Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8624,2,Mod(1,8624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8624, 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("8624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8624.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: | \(68.8629867032\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8624.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.23607 | −0.713644 | −0.356822 | − | 0.934172i | \(-0.616140\pi\) | ||||
−0.356822 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.47214 | −0.490712 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.23607 | −0.897524 | −0.448762 | − | 0.893651i | \(-0.648135\pi\) | ||||
−0.448762 | + | 0.893651i | \(0.648135\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.47214 | −0.638303 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.23607 | 0.784862 | 0.392431 | − | 0.919781i | \(-0.371634\pi\) | ||||
0.392431 | + | 0.919781i | \(0.371634\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.47214 | 1.48481 | 0.742405 | − | 0.669951i | \(-0.233685\pi\) | ||||
0.742405 | + | 0.669951i | \(0.233685\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.47214 | −0.515476 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.52786 | 1.06384 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.47214 | 1.57324 | 0.786618 | − | 0.617440i | \(-0.211830\pi\) | ||||
0.786618 | + | 0.617440i | \(0.211830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76393 | −0.496417 | −0.248208 | − | 0.968707i | \(-0.579842\pi\) | ||||
−0.248208 | + | 0.968707i | \(0.579842\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.23607 | −0.215172 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.47214 | −1.39281 | −0.696405 | − | 0.717649i | \(-0.745218\pi\) | ||||
−0.696405 | + | 0.717649i | \(0.745218\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2361 | 1.75478 | 0.877390 | − | 0.479779i | \(-0.159283\pi\) | ||||
0.877390 | + | 0.479779i | \(0.159283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.94427 | −0.438906 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.76393 | 0.403161 | 0.201580 | − | 0.979472i | \(-0.435392\pi\) | ||||
0.201580 | + | 0.979472i | \(0.435392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.23607 | −0.160922 | −0.0804612 | − | 0.996758i | \(-0.525639\pi\) | ||||
−0.0804612 | + | 0.996758i | \(0.525639\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23607 | 0.926484 | 0.463242 | − | 0.886232i | \(-0.346686\pi\) | ||||
0.463242 | + | 0.886232i | \(0.346686\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.47214 | −0.802770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.4721 | −1.76805 | −0.884026 | − | 0.467437i | \(-0.845177\pi\) | ||||
−0.884026 | + | 0.467437i | \(0.845177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.05573 | 0.367866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4721 | 1.24281 | 0.621407 | − | 0.783488i | \(-0.286561\pi\) | ||||
0.621407 | + | 0.783488i | \(0.286561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.763932 | 0.0894115 | 0.0447057 | − | 0.999000i | \(-0.485765\pi\) | ||||
0.0447057 | + | 0.999000i | \(0.485765\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.23607 | 0.142729 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.41641 | −0.268490 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.4164 | −1.25311 | −0.626557 | − | 0.779376i | \(-0.715536\pi\) | ||||
−0.626557 | + | 0.779376i | \(0.715536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.47214 | 0.702002 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4721 | −1.12273 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.41641 | 0.354265 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.9443 | 1.32805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.4164 | −1.76837 | −0.884184 | − | 0.467139i | \(-0.845285\pi\) | ||||
−0.884184 | + | 0.467139i | \(0.845285\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.47214 | −0.147955 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.76393 | 0.474029 | 0.237014 | − | 0.971506i | \(-0.423831\pi\) | ||||
0.237014 | + | 0.971506i | \(0.423831\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.70820 | 0.759512 | 0.379756 | − | 0.925087i | \(-0.376008\pi\) | ||||
0.379756 | + | 0.925087i | \(0.376008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.47214 | −0.428353 | −0.214176 | − | 0.976795i | \(-0.568707\pi\) | ||||
−0.214176 | + | 0.976795i | \(0.568707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4721 | 0.993971 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.94427 | −0.461056 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.76393 | 0.440426 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.8885 | −1.25229 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.05573 | −0.271152 | −0.135576 | − | 0.990767i | \(-0.543288\pi\) | ||||
−0.135576 | + | 0.990767i | \(0.543288\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.88854 | 0.870638 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.8885 | 1.91241 | 0.956205 | − | 0.292696i | \(-0.0945525\pi\) | ||||
0.956205 | + | 0.292696i | \(0.0945525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.0557 | 0.951526 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4721 | 1.40731 | 0.703655 | − | 0.710542i | \(-0.251550\pi\) | ||||
0.703655 | + | 0.710542i | \(0.251550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.52786 | −0.129592 | −0.0647959 | − | 0.997899i | \(-0.520640\pi\) | ||||
−0.0647959 | + | 0.997899i | \(0.520640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.41641 | −0.287713 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.23607 | −0.270614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.9443 | 1.40715 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0000 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.76393 | −0.385141 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.52786 | −0.444009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9443 | −0.873448 | −0.436724 | − | 0.899596i | \(-0.643861\pi\) | ||||
−0.436724 | + | 0.899596i | \(0.643861\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.583592 | 0.0462819 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.41641 | 0.267594 | 0.133797 | − | 0.991009i | \(-0.457283\pi\) | ||||
0.133797 | + | 0.991009i | \(0.457283\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.47214 | −0.192456 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.94427 | 0.382599 | 0.191300 | − | 0.981532i | \(-0.438730\pi\) | ||||
0.191300 | + | 0.981532i | \(0.438730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.52786 | −0.728614 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.7639 | 0.970424 | 0.485212 | − | 0.874397i | \(-0.338742\pi\) | ||||
0.485212 | + | 0.874397i | \(0.338742\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.52786 | 0.114841 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.94427 | 0.668526 | 0.334263 | − | 0.942480i | \(-0.391513\pi\) | ||||
0.334263 | + | 0.942480i | \(0.391513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.4164 | 1.88919 | 0.944593 | − | 0.328243i | \(-0.106456\pi\) | ||||
0.944593 | + | 0.328243i | \(0.106456\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.94427 | −0.661180 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.9443 | −1.24577 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.23607 | 0.236645 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.05573 | 0.221105 | 0.110552 | − | 0.993870i | \(-0.464738\pi\) | ||||
0.110552 | + | 0.993870i | \(0.464738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8885 | 0.855756 | 0.427878 | − | 0.903836i | \(-0.359261\pi\) | ||||
0.427878 | + | 0.903836i | \(0.359261\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.00000 | 0.572892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.18034 | −0.154560 | −0.0772801 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772801 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.8885 | 1.26176 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.4721 | 1.56952 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.63932 | 0.252950 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.47214 | 0.447687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8885 | 0.956127 | 0.478063 | − | 0.878325i | \(-0.341339\pi\) | ||||
0.478063 | + | 0.878325i | \(0.341339\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.9443 | −0.886927 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0000 | −1.09119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.944272 | −0.0638080 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4721 | −0.704432 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1803 | −0.681726 | −0.340863 | − | 0.940113i | \(-0.610719\pi\) | ||||
−0.340863 | + | 0.940113i | \(0.610719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.47214 | 0.0981424 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.88854 | 0.390836 | 0.195418 | − | 0.980720i | \(-0.437394\pi\) | ||||
0.195418 | + | 0.980720i | \(0.437394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.47214 | 0.295527 | 0.147764 | − | 0.989023i | \(-0.452793\pi\) | ||||
0.147764 | + | 0.989023i | \(0.452793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.41641 | 0.616889 | 0.308445 | − | 0.951242i | \(-0.400192\pi\) | ||||
0.308445 | + | 0.951242i | \(0.400192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.52786 | 0.360598 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0557 | −0.718147 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.88854 | 0.639637 | 0.319818 | − | 0.947479i | \(-0.396378\pi\) | ||||
0.319818 | + | 0.947479i | \(0.396378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1246 | 0.845431 | 0.422715 | − | 0.906263i | \(-0.361077\pi\) | ||||
0.422715 | + | 0.906263i | \(0.361077\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5967 | −0.872232 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.9443 | −1.33265 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.1115 | 0.894277 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.29180 | 0.270896 | 0.135448 | − | 0.990784i | \(-0.456753\pi\) | ||||
0.135448 | + | 0.990784i | \(0.456753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.47214 | −0.155422 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.4721 | −0.772006 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.944272 | −0.0580062 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.47214 | 0.151292 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4164 | −0.818013 | −0.409006 | − | 0.912532i | \(-0.634125\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4721 | −0.636137 | −0.318068 | − | 0.948068i | \(-0.603034\pi\) | ||||
−0.318068 | + | 0.948068i | \(0.603034\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.8885 | −1.19499 | −0.597493 | − | 0.801874i | \(-0.703837\pi\) | ||||
−0.597493 | + | 0.801874i | \(0.703837\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.06888 | 0.243598 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.52786 | −0.210455 | −0.105227 | − | 0.994448i | \(-0.533557\pi\) | ||||
−0.105227 | + | 0.994448i | \(0.533557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.8885 | 1.77669 | 0.888345 | − | 0.459177i | \(-0.151856\pi\) | ||||
0.888345 | + | 0.459177i | \(0.151856\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.0000 | −0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.52786 | −0.383992 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.5279 | 1.26199 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.1246 | 1.46780 | 0.733898 | − | 0.679260i | \(-0.237699\pi\) | ||||
0.733898 | + | 0.679260i | \(0.237699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.47214 | −0.143933 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.52786 | 0.320759 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.00000 | 0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.88854 | −0.338288 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.4721 | 0.828672 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.94427 | −0.510477 | −0.255238 | − | 0.966878i | \(-0.582154\pi\) | ||||
−0.255238 | + | 0.966878i | \(0.582154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.52786 | −0.542021 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.29180 | −0.470185 | −0.235092 | − | 0.971973i | \(-0.575539\pi\) | ||||
−0.235092 | + | 0.971973i | \(0.575539\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.9443 | −0.844700 | −0.422350 | − | 0.906433i | \(-0.638795\pi\) | ||||
−0.422350 | + | 0.906433i | \(0.638795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.47214 | 0.474349 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.94427 | −0.275962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.9443 | 1.16537 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.23607 | 0.179505 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.52786 | 0.305692 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8885 | 0.763383 | 0.381692 | − | 0.924290i | \(-0.375342\pi\) | ||||
0.381692 | + | 0.924290i | \(0.375342\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.4721 | 0.683469 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.9443 | −1.58139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5279 | −0.627963 | −0.313981 | − | 0.949429i | \(-0.601663\pi\) | ||||
−0.313981 | + | 0.949429i | \(0.601663\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.47214 | −0.134268 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.76393 | −0.149675 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.11146 | 0.329030 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.9443 | −1.12435 | −0.562174 | − | 0.827019i | \(-0.690035\pi\) | ||||
−0.562174 | + | 0.827019i | \(0.690035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.23607 | 0.387338 | 0.193669 | − | 0.981067i | \(-0.437961\pi\) | ||||
0.193669 | + | 0.981067i | \(0.437961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.8885 | −1.05856 | −0.529280 | − | 0.848447i | \(-0.677538\pi\) | ||||
−0.529280 | + | 0.848447i | \(0.677538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.9443 | 1.11161 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.9443 | 1.31651 | 0.658254 | − | 0.752796i | \(-0.271295\pi\) | ||||
0.658254 | + | 0.752796i | \(0.271295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.23607 | −0.0648767 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52786 | 0.0799721 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1246 | −1.20709 | −0.603547 | − | 0.797327i | \(-0.706247\pi\) | ||||
−0.603547 | + | 0.797327i | \(0.706247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.5410 | −0.861091 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.8328 | 0.765963 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.4164 | −1.41202 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.3050 | −1.91623 | −0.958113 | − | 0.286389i | \(-0.907545\pi\) | ||||
−0.958113 | + | 0.286389i | \(0.907545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.77709 | 0.193506 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.65248 | −0.237730 | −0.118865 | − | 0.992910i | \(-0.537926\pi\) | ||||
−0.118865 | + | 0.992910i | \(0.537926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.7771 | 0.598663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.8885 | 0.805581 | 0.402791 | − | 0.915292i | \(-0.368040\pi\) | ||||
0.402791 | + | 0.915292i | \(0.368040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.0557 | −1.36478 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.8885 | 0.900070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.8885 | 1.80119 | 0.900597 | − | 0.434655i | \(-0.143130\pi\) | ||||
0.900597 | + | 0.434655i | \(0.143130\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.9443 | 1.14578 | 0.572891 | − | 0.819631i | \(-0.305822\pi\) | ||||
0.572891 | + | 0.819631i | \(0.305822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.94427 | 0.445546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.83282 | −0.240145 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.47214 | −0.419948 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.12461 | −0.451183 | −0.225592 | − | 0.974222i | \(-0.572431\pi\) | ||||
−0.225592 | + | 0.974222i | \(0.572431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.3607 | −1.00432 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.8328 | −1.12082 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.88854 | 0.0924824 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.6525 | 1.20435 | 0.602176 | − | 0.798363i | \(-0.294300\pi\) | ||||
0.602176 | + | 0.798363i | \(0.294300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3607 | 1.08979 | 0.544896 | − | 0.838503i | \(-0.316569\pi\) | ||||
0.544896 | + | 0.838503i | \(0.316569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.06888 | −0.197836 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.23607 | −0.156972 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.47214 | 0.407145 | 0.203572 | − | 0.979060i | \(-0.434745\pi\) | ||||
0.203572 | + | 0.979060i | \(0.434745\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.9443 | −1.00420 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4721 | 0.499808 | 0.249904 | − | 0.968271i | \(-0.419601\pi\) | ||||
0.249904 | + | 0.968271i | \(0.419601\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.9443 | 1.18514 | 0.592569 | − | 0.805520i | \(-0.298114\pi\) | ||||
0.592569 | + | 0.805520i | \(0.298114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.00000 | −0.189618 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.3050 | −0.818496 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.4721 | −1.34368 | −0.671842 | − | 0.740695i | \(-0.734496\pi\) | ||||
−0.671842 | + | 0.740695i | \(0.734496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2361 | 0.529086 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.0557 | 0.519443 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.8328 | −1.34874 | −0.674371 | − | 0.738393i | \(-0.735585\pi\) | ||||
−0.674371 | + | 0.738393i | \(0.735585\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.8885 | 0.834966 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.1803 | 0.567295 | 0.283647 | − | 0.958929i | \(-0.408455\pi\) | ||||
0.283647 | + | 0.958929i | \(0.408455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.52786 | 0.256902 | 0.128451 | − | 0.991716i | \(-0.459000\pi\) | ||||
0.128451 | + | 0.991716i | \(0.459000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.83282 | 0.316864 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.0689 | 1.11378 | 0.556888 | − | 0.830588i | \(-0.311995\pi\) | ||||
0.556888 | + | 0.830588i | \(0.311995\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.5279 | 0.623331 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.00000 | −0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.47214 | −0.296962 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.695048 | 0.0318241 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.5279 | 0.618104 | 0.309052 | − | 0.951045i | \(-0.399988\pi\) | ||||
0.309052 | + | 0.951045i | \(0.399988\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.4164 | 1.25008 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.8328 | −1.58168 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.3607 | 1.64766 | 0.823830 | − | 0.566837i | \(-0.191833\pi\) | ||||
0.823830 | + | 0.566837i | \(0.191833\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.22291 | −0.190967 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.4164 | 1.23477 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.94427 | −0.132335 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.52786 | −0.0683966 | −0.0341983 | − | 0.999415i | \(-0.510888\pi\) | ||||
−0.0341983 | + | 0.999415i | \(0.510888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.11146 | −0.273040 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.4164 | 1.04409 | 0.522043 | − | 0.852919i | \(-0.325170\pi\) | ||||
0.522043 | + | 0.852919i | \(0.325170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.52786 | 0.423984 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.12461 | 0.138769 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −40.4721 | −1.79390 | −0.896948 | − | 0.442136i | \(-0.854221\pi\) | ||||
−0.896948 | + | 0.442136i | \(0.854221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.7771 | 1.57960 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.4164 | 0.679328 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.76393 | 0.121558 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.7771 | −0.692537 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.3607 | −1.33013 | −0.665063 | − | 0.746787i | \(-0.731595\pi\) | ||||
−0.665063 | + | 0.746787i | \(0.731595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.0000 | 1.92399 | 0.961993 | − | 0.273075i | \(-0.0880406\pi\) | ||||
0.961993 | + | 0.273075i | \(0.0880406\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.94427 | −0.389619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.81966 | 0.0789665 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.3607 | −1.57496 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | 0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.0557 | −0.477090 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.8328 | 0.895673 | 0.447836 | − | 0.894116i | \(-0.352195\pi\) | ||||
0.447836 | + | 0.894116i | \(0.352195\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31.4164 | −1.34821 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.94427 | −0.383131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.6525 | −0.454637 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.8328 | 2.33596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20.9443 | 0.889035 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.9443 | −1.65012 | −0.825061 | − | 0.565044i | \(-0.808859\pi\) | ||||
−0.825061 | + | 0.565044i | \(0.808859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.8885 | 1.09497 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.5836 | 0.530335 | 0.265168 | − | 0.964202i | \(-0.414573\pi\) | ||||
0.265168 | + | 0.964202i | \(0.414573\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | 0.168281 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.52786 | 0.315584 | 0.157792 | − | 0.987472i | \(-0.449562\pi\) | ||||
0.157792 | + | 0.987472i | \(0.449562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0557 | 0.630063 | 0.315031 | − | 0.949081i | \(-0.397985\pi\) | ||||
0.315031 | + | 0.949081i | \(0.397985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.77709 | −0.157790 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.47214 | 0.103095 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5279 | 0.812956 | 0.406478 | − | 0.913661i | \(-0.366757\pi\) | ||||
0.406478 | + | 0.913661i | \(0.366757\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.6950 | −0.610705 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.472136 | −0.0195539 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.52786 | 0.393929 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.1246 | 1.11955 | 0.559776 | − | 0.828644i | \(-0.310887\pi\) | ||||
0.559776 | + | 0.828644i | \(0.310887\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.8885 | −0.737085 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.47214 | 0.101690 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.7082 | 1.87701 | 0.938505 | − | 0.345264i | \(-0.112211\pi\) | ||||
0.938505 | + | 0.345264i | \(0.112211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.69505 | 0.110301 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.4164 | 0.956768 | 0.478384 | − | 0.878151i | \(-0.341223\pi\) | ||||
0.478384 | + | 0.878151i | \(0.341223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1246 | 1.51434 | 0.757172 | − | 0.653215i | \(-0.226580\pi\) | ||||
0.757172 | + | 0.653215i | \(0.226580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.3050 | 0.867605 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9443 | 0.525392 | 0.262696 | − | 0.964879i | \(-0.415388\pi\) | ||||
0.262696 | + | 0.964879i | \(0.415388\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.94427 | −0.361847 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.3050 | 0.618161 | 0.309081 | − | 0.951036i | \(-0.399979\pi\) | ||||
0.309081 | + | 0.951036i | \(0.399979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.7771 | −1.12008 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.58359 | 0.265045 | 0.132523 | − | 0.991180i | \(-0.457692\pi\) | ||||
0.132523 | + | 0.991180i | \(0.457692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1246 | 0.447136 | 0.223568 | − | 0.974688i | \(-0.428230\pi\) | ||||
0.223568 | + | 0.974688i | \(0.428230\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.6656 | −0.548383 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.00000 | −0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.4164 | −1.09316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.1672 | −0.682334 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.11146 | −0.242526 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.4164 | −0.609864 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.5279 | −0.613314 | −0.306657 | − | 0.951820i | \(-0.599210\pi\) | ||||
−0.306657 | + | 0.951820i | \(0.599210\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.1246 | 0.438712 | 0.219356 | − | 0.975645i | \(-0.429604\pi\) | ||||
0.219356 | + | 0.975645i | \(0.429604\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.7771 | 0.778722 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.0689 | 1.41801 | 0.709007 | − | 0.705201i | \(-0.249143\pi\) | ||||
0.709007 | + | 0.705201i | \(0.249143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.23607 | −0.0485199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.0557 | 0.980506 | 0.490253 | − | 0.871580i | \(-0.336904\pi\) | ||||
0.490253 | + | 0.871580i | \(0.336904\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.7771 | 1.71051 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.12461 | −0.0438753 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.8328 | 1.58821 | 0.794106 | − | 0.607779i | \(-0.207939\pi\) | ||||
0.794106 | + | 0.607779i | \(0.207939\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9443 | 0.502714 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.9443 | −0.810965 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.5836 | 0.486510 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.23607 | 0.279345 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.4164 | −0.825542 | −0.412771 | − | 0.910835i | \(-0.635439\pi\) | ||||
−0.412771 | + | 0.910835i | \(0.635439\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.52786 | −0.212768 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.70820 | 0.373117 | 0.186558 | − | 0.982444i | \(-0.440267\pi\) | ||||
0.186558 | + | 0.982444i | \(0.440267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.27864 | −0.278918 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.88854 | 0.225319 | 0.112659 | − | 0.993634i | \(-0.464063\pi\) | ||||
0.112659 | + | 0.993634i | \(0.464063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.9443 | 1.25874 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.52786 | −0.210901 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.52786 | 0.0582070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5410 | 0.705334 | 0.352667 | − | 0.935749i | \(-0.385275\pi\) | ||||
0.352667 | + | 0.935749i | \(0.385275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.05573 | −0.115910 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.3607 | 1.37726 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.6393 | −0.440240 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.5279 | −0.586479 | −0.293240 | − | 0.956039i | \(-0.594733\pi\) | ||||
−0.293240 | + | 0.956039i | \(0.594733\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.8328 | −2.06806 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.83282 | −0.257339 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9443 | −0.561244 | −0.280622 | − | 0.959818i | \(-0.590541\pi\) | ||||
−0.280622 | + | 0.959818i | \(0.590541\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.1672 | −0.493808 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.83282 | 0.255891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.47214 | −0.242044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.2229 | −0.456473 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.4853 | −1.92008 | −0.960039 | − | 0.279867i | \(-0.909710\pi\) | ||||
−0.960039 | + | 0.279867i | \(0.909710\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.2229 | −0.603337 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.47214 | −0.314647 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.0132 | 0.927687 | 0.463843 | − | 0.885917i | \(-0.346470\pi\) | ||||
0.463843 | + | 0.885917i | \(0.346470\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8885 | −0.957522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.76393 | −0.323703 | −0.161852 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161852 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.4721 | −0.533088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.9443 | −0.917590 | −0.458795 | − | 0.888542i | \(-0.651719\pi\) | ||||
−0.458795 | + | 0.888542i | \(0.651719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.8885 | 0.951039 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.88854 | −0.0692840 | −0.0346420 | − | 0.999400i | \(-0.511029\pi\) | ||||
−0.0346420 | + | 0.999400i | \(0.511029\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.0000 | 1.02584 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.8065 | 0.614918 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.5279 | −1.07749 | −0.538744 | − | 0.842470i | \(-0.681101\pi\) | ||||
−0.538744 | + | 0.842470i | \(0.681101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.30495 | −0.193323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.8885 | −0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8885 | 0.577479 | 0.288739 | − | 0.957408i | \(-0.406764\pi\) | ||||
0.288739 | + | 0.957408i | \(0.406764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.05573 | 0.110916 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.5967 | 1.14538 | 0.572691 | − | 0.819772i | \(-0.305900\pi\) | ||||
0.572691 | + | 0.819772i | \(0.305900\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.52786 | −0.344481 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | 0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.2918 | −0.659619 | −0.329810 | − | 0.944047i | \(-0.606985\pi\) | ||||
−0.329810 | + | 0.944047i | \(0.606985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.41641 | −0.267095 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.3607 | 1.37974 | 0.689869 | − | 0.723934i | \(-0.257668\pi\) | ||||
0.689869 | + | 0.723934i | \(0.257668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.76393 | 0.0992834 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 72.7214 | 2.60551 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4721 | 0.374722 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 46.8328 | 1.67367 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.8885 | −0.781236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.4164 | −1.54763 | −0.773814 | − | 0.633413i | \(-0.781653\pi\) | ||||
−0.773814 | + | 0.633413i | \(0.781653\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.4164 | −0.831541 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.16718 | 0.0413958 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.9443 | 0.529353 | 0.264677 | − | 0.964337i | \(-0.414735\pi\) | ||||
0.264677 | + | 0.964337i | \(0.414735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.94427 | 0.316426 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.94427 | 0.104031 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.763932 | 0.0269586 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.5836 | 0.583770 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.0557 | 0.740280 | 0.370140 | − | 0.928976i | \(-0.379310\pi\) | ||||
0.370140 | + | 0.928976i | \(0.379310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.8328 | −1.22315 | −0.611573 | − | 0.791188i | \(-0.709463\pi\) | ||||
−0.611573 | + | 0.791188i | \(0.709463\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9443 | 0.453975 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.83282 | 0.239343 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.7771 | −1.81145 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.8328 | 1.56468 | 0.782338 | − | 0.622854i | \(-0.214027\pi\) | ||||
0.782338 | + | 0.622854i | \(0.214027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1115 | 0.491894 | 0.245947 | − | 0.969283i | \(-0.420901\pi\) | ||||
0.245947 | + | 0.969283i | \(0.420901\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.23607 | 0.0430344 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9443 | 0.450116 | 0.225058 | − | 0.974345i | \(-0.427743\pi\) | ||||
0.225058 | + | 0.974345i | \(0.427743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.8328 | −1.27926 | −0.639628 | − | 0.768684i | \(-0.720912\pi\) | ||||
−0.639628 | + | 0.768684i | \(0.720912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.5836 | 0.852795 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.88854 | 0.342207 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.2786 | −0.528107 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.0689 | 1.52143 | 0.760713 | − | 0.649088i | \(-0.224849\pi\) | ||||
0.760713 | + | 0.649088i | \(0.224849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.36068 | 0.150190 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.05573 | −0.173922 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −36.9443 | −1.26792 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.9443 | 0.717960 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.6525 | 1.04952 | 0.524760 | − | 0.851250i | \(-0.324155\pi\) | ||||
0.524760 | + | 0.851250i | \(0.324155\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.0557 | −0.651692 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.2361 | −0.520454 | −0.260227 | − | 0.965547i | \(-0.583797\pi\) | ||||
−0.260227 | + | 0.965547i | \(0.583797\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.5410 | −0.905568 | −0.452784 | − | 0.891620i | \(-0.649569\pi\) | ||||
−0.452784 | + | 0.891620i | \(0.649569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.05573 | 0.104018 | 0.0520091 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520091 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.5279 | 0.867973 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.06888 | 0.274034 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.94427 | 0.303414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.8328 | 1.58687 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.6393 | 0.867760 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.5836 | 0.492453 | 0.246226 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246226 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.0557 | −1.04748 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.58359 | −0.0870434 | −0.0435217 | − | 0.999052i | \(-0.513858\pi\) | ||||
−0.0435217 | + | 0.999052i | \(0.513858\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.94427 | 0.300999 | 0.150499 | − | 0.988610i | \(-0.451912\pi\) | ||||
0.150499 | + | 0.988610i | \(0.451912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.05573 | 0.102717 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.36068 | −0.146417 | −0.0732086 | − | 0.997317i | \(-0.523324\pi\) | ||||
−0.0732086 | + | 0.997317i | \(0.523324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.41641 | −0.0809527 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.8885 | 0.598617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.8885 | 0.597948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.88854 | −0.330169 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.4164 | −0.780981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.52786 | −0.0509005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.8328 | 1.68974 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.4721 | −0.746175 | −0.373088 | − | 0.927796i | \(-0.621701\pi\) | ||||
−0.373088 | + | 0.927796i | \(0.621701\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.01316 | −0.232612 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.4721 | −1.40716 | −0.703582 | − | 0.710614i | \(-0.748417\pi\) | ||||
−0.703582 | + | 0.710614i | \(0.748417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.4164 | −0.377828 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.8885 | −0.591377 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.8885 | −1.38178 | −0.690888 | − | 0.722962i | \(-0.742780\pi\) | ||||
−0.690888 | + | 0.722962i | \(0.742780\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.0557 | 0.364299 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.8885 | −1.11546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.47214 | 0.278562 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.3475 | −0.372702 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.2492 | 1.71424 | 0.857121 | − | 0.515116i | \(-0.172251\pi\) | ||||
0.857121 | + | 0.515116i | \(0.172251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.2492 | 0.335545 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.47214 | 0.211661 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6525 | 0.348001 | 0.174001 | − | 0.984746i | \(-0.444331\pi\) | ||||
0.174001 | + | 0.984746i | \(0.444331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.4721 | 0.602815 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.59675 | −0.247647 | −0.123823 | − | 0.992304i | \(-0.539516\pi\) | ||||
−0.123823 | + | 0.992304i | \(0.539516\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.7771 | −0.904546 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.16718 | 0.167911 | 0.0839555 | − | 0.996470i | \(-0.473245\pi\) | ||||
0.0839555 | + | 0.996470i | \(0.473245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.47214 | −0.0802489 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.3050 | −0.561152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.9443 | 0.743238 | 0.371619 | − | 0.928385i | \(-0.378803\pi\) | ||||
0.371619 | + | 0.928385i | \(0.378803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.11146 | 0.197762 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.4721 | −0.338516 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3607 | −0.753570 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.88854 | −0.189756 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.7771 | 0.765412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.8885 | 0.446625 | 0.223313 | − | 0.974747i | \(-0.428313\pi\) | ||||
0.223313 | + | 0.974747i | \(0.428313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25.8885 | −0.831660 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.1246 | 0.357006 | 0.178503 | − | 0.983939i | \(-0.442875\pi\) | ||||
0.178503 | + | 0.983939i | \(0.442875\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.00000 | −0.128103 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.9443 | 0.734052 | 0.367026 | − | 0.930211i | \(-0.380376\pi\) | ||||
0.367026 | + | 0.930211i | \(0.380376\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.58359 | 0.210198 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.8197 | 0.695939 | 0.347970 | − | 0.937506i | \(-0.386871\pi\) | ||||
0.347970 | + | 0.937506i | \(0.386871\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.00000 | −0.127451 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.7771 | 0.628875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.2492 | −1.72328 | −0.861642 | − | 0.507517i | \(-0.830563\pi\) | ||||
−0.861642 | + | 0.507517i | \(0.830563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.1672 | −0.544784 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.36068 | −0.138243 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.34752 | −0.0426765 | −0.0213383 | − | 0.999772i | \(-0.506793\pi\) | ||||
−0.0213383 | + | 0.999772i | \(0.506793\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −46.8328 | −1.48172 |
(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 | 8624.2.a.ce.1.1 | 2 | ||
4.3 | odd | 2 | 539.2.a.f.1.2 | 2 | |||
7.6 | odd | 2 | 1232.2.a.m.1.2 | 2 | |||
12.11 | even | 2 | 4851.2.a.y.1.1 | 2 | |||
28.3 | even | 6 | 539.2.e.i.177.1 | 4 | |||
28.11 | odd | 6 | 539.2.e.j.177.1 | 4 | |||
28.19 | even | 6 | 539.2.e.i.67.1 | 4 | |||
28.23 | odd | 6 | 539.2.e.j.67.1 | 4 | |||
28.27 | even | 2 | 77.2.a.d.1.2 | ✓ | 2 | ||
44.43 | even | 2 | 5929.2.a.m.1.1 | 2 | |||
56.13 | odd | 2 | 4928.2.a.bv.1.1 | 2 | |||
56.27 | even | 2 | 4928.2.a.bm.1.2 | 2 | |||
84.83 | odd | 2 | 693.2.a.h.1.1 | 2 | |||
140.27 | odd | 4 | 1925.2.b.h.1849.3 | 4 | |||
140.83 | odd | 4 | 1925.2.b.h.1849.2 | 4 | |||
140.139 | even | 2 | 1925.2.a.r.1.1 | 2 | |||
308.27 | even | 10 | 847.2.f.a.729.1 | 4 | |||
308.83 | odd | 10 | 847.2.f.m.729.1 | 4 | |||
308.139 | odd | 10 | 847.2.f.b.148.1 | 4 | |||
308.167 | odd | 10 | 847.2.f.m.323.1 | 4 | |||
308.195 | odd | 10 | 847.2.f.b.372.1 | 4 | |||
308.223 | even | 10 | 847.2.f.n.372.1 | 4 | |||
308.251 | even | 10 | 847.2.f.a.323.1 | 4 | |||
308.279 | even | 10 | 847.2.f.n.148.1 | 4 | |||
308.307 | odd | 2 | 847.2.a.f.1.1 | 2 | |||
924.923 | even | 2 | 7623.2.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.d.1.2 | ✓ | 2 | 28.27 | even | 2 | ||
539.2.a.f.1.2 | 2 | 4.3 | odd | 2 | |||
539.2.e.i.67.1 | 4 | 28.19 | even | 6 | |||
539.2.e.i.177.1 | 4 | 28.3 | even | 6 | |||
539.2.e.j.67.1 | 4 | 28.23 | odd | 6 | |||
539.2.e.j.177.1 | 4 | 28.11 | odd | 6 | |||
693.2.a.h.1.1 | 2 | 84.83 | odd | 2 | |||
847.2.a.f.1.1 | 2 | 308.307 | odd | 2 | |||
847.2.f.a.323.1 | 4 | 308.251 | even | 10 | |||
847.2.f.a.729.1 | 4 | 308.27 | even | 10 | |||
847.2.f.b.148.1 | 4 | 308.139 | odd | 10 | |||
847.2.f.b.372.1 | 4 | 308.195 | odd | 10 | |||
847.2.f.m.323.1 | 4 | 308.167 | odd | 10 | |||
847.2.f.m.729.1 | 4 | 308.83 | odd | 10 | |||
847.2.f.n.148.1 | 4 | 308.279 | even | 10 | |||
847.2.f.n.372.1 | 4 | 308.223 | even | 10 | |||
1232.2.a.m.1.2 | 2 | 7.6 | odd | 2 | |||
1925.2.a.r.1.1 | 2 | 140.139 | even | 2 | |||
1925.2.b.h.1849.2 | 4 | 140.83 | odd | 4 | |||
1925.2.b.h.1849.3 | 4 | 140.27 | odd | 4 | |||
4851.2.a.y.1.1 | 2 | 12.11 | even | 2 | |||
4928.2.a.bm.1.2 | 2 | 56.27 | even | 2 | |||
4928.2.a.bv.1.1 | 2 | 56.13 | odd | 2 | |||
5929.2.a.m.1.1 | 2 | 44.43 | even | 2 | |||
7623.2.a.bl.1.2 | 2 | 924.923 | even | 2 | |||
8624.2.a.ce.1.1 | 2 | 1.1 | even | 1 | trivial |