Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(1,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, 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("912.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 456) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.1 |
$q$-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 | ||||||||
\(5\) | −3.70156 | −1.65539 | −0.827694 | − | 0.561179i | \(-0.810348\pi\) | ||||
−0.827694 | + | 0.561179i | \(0.810348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.70156 | −0.643130 | −0.321565 | − | 0.946888i | \(-0.604209\pi\) | ||||
−0.321565 | + | 0.946888i | \(0.604209\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.70156 | 0.513040 | 0.256520 | − | 0.966539i | \(-0.417424\pi\) | ||||
0.256520 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.70156 | −0.955739 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.70156 | 0.897761 | 0.448880 | − | 0.893592i | \(-0.351823\pi\) | ||||
0.448880 | + | 0.893592i | \(0.351823\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.70156 | −0.371311 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.70156 | 1.74031 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.40312 | 0.611219 | 0.305610 | − | 0.952157i | \(-0.401140\pi\) | ||||
0.305610 | + | 0.952157i | \(0.401140\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.70156 | 0.296204 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.29844 | 1.06463 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.40312 | 1.54586 | 0.772932 | − | 0.634489i | \(-0.218789\pi\) | ||||
0.772932 | + | 0.634489i | \(0.218789\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | 0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.40312 | 1.46852 | 0.734261 | − | 0.678868i | \(-0.237529\pi\) | ||||
0.734261 | + | 0.678868i | \(0.237529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.10469 | 1.38845 | 0.694226 | − | 0.719757i | \(-0.255747\pi\) | ||||
0.694226 | + | 0.719757i | \(0.255747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.70156 | −0.551796 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.70156 | −0.831658 | −0.415829 | − | 0.909443i | \(-0.636509\pi\) | ||||
−0.415829 | + | 0.909443i | \(0.636509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.10469 | −0.586384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.70156 | 0.518322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.29844 | −0.849281 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.70156 | 0.986084 | 0.493042 | − | 0.870006i | \(-0.335885\pi\) | ||||
0.493042 | + | 0.870006i | \(0.335885\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.70156 | −0.214377 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.2094 | −2.75473 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.298438 | 0.0349295 | 0.0174648 | − | 0.999847i | \(-0.494441\pi\) | ||||
0.0174648 | + | 0.999847i | \(0.494441\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.70156 | 1.00477 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.89531 | −0.329952 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.8062 | −1.66583 | −0.832917 | − | 0.553399i | \(-0.813331\pi\) | ||||
−0.832917 | + | 0.553399i | \(0.813331\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8062 | −1.62520 | −0.812598 | − | 0.582824i | \(-0.801948\pi\) | ||||
−0.812598 | + | 0.582824i | \(0.801948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.7016 | −1.48614 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8062 | 1.35746 | 0.678730 | − | 0.734388i | \(-0.262531\pi\) | ||||
0.678730 | + | 0.734388i | \(0.262531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2094 | −1.07023 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.40312 | 0.352888 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.70156 | 0.379772 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.70156 | 0.171013 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.80625 | −0.876254 | −0.438127 | − | 0.898913i | \(-0.644358\pi\) | ||||
−0.438127 | + | 0.898913i | \(0.644358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.40312 | −0.335320 | −0.167660 | − | 0.985845i | \(-0.553621\pi\) | ||||
−0.167660 | + | 0.985845i | \(0.553621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.29844 | 0.614665 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.40312 | 0.715687 | 0.357844 | − | 0.933782i | \(-0.383512\pi\) | ||||
0.357844 | + | 0.933782i | \(0.383512\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.40312 | 0.900656 | 0.450328 | − | 0.892863i | \(-0.351307\pi\) | ||||
0.450328 | + | 0.892863i | \(0.351307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.40312 | 0.892505 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.8062 | 1.38069 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | 0.554700 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.29844 | −0.577377 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.10469 | −0.736790 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.40312 | 0.847851 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.7016 | −1.22550 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.40312 | 0.301978 | 0.150989 | − | 0.988535i | \(-0.451754\pi\) | ||||
0.150989 | + | 0.988535i | \(0.451754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.10469 | 0.801623 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.29844 | 0.550297 | 0.275149 | − | 0.961402i | \(-0.411273\pi\) | ||||
0.275149 | + | 0.961402i | \(0.411273\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.70156 | 0.147544 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.70156 | −0.318580 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.29844 | −0.367240 | −0.183620 | − | 0.982997i | \(-0.558782\pi\) | ||||
−0.183620 | + | 0.982997i | \(0.558782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.7016 | −1.84070 | −0.920351 | − | 0.391093i | \(-0.872097\pi\) | ||||
−0.920351 | + | 0.391093i | \(0.872097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.70156 | −0.480158 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2094 | 0.853751 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.40312 | −0.614796 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.10469 | −0.338549 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.895314 | 0.0733470 | 0.0366735 | − | 0.999327i | \(-0.488324\pi\) | ||||
0.0366735 | + | 0.999327i | \(0.488324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.8062 | 1.85595 | 0.927973 | − | 0.372647i | \(-0.121550\pi\) | ||||
0.927973 | + | 0.372647i | \(0.121550\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.70156 | 0.299254 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.5969 | −1.01181 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.80625 | 0.536408 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.8062 | −0.846411 | −0.423205 | − | 0.906034i | \(-0.639095\pi\) | ||||
−0.423205 | + | 0.906034i | \(0.639095\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.29844 | −0.490333 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.2094 | 1.40908 | 0.704542 | − | 0.709663i | \(-0.251153\pi\) | ||||
0.704542 | + | 0.709663i | \(0.251153\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8062 | 1.27776 | 0.638878 | − | 0.769308i | \(-0.279399\pi\) | ||||
0.638878 | + | 0.769308i | \(0.279399\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.8062 | −1.11925 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.40312 | −0.553335 | −0.276668 | − | 0.960966i | \(-0.589230\pi\) | ||||
−0.276668 | + | 0.960966i | \(0.589230\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8062 | 1.54652 | 0.773258 | − | 0.634091i | \(-0.218626\pi\) | ||||
0.773258 | + | 0.634091i | \(0.218626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.70156 | 0.569316 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −34.8062 | −2.55901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.29844 | 0.460587 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.70156 | −0.123770 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.9109 | −1.73013 | −0.865067 | − | 0.501656i | \(-0.832724\pi\) | ||||
−0.865067 | + | 0.501656i | \(0.832724\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.40312 | −0.100999 | −0.0504995 | − | 0.998724i | \(-0.516081\pi\) | ||||
−0.0504995 | + | 0.998724i | \(0.516081\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22.2094 | −1.59045 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.0000 | 1.56744 | 0.783718 | − | 0.621117i | \(-0.213321\pi\) | ||||
0.783718 | + | 0.621117i | \(0.213321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.70156 | −0.687726 | −0.343863 | − | 0.939020i | \(-0.611735\pi\) | ||||
−0.343863 | + | 0.939020i | \(0.611735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | 0.846415 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.40312 | −0.238852 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −34.8062 | −2.43097 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.70156 | −0.117700 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.8062 | 1.29468 | 0.647338 | − | 0.762203i | \(-0.275882\pi\) | ||||
0.647338 | + | 0.762203i | \(0.275882\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.7016 | −2.29843 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.79063 | −0.393093 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.298438 | 0.0201666 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.2094 | 1.49396 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.19375 | −0.0799395 | −0.0399698 | − | 0.999201i | \(-0.512726\pi\) | ||||
−0.0399698 | + | 0.999201i | \(0.512726\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.70156 | 0.580104 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.4031 | 1.55332 | 0.776660 | − | 0.629920i | \(-0.216912\pi\) | ||||
0.776660 | + | 0.629920i | \(0.216912\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.5078 | −1.75169 | −0.875843 | − | 0.482597i | \(-0.839694\pi\) | ||||
−0.875843 | + | 0.482597i | \(0.839694\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.89531 | −0.190498 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.10469 | 0.465443 | 0.232722 | − | 0.972543i | \(-0.425237\pi\) | ||||
0.232722 | + | 0.972543i | \(0.425237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.1047 | 1.37672 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.8062 | −0.961769 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.1047 | −1.10641 | −0.553205 | − | 0.833045i | \(-0.686595\pi\) | ||||
−0.553205 | + | 0.833045i | \(0.686595\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.59688 | −0.167279 | −0.0836397 | − | 0.996496i | \(-0.526654\pi\) | ||||
−0.0836397 | + | 0.996496i | \(0.526654\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.1938 | 0.970693 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.8062 | −0.938308 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.7016 | −1.62227 | −0.811134 | − | 0.584860i | \(-0.801149\pi\) | ||||
−0.811134 | + | 0.584860i | \(0.801149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.80625 | −0.427905 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.7016 | −0.858025 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.59688 | −0.411502 | −0.205751 | − | 0.978604i | \(-0.565964\pi\) | ||||
−0.205751 | + | 0.978604i | \(0.565964\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.70156 | −0.351573 | −0.175787 | − | 0.984428i | \(-0.556247\pi\) | ||||
−0.175787 | + | 0.984428i | \(0.556247\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.2094 | 1.36431 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8062 | 0.783730 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8062 | 0.899416 | 0.449708 | − | 0.893176i | \(-0.351528\pi\) | ||||
0.449708 | + | 0.893176i | \(0.351528\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.2094 | −0.617899 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.8062 | 0.892850 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.70156 | −0.222405 | −0.111203 | − | 0.993798i | \(-0.535470\pi\) | ||||
−0.111203 | + | 0.993798i | \(0.535470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.40312 | 0.203740 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.8062 | −1.47982 | −0.739908 | − | 0.672708i | \(-0.765131\pi\) | ||||
−0.739908 | + | 0.672708i | \(0.765131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.29844 | 0.136628 | 0.0683140 | − | 0.997664i | \(-0.478238\pi\) | ||||
0.0683140 | + | 0.997664i | \(0.478238\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.70156 | 0.219262 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.0000 | −0.944450 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.29844 | −0.194026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.5969 | −0.619076 | −0.309538 | − | 0.950887i | \(-0.600174\pi\) | ||||
−0.309538 | + | 0.950887i | \(0.600174\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.8062 | −0.862053 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.70156 | 0.0987346 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.0000 | −1.38796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.4922 | −0.892955 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.80625 | −0.505906 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −28.5078 | −1.63235 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.8062 | 1.52991 | 0.764957 | − | 0.644082i | \(-0.222760\pi\) | ||||
0.764957 | + | 0.644082i | \(0.222760\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.40312 | −0.193597 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.50781 | −0.255614 | −0.127807 | − | 0.991799i | \(-0.540794\pi\) | ||||
−0.127807 | + | 0.991799i | \(0.540794\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.19375 | 0.180522 | 0.0902608 | − | 0.995918i | \(-0.471230\pi\) | ||||
0.0902608 | + | 0.995918i | \(0.471230\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.29844 | 0.354877 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.40312 | −0.528132 | −0.264066 | − | 0.964505i | \(-0.585064\pi\) | ||||
−0.264066 | + | 0.964505i | \(0.585064\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.40312 | 0.190538 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.40312 | 0.413202 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.70156 | −0.205960 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 52.2094 | 2.89605 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.40312 | 0.519994 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.70156 | 0.534864 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.19375 | 0.285474 | 0.142737 | − | 0.989761i | \(-0.454410\pi\) | ||||
0.142737 | + | 0.989761i | \(0.454410\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.40312 | 0.515288 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −44.4187 | −2.42686 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.8062 | −0.697601 | −0.348800 | − | 0.937197i | \(-0.613411\pi\) | ||||
−0.348800 | + | 0.937197i | \(0.613411\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0000 | −0.977626 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.79063 | 0.313580 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8953 | 1.02025 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.8062 | 0.797142 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2984 | 0.767580 | 0.383790 | − | 0.923420i | \(-0.374619\pi\) | ||||
0.383790 | + | 0.923420i | \(0.374619\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.89531 | −0.262040 | −0.131020 | − | 0.991380i | \(-0.541825\pi\) | ||||
−0.131020 | + | 0.991380i | \(0.541825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.8062 | 1.74610 | 0.873050 | − | 0.487630i | \(-0.162139\pi\) | ||||
0.873050 | + | 0.487630i | \(0.162139\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.29844 | −0.333349 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.5078 | 1.92681 | 0.963404 | − | 0.268053i | \(-0.0863801\pi\) | ||||
0.963404 | + | 0.268053i | \(0.0863801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.10469 | −0.425386 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.10469 | −0.0578219 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.40312 | 0.489507 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.2094 | 0.530044 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.40312 | 0.486875 | 0.243438 | − | 0.969917i | \(-0.421725\pi\) | ||||
0.243438 | + | 0.969917i | \(0.421725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.7016 | −0.707546 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.59688 | 0.441592 | 0.220796 | − | 0.975320i | \(-0.429135\pi\) | ||||
0.220796 | + | 0.975320i | \(0.429135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.40312 | 0.174347 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.2094 | 0.930455 | 0.465228 | − | 0.885191i | \(-0.345972\pi\) | ||||
0.465228 | + | 0.885191i | \(0.345972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.7172 | 0.546198 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.10469 | 0.462817 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.91093 | 0.502504 | 0.251252 | − | 0.967922i | \(-0.419158\pi\) | ||||
0.251252 | + | 0.967922i | \(0.419158\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8062 | −0.748784 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.29844 | 0.317714 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 54.8062 | 2.75760 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.50781 | −0.125863 | −0.0629317 | − | 0.998018i | \(-0.520045\pi\) | ||||
−0.0629317 | + | 0.998018i | \(0.520045\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.70156 | 0.0851847 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.2094 | −1.40871 | −0.704354 | − | 0.709848i | \(-0.748763\pi\) | ||||
−0.704354 | + | 0.709848i | \(0.748763\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.4187 | 1.01713 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.70156 | −0.183932 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.0000 | 0.793091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00000 | 0.0988936 | 0.0494468 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494468 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.29844 | −0.212026 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.80625 | −0.334914 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 54.8062 | 2.69033 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.7016 | −1.06273 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.80625 | 0.332507 | 0.166253 | − | 0.986083i | \(-0.446833\pi\) | ||||
0.166253 | + | 0.986083i | \(0.446833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.8062 | −1.20898 | −0.604491 | − | 0.796612i | \(-0.706624\pi\) | ||||
−0.604491 | + | 0.796612i | \(0.706624\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.70156 | −0.277219 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.2094 | 1.56238 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.1047 | −0.634180 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.2094 | 0.492913 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.4031 | 1.31996 | 0.659981 | − | 0.751282i | \(-0.270564\pi\) | ||||
0.659981 | + | 0.751282i | \(0.270564\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.6125 | −1.32697 | −0.663486 | − | 0.748189i | \(-0.730924\pi\) | ||||
−0.663486 | + | 0.748189i | \(0.730924\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.40312 | −0.354953 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | 0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4031 | −0.926061 | −0.463030 | − | 0.886342i | \(-0.653238\pi\) | ||||
−0.463030 | + | 0.886342i | \(0.653238\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.10469 | −0.195461 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.5078 | −1.16440 | −0.582201 | − | 0.813045i | \(-0.697808\pi\) | ||||
−0.582201 | + | 0.813045i | \(0.697808\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −47.4031 | −2.24712 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.895314 | 0.0423469 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.4031 | −0.632533 | −0.316266 | − | 0.948670i | \(-0.602429\pi\) | ||||
−0.316266 | + | 0.948670i | \(0.602429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000 | 0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.8062 | 1.07153 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 37.7906 | 1.77165 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.1047 | −1.64213 | −0.821064 | − | 0.570836i | \(-0.806619\pi\) | ||||
−0.821064 | + | 0.570836i | \(0.806619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.70156 | 0.172774 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.89531 | 0.414296 | 0.207148 | − | 0.978310i | \(-0.433582\pi\) | ||||
0.207148 | + | 0.978310i | \(0.433582\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.5078 | 1.13897 | 0.569487 | − | 0.822000i | \(-0.307142\pi\) | ||||
0.569487 | + | 0.822000i | \(0.307142\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.5969 | −0.584166 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.1047 | 1.71700 | 0.858500 | − | 0.512813i | \(-0.171397\pi\) | ||||
0.858500 | + | 0.512813i | \(0.171397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.4187 | −0.942850 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | −0.0921551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.4922 | 0.712332 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.70156 | −0.399255 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.80625 | 0.128221 | 0.0641104 | − | 0.997943i | \(-0.479579\pi\) | ||||
0.0641104 | + | 0.997943i | \(0.479579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.4187 | 2.57247 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.80625 | 0.309695 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.2094 | 1.00848 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.8062 | −1.39596 | −0.697982 | − | 0.716115i | \(-0.745919\pi\) | ||||
−0.697982 | + | 0.716115i | \(0.745919\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.8062 | −0.488675 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00000 | 0.361035 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.40312 | 0.333420 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.29844 | −0.283094 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.9109 | −1.07040 | −0.535200 | − | 0.844725i | \(-0.679764\pi\) | ||||
−0.535200 | + | 0.844725i | \(0.679764\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.2094 | 0.813535 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1938 | 0.588280 | 0.294140 | − | 0.955762i | \(-0.404967\pi\) | ||||
0.294140 | + | 0.955762i | \(0.404967\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.5969 | 1.45054 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.0000 | 1.02147 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.61250 | 0.337418 | 0.168709 | − | 0.985666i | \(-0.446040\pi\) | ||||
0.168709 | + | 0.985666i | \(0.446040\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.507811 | −0.0224642 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.5969 | 0.555085 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.70156 | −0.426674 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.8062 | 0.737712 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4031 | 1.11293 | 0.556466 | − | 0.830871i | \(-0.312157\pi\) | ||||
0.556466 | + | 0.830871i | \(0.312157\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2094 | −0.971148 | −0.485574 | − | 0.874196i | \(-0.661389\pi\) | ||||
−0.485574 | + | 0.874196i | \(0.661389\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.8062 | −0.646198 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.5969 | 0.548729 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 56.4187 | 2.44377 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.4031 | −1.18474 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.40312 | −0.319468 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.98438 | −0.300838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.7172 | −1.92254 | −0.961271 | − | 0.275605i | \(-0.911122\pi\) | ||||
−0.961271 | + | 0.275605i | \(0.911122\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.8062 | 0.892882 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −34.8062 | −1.49094 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.0156 | −1.92473 | −0.962364 | − | 0.271762i | \(-0.912394\pi\) | ||||
−0.962364 | + | 0.271762i | \(0.912394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.70156 | 0.328695 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.00000 | −0.0852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.1938 | 1.07135 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −34.8062 | −1.47744 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.2984 | −1.36853 | −0.684264 | − | 0.729234i | \(-0.739877\pi\) | ||||
−0.684264 | + | 0.729234i | \(0.739877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.6281 | 2.31052 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.29844 | 0.265920 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.00000 | 0.168580 | 0.0842900 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842900 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 66.6281 | 2.80307 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.70156 | −0.0714589 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.8062 | −1.03993 | −0.519966 | − | 0.854187i | \(-0.674055\pi\) | ||||
−0.519966 | + | 0.854187i | \(0.674055\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.8062 | −1.12181 | −0.560903 | − | 0.827881i | \(-0.689546\pi\) | ||||
−0.560903 | + | 0.827881i | \(0.689546\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.9109 | −0.998894 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.8062 | −1.45152 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.5078 | 1.43658 | 0.718289 | − | 0.695744i | \(-0.244925\pi\) | ||||
0.718289 | + | 0.695744i | \(0.244925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.40312 | −0.0583119 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.1938 | 1.04521 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.2094 | −0.422829 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.2094 | −0.918245 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.70156 | −0.400426 | −0.200213 | − | 0.979752i | \(-0.564163\pi\) | ||||
−0.200213 | + | 0.979752i | \(0.564163\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.40312 | −0.140223 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.0000 | 0.904959 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00000 | 0.0821302 | 0.0410651 | − | 0.999156i | \(-0.486925\pi\) | ||||
0.0410651 | + | 0.999156i | \(0.486925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.3141 | 0.955783 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.70156 | −0.397059 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.8062 | −0.604967 | −0.302483 | − | 0.953155i | \(-0.597816\pi\) | ||||
−0.302483 | + | 0.953155i | \(0.597816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2094 | −0.661194 | −0.330597 | − | 0.943772i | \(-0.607250\pi\) | ||||
−0.330597 | + | 0.943772i | \(0.607250\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.0000 | 1.21967 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2094 | 0.414386 | 0.207193 | − | 0.978300i | \(-0.433567\pi\) | ||||
0.207193 | + | 0.978300i | \(0.433567\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.40312 | −0.137902 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.2094 | −1.38396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.5078 | −1.71687 | −0.858437 | − | 0.512919i | \(-0.828564\pi\) | ||||
−0.858437 | + | 0.512919i | \(0.828564\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −34.8062 | −1.40352 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.50781 | 0.100961 | 0.0504803 | − | 0.998725i | \(-0.483925\pi\) | ||||
0.0504803 | + | 0.998725i | \(0.483925\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0000 | −0.482321 | −0.241160 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.7906 | −0.873023 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.20937 | 0.288375 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.70156 | −0.0679538 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.8062 | 1.38782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.5078 | −1.61259 | −0.806295 | − | 0.591513i | \(-0.798531\pi\) | ||||
−0.806295 | + | 0.591513i | \(0.798531\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.8062 | 0.747481 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.5969 | −0.499892 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.6281 | −0.975802 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.5078 | −0.493260 | −0.246630 | − | 0.969110i | \(-0.579323\pi\) | ||||
−0.246630 | + | 0.969110i | \(0.579323\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.7016 | −1.32700 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.7016 | 1.48220 | 0.741101 | − | 0.671394i | \(-0.234304\pi\) | ||||
0.741101 | + | 0.671394i | \(0.234304\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.80625 | 0.267169 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.79063 | −0.226953 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.89531 | 0.348101 | 0.174050 | − | 0.984737i | \(-0.444314\pi\) | ||||
0.174050 | + | 0.984737i | \(0.444314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.3141 | −0.910956 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.298438 | 0.0116432 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.4031 | −1.22329 | −0.611646 | − | 0.791132i | \(-0.709492\pi\) | ||||
−0.611646 | + | 0.791132i | \(0.709492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.209373 | 0.00814365 | 0.00407183 | − | 0.999992i | \(-0.498704\pi\) | ||||
0.00407183 | + | 0.999992i | \(0.498704\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.2094 | 0.862541 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.29844 | −0.244243 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.19375 | −0.0461531 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1047 | 0.505901 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.40312 | 0.208275 | 0.104138 | − | 0.994563i | \(-0.466792\pi\) | ||||
0.104138 | + | 0.994563i | \(0.466792\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.70156 | 0.334923 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.8062 | −0.492184 | −0.246092 | − | 0.969246i | \(-0.579147\pi\) | ||||
−0.246092 | + | 0.969246i | \(0.579147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.2094 | 0.391800 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.4031 | 0.896810 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.79063 | 0.374628 | 0.187314 | − | 0.982300i | \(-0.440022\pi\) | ||||
0.187314 | + | 0.982300i | \(0.440022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.9109 | 0.607926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.5078 | −1.01134 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.5078 | 0.780154 | 0.390077 | − | 0.920782i | \(-0.372448\pi\) | ||||
0.390077 | + | 0.920782i | \(0.372448\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.89531 | −0.109984 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 80.3297 | 3.04708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.8062 | 1.31838 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.10469 | 0.268724 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.8062 | 1.08800 | 0.543998 | − | 0.839086i | \(-0.316910\pi\) | ||||
0.543998 | + | 0.839086i | \(0.316910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.40312 | −0.354646 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.1047 | 0.794848 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.9844 | 0.563546 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.6125 | −0.886786 | −0.443393 | − | 0.896327i | \(-0.646225\pi\) | ||||
−0.443393 | + | 0.896327i | \(0.646225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.8062 | −0.555278 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.6125 | −0.509792 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.7906 | −1.41329 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.1047 | −0.638786 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2984 | −0.682417 | −0.341208 | − | 0.939988i | \(-0.610836\pi\) | ||||
−0.341208 | + | 0.939988i | \(0.610836\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.79063 | 0.215654 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.59688 | −0.0965788 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.4031 | 0.646336 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5078 | 0.612241 | 0.306120 | − | 0.951993i | \(-0.400969\pi\) | ||||
0.306120 | + | 0.951993i | \(0.400969\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.7016 | 1.24650 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.80625 | 0.177523 | 0.0887614 | − | 0.996053i | \(-0.471709\pi\) | ||||
0.0887614 | + | 0.996053i | \(0.471709\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.1938 | 0.560430 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.4187 | 0.752134 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.7016 | −1.09259 | −0.546295 | − | 0.837593i | \(-0.683962\pi\) | ||||
−0.546295 | + | 0.837593i | \(0.683962\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.8062 | 0.836680 | 0.418340 | − | 0.908290i | \(-0.362612\pi\) | ||||
0.418340 | + | 0.908290i | \(0.362612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.31406 | −0.121418 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.8062 | −0.541732 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.5969 | −0.460280 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6125 | 0.788651 | 0.394326 | − | 0.918971i | \(-0.370978\pi\) | ||||
0.394326 | + | 0.918971i | \(0.370978\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.7016 | −0.936617 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −84.4187 | −3.07231 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.7016 | 1.15221 | 0.576106 | − | 0.817375i | \(-0.304571\pi\) | ||||
0.576106 | + | 0.817375i | \(0.304571\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.80625 | −0.247051 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.9109 | −0.649271 | −0.324635 | − | 0.945839i | \(-0.605242\pi\) | ||||
−0.324635 | + | 0.945839i | \(0.605242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | −0.579239 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.7016 | −0.495381 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000 | 0.866590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.1203 | 1.73526 | 0.867631 | − | 0.497208i | \(-0.165641\pi\) | ||||
0.867631 | + | 0.497208i | \(0.165641\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.59688 | −0.237581 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.0156 | −1.11555 | −0.557777 | − | 0.829991i | \(-0.688346\pi\) | ||||
−0.557777 | + | 0.829991i | \(0.688346\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.6125 | 1.06371 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.0000 | −0.573997 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.40312 | −0.336902 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.40312 | 0.264229 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.1938 | −0.470306 | −0.235153 | − | 0.971958i | \(-0.575559\pi\) | ||||
−0.235153 | + | 0.971958i | \(0.575559\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.70156 | −0.202981 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.6281 | 1.08901 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.2094 | 1.64094 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.2094 | 0.787685 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.4031 | −0.899825 | −0.449912 | − | 0.893073i | \(-0.648545\pi\) | ||||
−0.449912 | + | 0.893073i | \(0.648545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.1047 | −0.746630 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.8062 | 0.452487 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.507811 | 0.0179202 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.1938 | −0.887963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0000 | 0.352017 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.7172 | 0.728377 | 0.364189 | − | 0.931325i | \(-0.381346\pi\) | ||||
0.364189 | + | 0.931325i | \(0.381346\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4031 | 0.540877 | 0.270438 | − | 0.962737i | \(-0.412831\pi\) | ||||
0.270438 | + | 0.962737i | \(0.412831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.8062 | 0.519278 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.0000 | 1.40114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.10469 | −0.318533 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.2094 | −0.356744 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.5078 | 1.62313 | 0.811567 | − | 0.584260i | \(-0.198615\pi\) | ||||
0.811567 | + | 0.584260i | \(0.198615\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.3141 | −1.64926 | −0.824632 | − | 0.565669i | \(-0.808618\pi\) | ||||
−0.824632 | + | 0.565669i | \(0.808618\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.8062 | 0.515487 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.4187 | −1.12731 | −0.563655 | − | 0.826010i | \(-0.690605\pi\) | ||||
−0.563655 | + | 0.826010i | \(0.690605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.2094 | 0.562975 | 0.281487 | − | 0.959565i | \(-0.409172\pi\) | ||||
0.281487 | + | 0.959565i | \(0.409172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.70156 | −0.128406 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.1938 | −0.526432 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −67.4031 | −2.33258 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.40312 | 0.117629 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.0156 | −1.13983 | −0.569913 | − | 0.821705i | \(-0.693023\pi\) | ||||
−0.569913 | + | 0.821705i | \(0.693023\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.8062 | −0.854373 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −85.1359 | −2.92876 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7906 | 0.473852 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.29844 | 0.0788822 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.6125 | −1.28934 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.8062 | 0.986307 | 0.493154 | − | 0.869942i | \(-0.335844\pi\) | ||||
0.493154 | + | 0.869942i | \(0.335844\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.70156 | 0.126591 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0156 | −0.376286 | −0.188143 | − | 0.982142i | \(-0.560247\pi\) | ||||
−0.188143 | + | 0.982142i | \(0.560247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.7016 | −1.28636 | −0.643180 | − | 0.765715i | \(-0.722385\pi\) | ||||
−0.643180 | + | 0.765715i | \(0.722385\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | −0.545279 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.19375 | 0.0406358 | 0.0203179 | − | 0.999794i | \(-0.493532\pi\) | ||||
0.0203179 | + | 0.999794i | \(0.493532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −62.2094 | −2.11518 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.29844 | −0.112021 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.1938 | −0.854639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 72.0000 | 2.43963 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.3141 | 0.788159 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.1938 | −0.918268 | −0.459134 | − | 0.888367i | \(-0.651840\pi\) | ||||
−0.459134 | + | 0.888367i | \(0.651840\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.5969 | −0.357424 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.8953 | 0.434454 | 0.217227 | − | 0.976121i | \(-0.430299\pi\) | ||||
0.217227 | + | 0.976121i | \(0.430299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.0890652 | −0.00299728 | −0.00149864 | − | 0.999999i | \(-0.500477\pi\) | ||||
−0.00149864 | + | 0.999999i | \(0.500477\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.8062 | −0.497707 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.6125 | −0.725677 | −0.362838 | − | 0.931852i | \(-0.618192\pi\) | ||||
−0.362838 | + | 0.931852i | \(0.618192\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.79063 | −0.194211 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.70156 | 0.0570045 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.70156 | 0.190796 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.4031 | 0.915985 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0000 | −0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.80625 | 0.227001 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.2094 | −0.739901 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.4922 | −0.515548 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −77.0156 | −2.56009 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0156 | 1.22908 | 0.614542 | − | 0.788884i | \(-0.289341\pi\) | ||||
0.614542 | + | 0.788884i | \(0.289341\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.80625 | −0.292085 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.2094 | −0.338252 | −0.169126 | − | 0.985594i | \(-0.554094\pi\) | ||||
−0.169126 | + | 0.985594i | \(0.554094\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.1938 | −0.833791 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.5078 | −0.942439 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.7172 | −0.353913 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.6125 | −0.712930 | −0.356465 | − | 0.934309i | \(-0.616018\pi\) | ||||
−0.356465 | + | 0.934309i | \(0.616018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.8062 | 0.883296 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 81.8219 | 2.69029 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.40312 | −0.111773 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1938 | 0.367255 | 0.183628 | − | 0.982996i | \(-0.441216\pi\) | ||||
0.183628 | + | 0.982996i | \(0.441216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.10469 | 0.134526 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.50781 | −0.147579 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.3141 | −0.762451 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.298438 | 0.00974954 | 0.00487477 | − | 0.999988i | \(-0.498448\pi\) | ||||
0.00487477 | + | 0.999988i | \(0.498448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.19375 | 0.104224 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0000 | 0.325991 | 0.162995 | − | 0.986627i | \(-0.447884\pi\) | ||||
0.162995 | + | 0.986627i | \(0.447884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.6125 | −1.22483 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.29844 | 0.204888 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.80625 | 0.221173 | 0.110587 | − | 0.993866i | \(-0.464727\pi\) | ||||
0.110587 | + | 0.993866i | \(0.464727\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.79063 | 0.0581262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.40312 | −0.304917 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.40312 | −0.175024 | −0.0875122 | − | 0.996163i | \(-0.527892\pi\) | ||||
−0.0875122 | + | 0.996163i | \(0.527892\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 88.5078 | 2.86405 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.40312 | 0.110007 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.31406 | 0.236183 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.4187 | −0.626411 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.40312 | 0.238562 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.19375 | 0.167193 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.0000 | −1.28631 | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.70156 | −0.118911 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.0000 | −0.641831 | −0.320915 | − | 0.947108i | \(-0.603990\pi\) | ||||
−0.320915 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.9266 | 1.18381 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 52.2094 | 1.67204 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7906 | 0.696431 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.40312 | 0.300219 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.4187 | 1.41674 | 0.708369 | − | 0.705842i | \(-0.249431\pi\) | ||||
0.708369 | + | 0.705842i | \(0.249431\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −81.4344 | −2.59471 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.70156 | 0.308804 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.4187 | −1.15805 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0000 | 1.52477 | 0.762385 | − | 0.647124i | \(-0.224028\pi\) | ||||
0.762385 | + | 0.647124i | \(0.224028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.19375 | 0.164819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.9109 | 1.13845 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.1047 | 1.11178 | 0.555888 | − | 0.831257i | \(-0.312378\pi\) | ||||
0.555888 | + | 0.831257i | \(0.312378\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.40312 | 0.297502 |
(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 | 912.2.a.o.1.1 | 2 | ||
3.2 | odd | 2 | 2736.2.a.bb.1.2 | 2 | |||
4.3 | odd | 2 | 456.2.a.e.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 3648.2.a.bs.1.2 | 2 | |||
8.5 | even | 2 | 3648.2.a.bn.1.2 | 2 | |||
12.11 | even | 2 | 1368.2.a.l.1.2 | 2 | |||
76.75 | even | 2 | 8664.2.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.a.e.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
912.2.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1368.2.a.l.1.2 | 2 | 12.11 | even | 2 | |||
2736.2.a.bb.1.2 | 2 | 3.2 | odd | 2 | |||
3648.2.a.bn.1.2 | 2 | 8.5 | even | 2 | |||
3648.2.a.bs.1.2 | 2 | 8.3 | odd | 2 | |||
8664.2.a.v.1.1 | 2 | 76.75 | even | 2 |