Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8112,2,Mod(1,8112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8112, 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("8112.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8112.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: | \(64.7746461197\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8112.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.35690 | 1.50125 | 0.750625 | − | 0.660729i | \(-0.229753\pi\) | ||||
0.750625 | + | 0.660729i | \(0.229753\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.24698 | −0.849278 | −0.424639 | − | 0.905363i | \(-0.639599\pi\) | ||||
−0.424639 | + | 0.905363i | \(0.639599\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.93900 | −1.48916 | −0.744582 | − | 0.667531i | \(-0.767351\pi\) | ||||
−0.744582 | + | 0.667531i | \(0.767351\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.35690 | 0.866747 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.911854 | 0.221157 | 0.110579 | − | 0.993867i | \(-0.464730\pi\) | ||||
0.110579 | + | 0.993867i | \(0.464730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.80194 | 0.872224 | 0.436112 | − | 0.899892i | \(-0.356355\pi\) | ||||
0.436112 | + | 0.899892i | \(0.356355\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.24698 | −0.490331 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.02715 | −0.422689 | −0.211345 | − | 0.977412i | \(-0.567784\pi\) | ||||
−0.211345 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.26875 | 1.25375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.93900 | −0.731454 | −0.365727 | − | 0.930722i | \(-0.619180\pi\) | ||||
−0.365727 | + | 0.930722i | \(0.619180\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.82908 | 1.58575 | 0.792875 | − | 0.609384i | \(-0.208583\pi\) | ||||
0.792875 | + | 0.609384i | \(0.208583\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.93900 | −0.859770 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.54288 | −1.27498 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.80194 | 1.44703 | 0.723515 | − | 0.690309i | \(-0.242525\pi\) | ||||
0.723515 | + | 0.690309i | \(0.242525\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.93900 | 1.08369 | 0.541845 | − | 0.840478i | \(-0.317726\pi\) | ||||
0.541845 | + | 0.840478i | \(0.317726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.28621 | 0.348643 | 0.174322 | − | 0.984689i | \(-0.444227\pi\) | ||||
0.174322 | + | 0.984689i | \(0.444227\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.35690 | 0.500416 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.80194 | −0.554570 | −0.277285 | − | 0.960788i | \(-0.589435\pi\) | ||||
−0.277285 | + | 0.960788i | \(0.589435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.95108 | −0.278726 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.911854 | 0.127685 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.542877 | 0.0745698 | 0.0372849 | − | 0.999305i | \(-0.488129\pi\) | ||||
0.0372849 | + | 0.999305i | \(0.488129\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.5797 | −2.23561 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.80194 | 0.503579 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.71379 | 0.613683 | 0.306842 | − | 0.951761i | \(-0.400728\pi\) | ||||
0.306842 | + | 0.951761i | \(0.400728\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.67994 | 0.471168 | 0.235584 | − | 0.971854i | \(-0.424300\pi\) | ||||
0.235584 | + | 0.971854i | \(0.424300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.24698 | −0.283093 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52111 | 0.185833 | 0.0929164 | − | 0.995674i | \(-0.470381\pi\) | ||||
0.0929164 | + | 0.995674i | \(0.470381\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.02715 | −0.244040 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.37867 | −0.282296 | −0.141148 | − | 0.989989i | \(-0.545079\pi\) | ||||
−0.141148 | + | 0.989989i | \(0.545079\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.41119 | 0.867414 | 0.433707 | − | 0.901054i | \(-0.357205\pi\) | ||||
0.433707 | + | 0.901054i | \(0.357205\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.26875 | 0.723853 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.0978 | 1.26472 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.74094 | 0.420888 | 0.210444 | − | 0.977606i | \(-0.432509\pi\) | ||||
0.210444 | + | 0.977606i | \(0.432509\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.30798 | −0.253334 | −0.126667 | − | 0.991945i | \(-0.540428\pi\) | ||||
−0.126667 | + | 0.991945i | \(0.540428\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.06100 | 0.332012 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.93900 | −0.422305 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0586 | −1.06621 | −0.533105 | − | 0.846049i | \(-0.678975\pi\) | ||||
−0.533105 | + | 0.846049i | \(0.678975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.82908 | 0.915533 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.7627 | 1.30943 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.1293 | −1.63768 | −0.818841 | − | 0.574021i | \(-0.805383\pi\) | ||||
−0.818841 | + | 0.574021i | \(0.805383\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.93900 | −0.496388 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.94869 | −0.989932 | −0.494966 | − | 0.868912i | \(-0.664819\pi\) | ||||
−0.494966 | + | 0.868912i | \(0.664819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9879 | 1.08267 | 0.541336 | − | 0.840806i | \(-0.317919\pi\) | ||||
0.541336 | + | 0.840806i | \(0.317919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.54288 | −0.736109 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.87263 | 0.954423 | 0.477211 | − | 0.878789i | \(-0.341648\pi\) | ||||
0.477211 | + | 0.878789i | \(0.341648\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.2446 | 1.93908 | 0.969540 | − | 0.244934i | \(-0.0787662\pi\) | ||||
0.969540 | + | 0.244934i | \(0.0787662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.80194 | 0.835443 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.69202 | 0.911749 | 0.455874 | − | 0.890044i | \(-0.349327\pi\) | ||||
0.455874 | + | 0.890044i | \(0.349327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.80492 | −0.634562 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.04892 | −0.187824 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.3937 | 1.21761 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.93900 | 0.625669 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.25906 | 0.380942 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.8116 | −1.22558 | −0.612792 | − | 0.790244i | \(-0.709954\pi\) | ||||
−0.612792 | + | 0.790244i | \(0.709954\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.28621 | 0.201289 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.99462 | −0.261641 | −0.130821 | − | 0.991406i | \(-0.541761\pi\) | ||||
−0.130821 | + | 0.991406i | \(0.541761\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.54288 | −0.740761 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.35690 | 0.288916 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 23.0194 | 1.96668 | 0.983339 | − | 0.181781i | \(-0.0581862\pi\) | ||||
0.983339 | + | 0.181781i | \(0.0581862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.982542 | −0.0833381 | −0.0416690 | − | 0.999131i | \(-0.513268\pi\) | ||||
−0.0416690 | + | 0.999131i | \(0.513268\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.80194 | −0.320181 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.2228 | −1.09810 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.95108 | −0.160923 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.2591 | 0.840455 | 0.420228 | − | 0.907419i | \(-0.361950\pi\) | ||||
0.420228 | + | 0.907419i | \(0.361950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1685 | 1.64129 | 0.820646 | − | 0.571438i | \(-0.193614\pi\) | ||||
0.820646 | + | 0.571438i | \(0.193614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.911854 | 0.0737190 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29.6383 | 2.38061 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4383 | 0.833070 | 0.416535 | − | 0.909120i | \(-0.363244\pi\) | ||||
0.416535 | + | 0.909120i | \(0.363244\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.542877 | 0.0430529 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.55496 | 0.358981 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0465 | 0.865231 | 0.432615 | − | 0.901579i | \(-0.357591\pi\) | ||||
0.432615 | + | 0.901579i | \(0.357591\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.5797 | −1.29073 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.10992 | −0.627564 | −0.313782 | − | 0.949495i | \(-0.601596\pi\) | ||||
−0.313782 | + | 0.949495i | \(0.601596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.80194 | 0.290741 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0562 | −1.37279 | −0.686394 | − | 0.727230i | \(-0.740808\pi\) | ||||
−0.686394 | + | 0.727230i | \(0.740808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.0858 | −1.06478 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.71379 | 0.354310 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.8702 | 1.48517 | 0.742585 | − | 0.669751i | \(-0.233599\pi\) | ||||
0.742585 | + | 0.669751i | \(0.233599\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0828 | −0.749446 | −0.374723 | − | 0.927137i | \(-0.622262\pi\) | ||||
−0.374723 | + | 0.927137i | \(0.622262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.67994 | 0.272029 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.5472 | 2.17235 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.50365 | −0.329339 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.24698 | −0.163444 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.58748 | 0.476653 | 0.238327 | − | 0.971185i | \(-0.423401\pi\) | ||||
0.238327 | + | 0.971185i | \(0.423401\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8672 | 0.782242 | 0.391121 | − | 0.920339i | \(-0.372087\pi\) | ||||
0.391121 | + | 0.920339i | \(0.372087\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.24160 | 0.658437 | 0.329218 | − | 0.944254i | \(-0.393215\pi\) | ||||
0.329218 | + | 0.944254i | \(0.393215\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.56465 | 0.110915 | 0.0554574 | − | 0.998461i | \(-0.482338\pi\) | ||||
0.0554574 | + | 0.998461i | \(0.482338\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52111 | 0.107291 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.85086 | 0.621208 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.2935 | 1.62689 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.02715 | −0.140896 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.7778 | −1.29889 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.2446 | −1.60022 | −0.800112 | − | 0.599851i | \(-0.795226\pi\) | ||||
−0.800112 | + | 0.599851i | \(0.795226\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.37867 | −0.162984 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.67456 | 0.523401 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.8388 | −1.34674 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.41119 | 0.500802 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7385 | −0.719106 | −0.359553 | − | 0.933125i | \(-0.617071\pi\) | ||||
−0.359553 | + | 0.933125i | \(0.617071\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.26875 | 0.417917 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.97584 | 0.463003 | 0.231501 | − | 0.972835i | \(-0.425636\pi\) | ||||
0.231501 | + | 0.972835i | \(0.425636\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.8049 | −1.11050 | −0.555250 | − | 0.831683i | \(-0.687378\pi\) | ||||
−0.555250 | + | 0.831683i | \(0.687378\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.0978 | 0.730184 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.69202 | 0.569433 | 0.284717 | − | 0.958612i | \(-0.408100\pi\) | ||||
0.284717 | + | 0.958612i | \(0.408100\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.7627 | −0.832547 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.74094 | 0.243000 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.9191 | 1.48252 | 0.741258 | − | 0.671220i | \(-0.234229\pi\) | ||||
0.741258 | + | 0.671220i | \(0.234229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9801 | 1.41587 | 0.707933 | − | 0.706280i | \(-0.249628\pi\) | ||||
0.707933 | + | 0.706280i | \(0.249628\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.54958 | −0.418437 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.30798 | −0.146262 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.6437 | −1.68174 | −0.840868 | − | 0.541241i | \(-0.817955\pi\) | ||||
−0.840868 | + | 0.541241i | \(0.817955\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0121 | 0.629454 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.06100 | 0.191687 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.1444 | 1.44371 | 0.721853 | − | 0.692047i | \(-0.243291\pi\) | ||||
0.721853 | + | 0.692047i | \(0.243291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.7778 | −1.22893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.93900 | −0.243818 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.5284 | 1.14251 | 0.571255 | − | 0.820773i | \(-0.306457\pi\) | ||||
0.571255 | + | 0.820773i | \(0.306457\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82238 | 0.111948 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0586 | −0.615577 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.75840 | 0.594980 | 0.297490 | − | 0.954725i | \(-0.403851\pi\) | ||||
0.297490 | + | 0.954725i | \(0.403851\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.8019 | 1.38512 | 0.692560 | − | 0.721361i | \(-0.256483\pi\) | ||||
0.692560 | + | 0.721361i | \(0.256483\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −30.9614 | −1.86704 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.9705 | −1.44025 | −0.720123 | − | 0.693847i | \(-0.755914\pi\) | ||||
−0.720123 | + | 0.693847i | \(0.755914\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.82908 | 0.528583 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.12498 | −0.246076 | −0.123038 | − | 0.992402i | \(-0.539264\pi\) | ||||
−0.123038 | + | 0.992402i | \(0.539264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6558 | 0.930639 | 0.465320 | − | 0.885143i | \(-0.345939\pi\) | ||||
0.465320 | + | 0.885143i | \(0.345939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.7627 | 0.755998 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.5918 | −0.920354 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1685 | −0.951090 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.1293 | −0.945516 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.5948 | 1.32000 | 0.660001 | − | 0.751265i | \(-0.270556\pi\) | ||||
0.660001 | + | 0.751265i | \(0.270556\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.8237 | 0.921292 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.93900 | −0.286590 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.13706 | −0.296095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.94869 | −0.571537 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.3532 | 0.707341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.55496 | 0.374111 | 0.187056 | − | 0.982349i | \(-0.440106\pi\) | ||||
0.187056 | + | 0.982349i | \(0.440106\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.9879 | 0.625081 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0392 | 0.682682 | 0.341341 | − | 0.939940i | \(-0.389119\pi\) | ||||
0.341341 | + | 0.939940i | \(0.389119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.8950 | −1.91586 | −0.957929 | − | 0.287005i | \(-0.907340\pi\) | ||||
−0.957929 | + | 0.287005i | \(0.907340\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.54288 | −0.424993 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.49827 | −0.252648 | −0.126324 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126324 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.4547 | 1.08926 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.87263 | 0.551036 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.46681 | 0.192899 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.2446 | 1.11953 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.54288 | 0.470984 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2131 | 0.616329 | 0.308165 | − | 0.951333i | \(-0.400285\pi\) | ||||
0.308165 | + | 0.951333i | \(0.400285\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.80194 | 0.482343 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.10620 | 0.278981 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.04892 | 0.383979 | 0.191989 | − | 0.981397i | \(-0.438506\pi\) | ||||
0.191989 | + | 0.981397i | \(0.438506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.69202 | 0.526398 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −43.6069 | −2.36144 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1129 | 1.08599 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.80492 | −0.366365 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.70410 | 0.145164 | 0.0725819 | − | 0.997362i | \(-0.476876\pi\) | ||||
0.0725819 | + | 0.997362i | \(0.476876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.415502 | −0.0222413 | −0.0111207 | − | 0.999938i | \(-0.503540\pi\) | ||||
−0.0111207 | + | 0.999938i | \(0.503540\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.1672 | −1.71209 | −0.856044 | − | 0.516904i | \(-0.827084\pi\) | ||||
−0.856044 | + | 0.516904i | \(0.827084\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.98493 | −0.423796 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.04892 | −0.108440 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3521 | −1.17970 | −0.589850 | − | 0.807513i | \(-0.700813\pi\) | ||||
−0.589850 | + | 0.807513i | \(0.700813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.54527 | −0.239225 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.3937 | 0.702989 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.8786 | 1.30221 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.30260 | 0.120195 | 0.0600974 | − | 0.998193i | \(-0.480859\pi\) | ||||
0.0600974 | + | 0.998193i | \(0.480859\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.93900 | 0.361230 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.21983 | −0.0633305 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.2760 | −0.998076 | −0.499038 | − | 0.866580i | \(-0.666313\pi\) | ||||
−0.499038 | + | 0.866580i | \(0.666313\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.25906 | 0.219937 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.33944 | 0.377002 | 0.188501 | − | 0.982073i | \(-0.439637\pi\) | ||||
0.188501 | + | 0.982073i | \(0.439637\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.8116 | −0.707591 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.0901 | −0.975457 | −0.487728 | − | 0.872995i | \(-0.662174\pi\) | ||||
−0.487728 | + | 0.872995i | \(0.662174\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37.2543 | 1.89865 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.28621 | 0.116214 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.9879 | −1.21624 | −0.608118 | − | 0.793847i | \(-0.708075\pi\) | ||||
−0.608118 | + | 0.793847i | \(0.708075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.84846 | −0.0934807 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.99462 | −0.151059 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.5579 | 0.631859 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.41789 | −0.221728 | −0.110864 | − | 0.993836i | \(-0.535362\pi\) | ||||
−0.110864 | + | 0.993836i | \(0.535362\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.54288 | −0.427679 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.4088 | −1.01917 | −0.509583 | − | 0.860421i | \(-0.670200\pi\) | ||||
−0.509583 | + | 0.860421i | \(0.670200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.35690 | 0.166805 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −43.4728 | −2.15487 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.1491 | −1.09520 | −0.547602 | − | 0.836739i | \(-0.684459\pi\) | ||||
−0.547602 | + | 0.836739i | \(0.684459\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.0194 | 1.13546 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.5918 | −0.521188 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.74764 | −0.380317 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.982542 | −0.0481153 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.7560 | −0.720878 | −0.360439 | − | 0.932783i | \(-0.617373\pi\) | ||||
−0.360439 | + | 0.932783i | \(0.617373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.47219 | 0.412909 | 0.206455 | − | 0.978456i | \(-0.433807\pi\) | ||||
0.206455 | + | 0.978456i | \(0.433807\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.80194 | −0.184857 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.71618 | 0.277276 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.26875 | −0.400153 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.39181 | −0.115210 | −0.0576048 | − | 0.998339i | \(-0.518346\pi\) | ||||
−0.0576048 | + | 0.998339i | \(0.518346\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.4286 | −0.501169 | −0.250584 | − | 0.968095i | \(-0.580623\pi\) | ||||
−0.250584 | + | 0.968095i | \(0.580623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.2228 | −0.633986 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.70709 | −0.368680 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.5502 | 1.55353 | 0.776767 | − | 0.629787i | \(-0.216858\pi\) | ||||
0.776767 | + | 0.629787i | \(0.216858\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.95108 | −0.0929087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.58211 | −0.455260 | −0.227630 | − | 0.973748i | \(-0.573098\pi\) | ||||
−0.227630 | + | 0.973748i | \(0.573098\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.7657 | −1.60065 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.2591 | 0.485237 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.3937 | −1.33998 | −0.669992 | − | 0.742369i | \(-0.733702\pi\) | ||||
−0.669992 | + | 0.742369i | \(0.733702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.2717 | −1.61379 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.1685 | 0.947600 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.99569 | 0.233688 | 0.116844 | − | 0.993150i | \(-0.462722\pi\) | ||||
0.116844 | + | 0.993150i | \(0.462722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.911854 | 0.0425617 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.35258 | 0.0629961 | 0.0314981 | − | 0.999504i | \(-0.489972\pi\) | ||||
0.0314981 | + | 0.999504i | \(0.489972\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.36467 | 0.156369 | 0.0781846 | − | 0.996939i | \(-0.475088\pi\) | ||||
0.0781846 | + | 0.996939i | \(0.475088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 29.6383 | 1.37444 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.91079 | −0.319793 | −0.159897 | − | 0.987134i | \(-0.551116\pi\) | ||||
−0.159897 | + | 0.987134i | \(0.551116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.41789 | −0.157824 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.4383 | 0.480973 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.2916 | −0.519188 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.8334 | 1.09355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.542877 | 0.0248566 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.51573 | −0.160638 | −0.0803189 | − | 0.996769i | \(-0.525594\pi\) | ||||
−0.0803189 | + | 0.996769i | \(0.525594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.55496 | 0.207258 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −54.1444 | −2.45857 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.8479 | 0.582193 | 0.291096 | − | 0.956694i | \(-0.405980\pi\) | ||||
0.291096 | + | 0.956694i | \(0.405980\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.0465 | 0.499541 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6708 | −1.29390 | −0.646948 | − | 0.762534i | \(-0.723955\pi\) | ||||
−0.646948 | + | 0.762534i | \(0.723955\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.59179 | −0.161766 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.5797 | −0.745203 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.34481 | 0.239748 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.5555 | 1.50215 | 0.751076 | − | 0.660215i | \(-0.229535\pi\) | ||||
0.751076 | + | 0.660215i | \(0.229535\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.10992 | −0.362324 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.5633 | −0.961461 | −0.480730 | − | 0.876868i | \(-0.659628\pi\) | ||||
−0.480730 | + | 0.876868i | \(0.659628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.3967 | −1.48613 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.89008 | −0.394046 | −0.197023 | − | 0.980399i | \(-0.563127\pi\) | ||||
−0.197023 | + | 0.980399i | \(0.563127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.6528 | −0.736676 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.80194 | 0.167860 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 36.8853 | 1.62536 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.7778 | 0.825846 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.0562 | −0.792580 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.3478 | 0.847642 | 0.423821 | − | 0.905746i | \(-0.360688\pi\) | ||||
0.423821 | + | 0.905746i | \(0.360688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5948 | 0.550731 | 0.275366 | − | 0.961340i | \(-0.411201\pi\) | ||||
0.275366 | + | 0.961340i | \(0.411201\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.0858 | −0.614753 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.05084 | 0.350700 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.8907 | −0.821334 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.71379 | 0.204561 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.1414 | 1.43283 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.8702 | 0.857464 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.63640 | 0.415069 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0019 | 1.24689 | 0.623445 | − | 0.781867i | \(-0.285733\pi\) | ||||
0.623445 | + | 0.781867i | \(0.285733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.0828 | −0.432693 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 67.9590 | 2.91104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.7006 | −1.18439 | −0.592197 | − | 0.805793i | \(-0.701739\pi\) | ||||
−0.592197 | + | 0.805793i | \(0.701739\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.67994 | 0.157056 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.9758 | −0.637992 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.40581 | −0.357452 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.5472 | 1.25421 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.80971 | 0.288537 | 0.144268 | − | 0.989539i | \(-0.453917\pi\) | ||||
0.144268 | + | 0.989539i | \(0.453917\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.50365 | −0.190144 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.2524 | 0.811390 | 0.405695 | − | 0.914008i | \(-0.367030\pi\) | ||||
0.405695 | + | 0.914008i | \(0.367030\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.5351 | 1.36876 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.24698 | −0.0943643 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.84846 | 0.329025 | 0.164512 | − | 0.986375i | \(-0.447395\pi\) | ||||
0.164512 | + | 0.986375i | \(0.447395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.8568 | −1.24947 | −0.624735 | − | 0.780837i | \(-0.714793\pi\) | ||||
−0.624735 | + | 0.780837i | \(0.714793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.58748 | 0.275196 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.7077 | −0.529947 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.97823 | 0.373769 | 0.186884 | − | 0.982382i | \(-0.440161\pi\) | ||||
0.186884 | + | 0.982382i | \(0.440161\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8672 | 0.451627 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.18598 | 0.215151 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.68127 | −0.111047 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.8538 | −0.984553 | −0.492277 | − | 0.870439i | \(-0.663835\pi\) | ||||
−0.492277 | + | 0.870439i | \(0.663835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.5676 | 1.38313 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.24160 | 0.380149 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.9866 | 0.492230 | 0.246115 | − | 0.969241i | \(-0.420846\pi\) | ||||
0.246115 | + | 0.969241i | \(0.420846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.87800 | −0.281971 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.56465 | 0.0640367 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.1142 | −1.18958 | −0.594788 | − | 0.803883i | \(-0.702764\pi\) | ||||
−0.594788 | + | 0.803883i | \(0.702764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1366 | 1.51483 | 0.757417 | − | 0.652932i | \(-0.226461\pi\) | ||||
0.757417 | + | 0.652932i | \(0.226461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.52111 | 0.0619442 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 44.9614 | 1.82794 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.2325 | 0.577680 | 0.288840 | − | 0.957377i | \(-0.406731\pi\) | ||||
0.288840 | + | 0.957377i | \(0.406731\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.85086 | 0.358655 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.3139 | 1.22437 | 0.612184 | − | 0.790715i | \(-0.290291\pi\) | ||||
0.612184 | + | 0.790715i | \(0.290291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.2935 | 0.939285 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.9638 | −1.00500 | −0.502501 | − | 0.864576i | \(-0.667587\pi\) | ||||
−0.502501 | + | 0.864576i | \(0.667587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.6122 | −1.43138 | −0.715688 | − | 0.698420i | \(-0.753887\pi\) | ||||
−0.715688 | + | 0.698420i | \(0.753887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.02715 | −0.0813466 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.6015 | 0.905509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0465 | −0.681861 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.7778 | −0.749912 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.02608 | 0.320021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.8829 | −0.950763 | −0.475382 | − | 0.879780i | \(-0.657690\pi\) | ||||
−0.475382 | + | 0.879780i | \(0.657690\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.2446 | −0.923889 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.3642 | −1.83991 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.37867 | −0.0940986 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.6577 | −0.973920 | −0.486960 | − | 0.873424i | \(-0.661894\pi\) | ||||
−0.486960 | + | 0.873424i | \(0.661894\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.8165 | −1.88570 | −0.942850 | − | 0.333218i | \(-0.891866\pi\) | ||||
−0.942850 | + | 0.333218i | \(0.891866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.67456 | 0.302186 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.38942 | 0.211880 | 0.105940 | − | 0.994373i | \(-0.466215\pi\) | ||||
0.105940 | + | 0.994373i | \(0.466215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.2814 | −0.913876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.8388 | −0.777543 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.03790 | −0.197148 | −0.0985741 | − | 0.995130i | \(-0.531428\pi\) | ||||
−0.0985741 | + | 0.995130i | \(0.531428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.0526 | −0.392789 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.41119 | 0.289138 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.9812 | 1.71326 | 0.856632 | − | 0.515927i | \(-0.172553\pi\) | ||||
0.856632 | + | 0.515927i | \(0.172553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.2194 | −1.48656 | −0.743280 | − | 0.668980i | \(-0.766731\pi\) | ||||
−0.743280 | + | 0.668980i | \(0.766731\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28.6775 | −1.11207 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.98493 | 0.309178 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.7385 | −0.415176 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.1752 | −0.701647 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.66487 | −0.256912 | −0.128456 | − | 0.991715i | \(-0.541002\pi\) | ||||
−0.128456 | + | 0.991715i | \(0.541002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.26875 | 0.241284 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.80194 | 0.184553 | 0.0922767 | − | 0.995733i | \(-0.470586\pi\) | ||||
0.0922767 | + | 0.995733i | \(0.470586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.2422 | 1.39085 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.97584 | 0.267315 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.2591 | −0.430816 | −0.215408 | − | 0.976524i | \(-0.569108\pi\) | ||||
−0.215408 | + | 0.976524i | \(0.569108\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 77.2737 | 2.95247 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.8049 | −0.641148 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.7144 | 0.940179 | 0.470090 | − | 0.882619i | \(-0.344222\pi\) | ||||
0.470090 | + | 0.882619i | \(0.344222\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.0978 | 0.421572 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.29829 | −0.125111 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.32736 | 0.239666 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.69202 | 0.328762 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.8920 | 0.977927 | 0.488964 | − | 0.872304i | \(-0.337375\pi\) | ||||
0.488964 | + | 0.872304i | \(0.337375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.4644 | 1.26213 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.7627 | −0.480671 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.3545 | 0.840728 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0851621 | 0.00319833 | 0.00159916 | − | 0.999999i | \(-0.499491\pi\) | ||||
0.00159916 | + | 0.999999i | \(0.499491\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.74094 | 0.140296 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.8979 | −0.670280 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.9191 | 0.855931 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.0508 | −1.00883 | −0.504413 | − | 0.863463i | \(-0.668291\pi\) | ||||
−0.504413 | + | 0.863463i | \(0.668291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.6896 | −0.919490 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.9801 | 0.817451 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.6926 | −0.917061 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.1584 | 1.74901 | 0.874503 | − | 0.485019i | \(-0.161187\pi\) | ||||
0.874503 | + | 0.485019i | \(0.161187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.08469 | 0.0771050 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.68186 | −0.357608 | −0.178804 | − | 0.983885i | \(-0.557223\pi\) | ||||
−0.178804 | + | 0.983885i | \(0.557223\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.54958 | −0.241585 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.51275 | −0.276736 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.3139 | −1.33583 | −0.667915 | − | 0.744238i | \(-0.732813\pi\) | ||||
−0.667915 | + | 0.744238i | \(0.732813\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.7536 | 1.53179 | 0.765896 | − | 0.642965i | \(-0.222296\pi\) | ||||
0.765896 | + | 0.642965i | \(0.222296\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.4386 | 1.26173 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.30798 | −0.0844445 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.1836 | −0.810571 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.1927 | 0.809823 | 0.404911 | − | 0.914356i | \(-0.367302\pi\) | ||||
0.404911 | + | 0.914356i | \(0.367302\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.6437 | −0.970950 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 67.7036 | 2.46399 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.23729 | 0.335735 | 0.167868 | − | 0.985810i | \(-0.446312\pi\) | ||||
0.167868 | + | 0.985810i | \(0.446312\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.0121 | 0.363416 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.50173 | −0.271937 | −0.135969 | − | 0.990713i | \(-0.543415\pi\) | ||||
−0.135969 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −45.4892 | −1.64682 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.06100 | 0.110671 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.14005 | 0.185355 | 0.0926774 | − | 0.995696i | \(-0.470457\pi\) | ||||
0.0926774 | + | 0.995696i | \(0.470457\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.1444 | 0.833524 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.50173 | −0.305786 | −0.152893 | − | 0.988243i | \(-0.548859\pi\) | ||||
−0.152893 | + | 0.988243i | \(0.548859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.3473 | 1.98813 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.7778 | −0.709524 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.3817 | 0.945221 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7482 | 0.420385 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.93900 | −0.140768 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.0404 | 1.25065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.78554 | 0.277525 | 0.138762 | − | 0.990326i | \(-0.455688\pi\) | ||||
0.138762 | + | 0.990326i | \(0.455688\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.5284 | 0.659629 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.7778 | −0.774329 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.82238 | 0.0646332 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.3840 | 0.757462 | 0.378731 | − | 0.925507i | \(-0.376361\pi\) | ||||
0.378731 | + | 0.925507i | \(0.376361\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.46681 | −0.122647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0586 | −0.355403 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.6039 | −1.29172 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2905 | 0.538920 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.75840 | 0.343512 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.28621 | 0.0803788 | 0.0401894 | − | 0.999192i | \(-0.487204\pi\) | ||||
0.0401894 | + | 0.999192i | \(0.487204\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.8079 | −0.625320 | −0.312660 | − | 0.949865i | \(-0.601220\pi\) | ||||
−0.312660 | + | 0.949865i | \(0.601220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.8019 | 0.799699 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.0820 | 1.29893 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.69202 | 0.304095 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9054 | 0.485302 | 0.242651 | − | 0.970114i | \(-0.421983\pi\) | ||||
0.242651 | + | 0.970114i | \(0.421983\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.24831 | 0.252660 | 0.126330 | − | 0.991988i | \(-0.459680\pi\) | ||||
0.126330 | + | 0.991988i | \(0.459680\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.9614 | −1.07794 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.1191 | −1.88191 | −0.940953 | − | 0.338536i | \(-0.890068\pi\) | ||||
−0.940953 | + | 0.338536i | \(0.890068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.79178 | −0.201157 | −0.100578 | − | 0.994929i | \(-0.532069\pi\) | ||||
−0.100578 | + | 0.994929i | \(0.532069\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.9705 | −0.831526 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.77910 | −0.0616422 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.2241 | −0.942130 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.82908 | 0.305178 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.29350 | 0.182752 | 0.0913760 | − | 0.995816i | \(-0.470873\pi\) | ||||
0.0913760 | + | 0.995816i | \(0.470873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4843 | −0.464975 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.12498 | −0.142072 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.0954 | −1.03409 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.6558 | 0.537305 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.8428 | −0.611644 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.5961 | −0.465522 | −0.232761 | − | 0.972534i | \(-0.574776\pi\) | ||||
−0.232761 | + | 0.972534i | \(0.574776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.7627 | 0.436475 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.8323 | −0.814097 | −0.407048 | − | 0.913407i | \(-0.633442\pi\) | ||||
−0.407048 | + | 0.913407i | \(0.633442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.9861 | 0.920754 | 0.460377 | − | 0.887723i | \(-0.347714\pi\) | ||||
0.460377 | + | 0.887723i | \(0.347714\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.5918 | −0.531367 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.0291 | 0.920080 | 0.460040 | − | 0.887898i | \(-0.347835\pi\) | ||||
0.460040 | + | 0.887898i | \(0.347835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.6128 | −2.06090 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.1685 | −0.549112 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.4765 | −0.626772 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.1293 | −0.545894 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.57002 | −0.323526 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.8780 | 1.38035 | 0.690176 | − | 0.723642i | \(-0.257533\pi\) | ||||
0.690176 | + | 0.723642i | \(0.257533\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.5948 | 0.762103 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.4964 | −0.757921 | −0.378961 | − | 0.925413i | \(-0.623718\pi\) | ||||
−0.378961 | + | 0.925413i | \(0.623718\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.16315 | 0.140101 | 0.0700505 | − | 0.997543i | \(-0.477684\pi\) | ||||
0.0700505 | + | 0.997543i | \(0.477684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.8237 | 0.531908 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.3002 | 0.883075 | 0.441537 | − | 0.897243i | \(-0.354433\pi\) | ||||
0.441537 | + | 0.897243i | \(0.354433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.0344 | 1.04086 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.93900 | −0.165463 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.4547 | −0.483709 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 66.7023 | 2.22961 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.7778 | −1.15990 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.495024 | 0.0164916 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.13706 | −0.170951 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.8468 | −1.12511 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 57.9114 | 1.92292 | 0.961458 | − | 0.274952i | \(-0.0886620\pi\) | ||||
0.961458 | + | 0.274952i | \(0.0886620\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.94869 | −0.329977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.286799 | 0.00950208 | 0.00475104 | − | 0.999989i | \(-0.498488\pi\) | ||||
0.00475104 | + | 0.999989i | \(0.498488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3991 | 0.377255 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.3532 | 0.408383 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.72886 | 0.222206 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.1239 | 1.02668 | 0.513342 | − | 0.858184i | \(-0.328407\pi\) | ||||
0.513342 | + | 0.858184i | \(0.328407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.55496 | 0.215993 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.1771 | 1.81421 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.9879 | 0.360891 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.62671 | 0.250224 | 0.125112 | − | 0.992143i | \(-0.460071\pi\) | ||||
0.125112 | + | 0.992143i | \(0.460071\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.41789 | −0.243112 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.0392 | 0.394147 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.1183 | −0.494421 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.67324 | −0.185337 | −0.0926683 | − | 0.995697i | \(-0.529540\pi\) | ||||
−0.0926683 | + | 0.995697i | \(0.529540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33.8950 | −1.10612 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.5394 | 1.35415 | 0.677073 | − | 0.735916i | \(-0.263248\pi\) | ||||
0.677073 | + | 0.735916i | \(0.263248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.0664 | −0.458064 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.54288 | −0.245370 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.3110 | 1.53740 | 0.768700 | − | 0.639610i | \(-0.220904\pi\) | ||||
0.768700 | + | 0.639610i | \(0.220904\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.49827 | −0.145866 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.3435 | −1.11249 | −0.556247 | − | 0.831017i | \(-0.687759\pi\) | ||||
−0.556247 | + | 0.831017i | \(0.687759\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.1135 | 0.715576 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.4547 | 0.628882 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51.7241 | −1.67026 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.9527 | 1.51460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.87263 | 0.318141 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.4802 | 1.17434 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.5096 | −1.55996 | −0.779982 | − | 0.625802i | \(-0.784772\pi\) | ||||
−0.779982 | + | 0.625802i | \(0.784772\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.46681 | 0.111370 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.4650 | −1.33068 | −0.665338 | − | 0.746542i | \(-0.731712\pi\) | ||||
−0.665338 | + | 0.746542i | \(0.731712\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.20775 | 0.0707772 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.09677 | −0.0670816 | −0.0335408 | − | 0.999437i | \(-0.510678\pi\) | ||||
−0.0335408 | + | 0.999437i | \(0.510678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.6795 | 1.58776 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.2446 | 0.646360 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.2336 | −0.804826 | −0.402413 | − | 0.915458i | \(-0.631828\pi\) | ||||
−0.402413 | + | 0.915458i | \(0.631828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.0231 | 0.988478 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.54288 | 0.271923 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.63448 | −0.147368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0489 | −0.382746 | −0.191373 | − | 0.981517i | \(-0.561294\pi\) | ||||
−0.191373 | + | 0.981517i | \(0.561294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.2131 | 0.355838 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.25236 | 0.166511 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.43403 | −0.0454160 | −0.0227080 | − | 0.999742i | \(-0.507229\pi\) | ||||
−0.0227080 | + | 0.999742i | \(0.507229\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.80194 | 0.278481 |
(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 | 8112.2.a.cp.1.2 | 3 | ||
4.3 | odd | 2 | 507.2.a.l.1.1 | yes | 3 | ||
12.11 | even | 2 | 1521.2.a.n.1.3 | 3 | |||
13.12 | even | 2 | 8112.2.a.cg.1.2 | 3 | |||
52.3 | odd | 6 | 507.2.e.i.22.3 | 6 | |||
52.7 | even | 12 | 507.2.j.i.361.3 | 12 | |||
52.11 | even | 12 | 507.2.j.i.316.4 | 12 | |||
52.15 | even | 12 | 507.2.j.i.316.3 | 12 | |||
52.19 | even | 12 | 507.2.j.i.361.4 | 12 | |||
52.23 | odd | 6 | 507.2.e.l.22.1 | 6 | |||
52.31 | even | 4 | 507.2.b.f.337.4 | 6 | |||
52.35 | odd | 6 | 507.2.e.i.484.3 | 6 | |||
52.43 | odd | 6 | 507.2.e.l.484.1 | 6 | |||
52.47 | even | 4 | 507.2.b.f.337.3 | 6 | |||
52.51 | odd | 2 | 507.2.a.i.1.3 | ✓ | 3 | ||
156.47 | odd | 4 | 1521.2.b.k.1351.4 | 6 | |||
156.83 | odd | 4 | 1521.2.b.k.1351.3 | 6 | |||
156.155 | even | 2 | 1521.2.a.s.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.3 | ✓ | 3 | 52.51 | odd | 2 | ||
507.2.a.l.1.1 | yes | 3 | 4.3 | odd | 2 | ||
507.2.b.f.337.3 | 6 | 52.47 | even | 4 | |||
507.2.b.f.337.4 | 6 | 52.31 | even | 4 | |||
507.2.e.i.22.3 | 6 | 52.3 | odd | 6 | |||
507.2.e.i.484.3 | 6 | 52.35 | odd | 6 | |||
507.2.e.l.22.1 | 6 | 52.23 | odd | 6 | |||
507.2.e.l.484.1 | 6 | 52.43 | odd | 6 | |||
507.2.j.i.316.3 | 12 | 52.15 | even | 12 | |||
507.2.j.i.316.4 | 12 | 52.11 | even | 12 | |||
507.2.j.i.361.3 | 12 | 52.7 | even | 12 | |||
507.2.j.i.361.4 | 12 | 52.19 | even | 12 | |||
1521.2.a.n.1.3 | 3 | 12.11 | even | 2 | |||
1521.2.a.s.1.1 | 3 | 156.155 | even | 2 | |||
1521.2.b.k.1351.3 | 6 | 156.83 | odd | 4 | |||
1521.2.b.k.1351.4 | 6 | 156.47 | odd | 4 | |||
8112.2.a.cg.1.2 | 3 | 13.12 | even | 2 | |||
8112.2.a.cp.1.2 | 3 | 1.1 | even | 1 | trivial |