −17.6603 | −0.572673 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.1769 | −0.815560 | −0.407780 | − | 0.913080i | \(-0.633697\pi\) | ||||
−0.407780 | + | 0.913080i | \(0.633697\pi\) | |||||||
\(954\) | 76.7654 | 2.48537 | ||||||||
\(955\) | 8.19615 | 0.265221 | ||||||||
\(956\) | 15.8038 | 0.511133 | ||||||||
\(957\) | −10.3923 | −0.335936 | ||||||||
\(958\) | −2.19615 | −0.0709545 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.73205 | −0.152726 | ||||||||
\(961\) | −13.3923 | −0.432010 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35.0718 | −1.13017 | ||||||||
\(964\) | −21.1962 | −0.682682 | ||||||||
\(965\) | −8.66025 | −0.278783 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.9808 | −1.76806 | −0.884031 | − | 0.467428i | \(-0.845181\pi\) | ||||
−0.884031 | + | 0.467428i | \(0.845181\pi\) | |||||||
\(968\) | −16.2679 | −0.522872 | ||||||||
\(969\) | −42.2487 | −1.35722 | ||||||||
\(970\) | −19.1769 | −0.615734 | ||||||||
\(971\) | 52.6410 | 1.68933 | 0.844665 | − | 0.535295i | \(-0.179799\pi\) | ||||
0.844665 | + | 0.535295i | \(0.179799\pi\) | |||||||
\(972\) | 18.7321 | 0.600831 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 70.6410 | 2.26348 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.0192 | −0.768837 | ||||||||
\(977\) | −31.6410 | −1.01229 | −0.506143 | − | 0.862450i | \(-0.668929\pi\) | ||||
−0.506143 | + | 0.862450i | \(0.668929\pi\) | |||||||
\(978\) | −76.6410 | −2.45071 | ||||||||
\(979\) | −16.3923 | −0.523900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.4641 | 1.19614 | ||||||||
\(982\) | −13.1769 | −0.420492 | ||||||||
\(983\) | −17.3205 | −0.552438 | −0.276219 | − | 0.961095i | \(-0.589082\pi\) | ||||
−0.276219 | + | 0.961095i | \(0.589082\pi\) | |||||||
\(984\) | 24.5885 | 0.783851 | ||||||||
\(985\) | −20.7846 | −0.662253 | ||||||||
\(986\) | 40.1769 | 1.27949 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.928203 | −0.0295151 | ||||||||
\(990\) | 16.9808 | 0.539684 | ||||||||
\(991\) | 18.9808 | 0.602944 | 0.301472 | − | 0.953475i | \(-0.402522\pi\) | ||||
0.301472 | + | 0.953475i | \(0.402522\pi\) | |||||||
\(992\) | 21.8038 | 0.692273 | ||||||||
\(993\) | 68.2487 | 2.16581 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.46410 | −0.109819 | ||||||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | 4.80385 | 0.152139 | 0.0760697 | − | 0.997103i | \(-0.475763\pi\) | ||||
0.0760697 | + | 0.997103i | \(0.475763\pi\) | |||||||
\(998\) | −67.5167 | −2.13720 | ||||||||
\(999\) | −28.0000 | −0.885881 |
(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 | 8281.2.a.t.1.1 | 2 | ||
7.6 | odd | 2 | 1183.2.a.e.1.1 | 2 | |||
13.4 | even | 6 | 637.2.f.d.393.1 | 4 | |||
13.10 | even | 6 | 637.2.f.d.295.1 | 4 | |||
13.12 | even | 2 | 8281.2.a.r.1.2 | 2 | |||
91.4 | even | 6 | 637.2.h.e.471.2 | 4 | |||
91.10 | odd | 6 | 637.2.g.e.373.1 | 4 | |||
91.17 | odd | 6 | 637.2.h.d.471.2 | 4 | |||
91.23 | even | 6 | 637.2.h.e.165.2 | 4 | |||
91.30 | even | 6 | 637.2.g.d.263.1 | 4 | |||
91.34 | even | 4 | 1183.2.c.e.337.2 | 4 | |||
91.62 | odd | 6 | 91.2.f.b.22.1 | ✓ | 4 | ||
91.69 | odd | 6 | 91.2.f.b.29.1 | yes | 4 | ||
91.75 | odd | 6 | 637.2.h.d.165.2 | 4 | |||
91.82 | odd | 6 | 637.2.g.e.263.1 | 4 | |||
91.83 | even | 4 | 1183.2.c.e.337.4 | 4 | |||
91.88 | even | 6 | 637.2.g.d.373.1 | 4 | |||
91.90 | odd | 2 | 1183.2.a.f.1.2 | 2 | |||
273.62 | even | 6 | 819.2.o.b.568.2 | 4 | |||
273.251 | even | 6 | 819.2.o.b.757.2 | 4 | |||
364.251 | even | 6 | 1456.2.s.o.1121.2 | 4 | |||
364.335 | even | 6 | 1456.2.s.o.113.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.b.22.1 | ✓ | 4 | 91.62 | odd | 6 | ||
91.2.f.b.29.1 | yes | 4 | 91.69 | odd | 6 | ||
637.2.f.d.295.1 | 4 | 13.10 | even | 6 | |||
637.2.f.d.393.1 | 4 | 13.4 | even | 6 | |||
637.2.g.d.263.1 | 4 | 91.30 | even | 6 | |||
637.2.g.d.373.1 | 4 | 91.88 | even | 6 | |||
637.2.g.e.263.1 | 4 | 91.82 | odd | 6 | |||
637.2.g.e.373.1 | 4 | 91.10 | odd | 6 | |||
637.2.h.d.165.2 | 4 | 91.75 | odd | 6 | |||
637.2.h.d.471.2 | 4 | 91.17 | odd | 6 | |||
637.2.h.e.165.2 | 4 | 91.23 | even | 6 | |||
637.2.h.e.471.2 | 4 | 91.4 | even | 6 | |||
819.2.o.b.568.2 | 4 | 273.62 | even | 6 | |||
819.2.o.b.757.2 | 4 | 273.251 | even | 6 | |||
1183.2.a.e.1.1 | 2 | 7.6 | odd | 2 | |||
1183.2.a.f.1.2 | 2 | 91.90 | odd | 2 | |||
1183.2.c.e.337.2 | 4 | 91.34 | even | 4 | |||
1183.2.c.e.337.4 | 4 | 91.83 | even | 4 | |||
1456.2.s.o.113.2 | 4 | 364.335 | even | 6 | |||
1456.2.s.o.1121.2 | 4 | 364.251 | even | 6 | |||
8281.2.a.r.1.2 | 2 | 13.12 | even | 2 | |||
8281.2.a.t.1.1 | 2 | 1.1 | even | 1 | trivial |