Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(1,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5184.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.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: | \(41.3944484078\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13068.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 288) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.82405\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.37228 | −1.50813 | −0.754065 | − | 0.656800i | \(-0.771910\pi\) | ||||
−0.754065 | + | 0.656800i | \(0.771910\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.70285 | −1.77751 | −0.888756 | − | 0.458381i | \(-0.848430\pi\) | ||||
−0.888756 | + | 0.458381i | \(0.848430\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.875393 | −0.263941 | −0.131970 | − | 0.991254i | \(-0.542130\pi\) | ||||
−0.131970 | + | 0.991254i | \(0.542130\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37228 | 0.380602 | 0.190301 | − | 0.981726i | \(-0.439054\pi\) | ||||
0.190301 | + | 0.981726i | \(0.439054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.37228 | 0.575363 | 0.287681 | − | 0.957726i | \(-0.407116\pi\) | ||||
0.287681 | + | 0.957726i | \(0.407116\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.57825 | 1.27974 | 0.639869 | − | 0.768484i | \(-0.278989\pi\) | ||||
0.639869 | + | 0.768484i | \(0.278989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.70285 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.37228 | 1.27446 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.37228 | −0.997608 | −0.498804 | − | 0.866715i | \(-0.666227\pi\) | ||||
−0.498804 | + | 0.866715i | \(0.666227\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.45364 | 1.15911 | 0.579554 | − | 0.814934i | \(-0.303227\pi\) | ||||
0.579554 | + | 0.814934i | \(0.303227\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.8593 | 2.68072 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | −0.0780869 | − | 0.996947i | \(-0.524881\pi\) | ||||
−0.0780869 | + | 0.996947i | \(0.524881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.875393 | −0.133496 | −0.0667481 | − | 0.997770i | \(-0.521262\pi\) | ||||
−0.0667481 | + | 0.997770i | \(0.521262\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.70285 | 0.685982 | 0.342991 | − | 0.939339i | \(-0.388560\pi\) | ||||
0.342991 | + | 0.939339i | \(0.388560\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.1168 | 2.15955 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.95207 | 0.398057 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.53032 | −1.11055 | −0.555276 | − | 0.831666i | \(-0.687388\pi\) | ||||
−0.555276 | + | 0.831666i | \(0.687388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.11684 | 0.271034 | 0.135517 | − | 0.990775i | \(-0.456730\pi\) | ||||
0.135517 | + | 0.990775i | \(0.456730\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.62772 | −0.573998 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.53032 | −1.04214 | −0.521072 | − | 0.853513i | \(-0.674468\pi\) | ||||
−0.521072 | + | 0.853513i | \(0.674468\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.40571 | 1.11625 | 0.558126 | − | 0.829756i | \(-0.311520\pi\) | ||||
0.558126 | + | 0.829756i | \(0.311520\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3723 | 1.21398 | 0.606992 | − | 0.794708i | \(-0.292376\pi\) | ||||
0.606992 | + | 0.794708i | \(0.292376\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.11684 | 0.469158 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.45364 | −0.726091 | −0.363046 | − | 0.931771i | \(-0.618263\pi\) | ||||
−0.363046 | + | 0.931771i | \(0.618263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.95207 | 0.324032 | 0.162016 | − | 0.986788i | \(-0.448200\pi\) | ||||
0.162016 | + | 0.986788i | \(0.448200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7446 | −1.35092 | −0.675460 | − | 0.737396i | \(-0.736055\pi\) | ||||
−0.675460 | + | 0.737396i | \(0.736055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.45364 | −0.676525 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.8114 | −1.93001 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.00000 | 0.913812 | 0.456906 | − | 0.889515i | \(-0.348958\pi\) | ||||
0.456906 | + | 0.889515i | \(0.348958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.11684 | 0.210634 | 0.105317 | − | 0.994439i | \(-0.466414\pi\) | ||||
0.105317 | + | 0.994439i | \(0.466414\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.70285 | 0.463386 | 0.231693 | − | 0.972789i | \(-0.425574\pi\) | ||||
0.231693 | + | 0.972789i | \(0.425574\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.57825 | −0.539270 | −0.269635 | − | 0.962963i | \(-0.586903\pi\) | ||||
−0.269635 | + | 0.962963i | \(0.586903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.48913 | 0.525763 | 0.262881 | − | 0.964828i | \(-0.415327\pi\) | ||||
0.262881 | + | 0.964828i | \(0.415327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.3723 | −1.63425 | −0.817123 | − | 0.576463i | \(-0.804433\pi\) | ||||
−0.817123 | + | 0.576463i | \(0.804433\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8593 | −1.47889 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.1565 | −1.02271 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2337 | −0.930335 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.62772 | −0.413916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.1565 | 0.989979 | 0.494989 | − | 0.868899i | \(-0.335172\pi\) | ||||
0.494989 | + | 0.868899i | \(0.335172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.45364 | −0.563857 | −0.281929 | − | 0.959435i | \(-0.590974\pi\) | ||||
−0.281929 | + | 0.959435i | \(0.590974\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26.2337 | −2.27475 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4891 | −0.896146 | −0.448073 | − | 0.893997i | \(-0.647890\pi\) | ||||
−0.448073 | + | 0.893997i | \(0.647890\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.6868 | 1.66981 | 0.834907 | − | 0.550391i | \(-0.185521\pi\) | ||||
0.834907 | + | 0.550391i | \(0.185521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.20128 | −0.100456 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.1168 | 1.50452 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3723 | −1.42319 | −0.711596 | − | 0.702589i | \(-0.752027\pi\) | ||||
−0.711596 | + | 0.702589i | \(0.752027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.70285 | 0.382713 | 0.191356 | − | 0.981521i | \(-0.438711\pi\) | ||||
0.191356 | + | 0.981521i | \(0.438711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.7635 | −1.74809 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1168 | −1.12665 | −0.563323 | − | 0.826236i | \(-0.690477\pi\) | ||||
−0.563323 | + | 0.826236i | \(0.690477\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.1168 | −1.74305 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.8114 | 1.47342 | 0.736712 | − | 0.676207i | \(-0.236377\pi\) | ||||
0.736712 | + | 0.676207i | \(0.236377\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.45364 | 0.499398 | 0.249699 | − | 0.968324i | \(-0.419668\pi\) | ||||
0.249699 | + | 0.968324i | \(0.419668\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1168 | −0.855142 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.37228 | 0.408447 | 0.204223 | − | 0.978924i | \(-0.434533\pi\) | ||||
0.204223 | + | 0.978924i | \(0.434533\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −29.9679 | −2.26536 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8114 | −1.40603 | −0.703016 | − | 0.711174i | \(-0.748164\pi\) | ||||
−0.703016 | + | 0.711174i | \(0.748164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.2337 | −1.94993 | −0.974967 | − | 0.222348i | \(-0.928628\pi\) | ||||
−0.974967 | + | 0.222348i | \(0.928628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.4891 | 0.991740 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.07668 | −0.151862 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.6101 | −1.27422 | −0.637112 | − | 0.770771i | \(-0.719871\pi\) | ||||
−0.637112 | + | 0.770771i | \(0.719871\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | 0.0719816 | 0.0359908 | − | 0.999352i | \(-0.488541\pi\) | ||||
0.0359908 | + | 0.999352i | \(0.488541\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7446 | −0.765518 | −0.382759 | − | 0.923848i | \(-0.625026\pi\) | ||||
−0.382759 | + | 0.923848i | \(0.625026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0606 | −1.20940 | −0.604698 | − | 0.796455i | \(-0.706706\pi\) | ||||
−0.604698 | + | 0.796455i | \(0.706706\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.2651 | 1.77326 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.37228 | 0.235530 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.88316 | −0.337775 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8593 | 1.09180 | 0.545901 | − | 0.837849i | \(-0.316187\pi\) | ||||
0.545901 | + | 0.837849i | \(0.316187\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.95207 | 0.201329 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.3505 | −2.06033 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.25544 | 0.218984 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.70285 | −0.314926 | −0.157463 | − | 0.987525i | \(-0.550332\pi\) | ||||
−0.157463 | + | 0.987525i | \(0.550332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.4376 | 1.42286 | 0.711432 | − | 0.702755i | \(-0.248047\pi\) | ||||
0.711432 | + | 0.702755i | \(0.248047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.37228 | −0.0906829 | −0.0453415 | − | 0.998972i | \(-0.514438\pi\) | ||||
−0.0453415 | + | 0.998972i | \(0.514438\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.8614 | 1.69424 | 0.847119 | − | 0.531404i | \(-0.178335\pi\) | ||||
0.847119 | + | 0.531404i | \(0.178335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8593 | −1.03455 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.6101 | −1.13910 | −0.569552 | − | 0.821955i | \(-0.692883\pi\) | ||||
−0.569552 | + | 0.821955i | \(0.692883\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7446 | 0.756534 | 0.378267 | − | 0.925697i | \(-0.376520\pi\) | ||||
0.378267 | + | 0.925697i | \(0.376520\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −50.9783 | −3.25688 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.65492 | 0.487071 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.7347 | −1.05629 | −0.528144 | − | 0.849155i | \(-0.677112\pi\) | ||||
−0.528144 | + | 0.849155i | \(0.677112\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.11684 | −0.258824 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.4891 | −1.02856 | −0.514282 | − | 0.857621i | \(-0.671941\pi\) | ||||
−0.514282 | + | 0.857621i | \(0.671941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.8114 | 1.16888 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.6101 | 1.08589 | 0.542944 | − | 0.839769i | \(-0.317310\pi\) | ||||
0.542944 | + | 0.839769i | \(0.317310\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.4891 | 0.828630 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4891 | −0.822446 | −0.411223 | − | 0.911535i | \(-0.634898\pi\) | ||||
−0.411223 | + | 0.911535i | \(0.634898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.3130 | 1.35542 | 0.677709 | − | 0.735330i | \(-0.262973\pi\) | ||||
0.677709 | + | 0.735330i | \(0.262973\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.57825 | −0.336381 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.11684 | 0.247357 | 0.123679 | − | 0.992322i | \(-0.460531\pi\) | ||||
0.123679 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.86141 | 0.170697 | 0.0853486 | − | 0.996351i | \(-0.472800\pi\) | ||||
0.0853486 | + | 0.996351i | \(0.472800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.8593 | −0.942740 | −0.471370 | − | 0.881935i | \(-0.656240\pi\) | ||||
−0.471370 | + | 0.881935i | \(0.656240\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.70285 | 0.277601 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.3723 | −0.668958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6277 | −0.854560 | −0.427280 | − | 0.904119i | \(-0.640528\pi\) | ||||
−0.427280 | + | 0.904119i | \(0.640528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.7666 | 1.67486 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.45364 | 0.373224 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.11684 | 0.237291 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.13859 | −0.408755 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.8881 | −1.19215 | −0.596073 | − | 0.802930i | \(-0.703273\pi\) | ||||
−0.596073 | + | 0.802930i | \(0.703273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.0158 | 1.53193 | 0.765964 | − | 0.642883i | \(-0.222262\pi\) | ||||
0.765964 | + | 0.642883i | \(0.222262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.2337 | −0.861059 | −0.430529 | − | 0.902577i | \(-0.641673\pi\) | ||||
−0.430529 | + | 0.902577i | \(0.641673\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.62772 | 0.147587 | 0.0737937 | − | 0.997274i | \(-0.476489\pi\) | ||||
0.0737937 | + | 0.997274i | \(0.476489\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.70285 | 0.263309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.2332 | 0.736313 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.74456 | 0.485061 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.1168 | −1.21934 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.95521 | 0.547188 | 0.273594 | − | 0.961845i | \(-0.411788\pi\) | ||||
0.273594 | + | 0.961845i | \(0.411788\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.7666 | 1.57169 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.00000 | −0.490261 | −0.245131 | − | 0.969490i | \(-0.578831\pi\) | ||||
−0.245131 | + | 0.969490i | \(0.578831\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.64947 | −0.305936 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −38.1723 | −2.06111 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.53032 | 0.457931 | 0.228966 | − | 0.973434i | \(-0.426466\pi\) | ||||
0.228966 | + | 0.973434i | \(0.426466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.88316 | 0.314918 | 0.157459 | − | 0.987526i | \(-0.449670\pi\) | ||||
0.157459 | + | 0.987526i | \(0.449670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.2337 | −0.810807 | −0.405404 | − | 0.914138i | \(-0.632869\pi\) | ||||
−0.405404 | + | 0.914138i | \(0.632869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.7187 | −1.68345 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.4695 | −1.76645 | −0.883226 | − | 0.468948i | \(-0.844633\pi\) | ||||
−0.883226 | + | 0.468948i | \(0.844633\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1168 | 0.637729 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.9783 | −1.83085 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.1692 | 1.62702 | 0.813509 | − | 0.581552i | \(-0.197554\pi\) | ||||
0.813509 | + | 0.581552i | \(0.197554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.8114 | 0.976640 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.116844 | −0.00604995 | −0.00302498 | − | 0.999995i | \(-0.500963\pi\) | ||||
−0.00302498 | + | 0.999995i | \(0.500963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.37228 | −0.379692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.82746 | −0.196604 | −0.0983018 | − | 0.995157i | \(-0.531341\pi\) | ||||
−0.0983018 | + | 0.995157i | \(0.531341\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.7635 | 1.11206 | 0.556031 | − | 0.831161i | \(-0.312324\pi\) | ||||
0.556031 | + | 0.831161i | \(0.312324\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.8832 | −0.707551 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.3505 | 1.64024 | 0.820119 | − | 0.572194i | \(-0.193907\pi\) | ||||
0.820119 | + | 0.572194i | \(0.193907\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.1565 | 0.564208 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.7635 | 1.09504 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000 | 0.200754 | 0.100377 | − | 0.994949i | \(-0.467995\pi\) | ||||
0.100377 | + | 0.994949i | \(0.467995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.9783 | 0.897791 | 0.448895 | − | 0.893584i | \(-0.351818\pi\) | ||||
0.448895 | + | 0.893584i | \(0.351818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.85621 | 0.441159 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.50157 | 0.173566 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.7446 | −1.47077 | −0.735387 | − | 0.677647i | \(-0.763000\pi\) | ||||
−0.735387 | + | 0.677647i | \(0.763000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.1168 | 1.97402 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.95521 | −0.488682 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.8593 | −0.774780 | −0.387390 | − | 0.921916i | \(-0.626623\pi\) | ||||
−0.387390 | + | 0.921916i | \(0.626623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6277 | 0.810385 | 0.405193 | − | 0.914231i | \(-0.367204\pi\) | ||||
0.405193 | + | 0.914231i | \(0.367204\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.1168 | 0.733275 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.95521 | −0.481766 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1565 | −0.537389 | −0.268695 | − | 0.963225i | \(-0.586592\pi\) | ||||
−0.268695 | + | 0.963225i | \(0.586592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.883156 | −0.0424418 | −0.0212209 | − | 0.999775i | \(-0.506755\pi\) | ||||
−0.0212209 | + | 0.999775i | \(0.506755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.2337 | 1.25493 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.7635 | −1.03871 | −0.519357 | − | 0.854557i | \(-0.673829\pi\) | ||||
−0.519357 | + | 0.854557i | \(0.673829\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.4376 | −1.01853 | −0.509265 | − | 0.860609i | \(-0.670083\pi\) | ||||
−0.509265 | + | 0.860609i | \(0.670083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 42.9783 | 2.03736 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.883156 | 0.0416787 | 0.0208394 | − | 0.999783i | \(-0.493366\pi\) | ||||
0.0208394 | + | 0.999783i | \(0.493366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.875393 | 0.0412206 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.7635 | 1.02029 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.9783 | 0.934543 | 0.467272 | − | 0.884114i | \(-0.345237\pi\) | ||||
0.467272 | + | 0.884114i | \(0.345237\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8832 | −0.553454 | −0.276727 | − | 0.960949i | \(-0.589250\pi\) | ||||
−0.276727 | + | 0.960949i | \(0.589250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.549500 | −0.0255374 | −0.0127687 | − | 0.999918i | \(-0.504065\pi\) | ||||
−0.0127687 | + | 0.999918i | \(0.504065\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.73160 | −0.450325 | −0.225162 | − | 0.974321i | \(-0.572291\pi\) | ||||
−0.225162 | + | 0.974321i | \(0.572291\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.1168 | 1.85242 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.766312 | 0.0352351 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.5462 | 1.63097 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.70285 | −0.214879 | −0.107439 | − | 0.994212i | \(-0.534265\pi\) | ||||
−0.107439 | + | 0.994212i | \(0.534265\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.48913 | −0.250283 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.3505 | −1.37815 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1565 | 0.505549 | 0.252775 | − | 0.967525i | \(-0.418657\pi\) | ||||
0.252775 | + | 0.967525i | \(0.418657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.2490 | 1.81641 | 0.908206 | − | 0.418523i | \(-0.137452\pi\) | ||||
0.908206 | + | 0.418523i | \(0.137452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7446 | −0.573986 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −44.2337 | −1.98415 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.7827 | −0.616997 | −0.308499 | − | 0.951225i | \(-0.599827\pi\) | ||||
−0.308499 | + | 0.951225i | \(0.599827\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.7187 | −1.41427 | −0.707133 | − | 0.707080i | \(-0.750012\pi\) | ||||
−0.707133 | + | 0.707080i | \(0.750012\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.13859 | −0.317663 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.3505 | 1.69986 | 0.849929 | − | 0.526898i | \(-0.176645\pi\) | ||||
0.849929 | + | 0.526898i | \(0.176645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.7793 | −2.15787 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.8593 | −0.698846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.11684 | −0.181059 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.3505 | −1.54873 | −0.774367 | − | 0.632736i | \(-0.781932\pi\) | ||||
−0.774367 | + | 0.632736i | \(0.781932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9073 | 0.564396 | 0.282198 | − | 0.959356i | \(-0.408936\pi\) | ||||
0.282198 | + | 0.959356i | \(0.408936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.3098 | 0.666908 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.883156 | −0.0383981 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.37228 | −0.0594401 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.8114 | 0.813289 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2332 | −0.569993 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.74456 | 0.117998 | 0.0589990 | − | 0.998258i | \(-0.481209\pi\) | ||||
0.0589990 | + | 0.998258i | \(0.481209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.5109 | −0.792919 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.2811 | −0.439588 | −0.219794 | − | 0.975546i | \(-0.570539\pi\) | ||||
−0.219794 | + | 0.975546i | \(0.570539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.9679 | −1.27668 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.3505 | 1.29064 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.25544 | −0.307423 | −0.153711 | − | 0.988116i | \(-0.549123\pi\) | ||||
−0.153711 | + | 0.988116i | \(0.549123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.20128 | −0.0508089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.77953 | −0.285723 | −0.142862 | − | 0.989743i | \(-0.545630\pi\) | ||||
−0.142862 | + | 0.989743i | \(0.545630\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 58.5842 | 2.46466 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2554 | 1.18453 | 0.592265 | − | 0.805743i | \(-0.298234\pi\) | ||||
0.592265 | + | 0.805743i | \(0.298234\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.2490 | 1.68437 | 0.842184 | − | 0.539190i | \(-0.181269\pi\) | ||||
0.842184 | + | 0.539190i | \(0.181269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.9679 | 1.24975 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.883156 | 0.0367663 | 0.0183831 | − | 0.999831i | \(-0.494148\pi\) | ||||
0.0183831 | + | 0.999831i | \(0.494148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.8832 | −0.575970 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.50157 | 0.145020 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.4982 | 1.58899 | 0.794496 | − | 0.607269i | \(-0.207735\pi\) | ||||
0.794496 | + | 0.607269i | \(0.207735\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.0000 | 1.48335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.7228 | −1.63122 | −0.815610 | − | 0.578602i | \(-0.803599\pi\) | ||||
−0.815610 | + | 0.578602i | \(0.803599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37.6228 | 1.54239 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.1692 | −1.27354 | −0.636769 | − | 0.771054i | \(-0.719730\pi\) | ||||
−0.636769 | + | 0.771054i | \(0.719730\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.2337 | −1.51879 | −0.759397 | − | 0.650628i | \(-0.774506\pi\) | ||||
−0.759397 | + | 0.650628i | \(0.774506\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.5109 | 1.40307 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.549500 | 0.0223035 | 0.0111518 | − | 0.999938i | \(-0.496450\pi\) | ||||
0.0111518 | + | 0.999938i | \(0.496450\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.45364 | 0.261086 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.4674 | 1.31134 | 0.655672 | − | 0.755045i | \(-0.272385\pi\) | ||||
0.655672 | + | 0.755045i | \(0.272385\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.2554 | 1.05700 | 0.528502 | − | 0.848932i | \(-0.322754\pi\) | ||||
0.528502 | + | 0.848932i | \(0.322754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.2811 | −0.413232 | −0.206616 | − | 0.978422i | \(-0.566245\pi\) | ||||
−0.206616 | + | 0.978422i | \(0.566245\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 59.9358 | 2.40128 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.2554 | −0.650217 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.48913 | −0.378356 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −37.6228 | −1.49302 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.7446 | 0.821929 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.25544 | −0.0890844 | −0.0445422 | − | 0.999008i | \(-0.514183\pi\) | ||||
−0.0445422 | + | 0.999008i | \(0.514183\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.62618 | 0.103566 | 0.0517832 | − | 0.998658i | \(-0.483510\pi\) | ||||
0.0517832 | + | 0.998658i | \(0.483510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.15335 | −0.163285 | −0.0816426 | − | 0.996662i | \(-0.526017\pi\) | ||||
−0.0816426 | + | 0.996662i | \(0.526017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.46738 | 0.293120 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.8832 | 0.934620 | 0.467310 | − | 0.884093i | \(-0.345223\pi\) | ||||
0.467310 | + | 0.884093i | \(0.345223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.7635 | 0.850370 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.5749 | −1.58057 | −0.790287 | − | 0.612737i | \(-0.790069\pi\) | ||||
−0.790287 | + | 0.612737i | \(0.790069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.1168 | −0.549082 | −0.274541 | − | 0.961575i | \(-0.588526\pi\) | ||||
−0.274541 | + | 0.961575i | \(0.588526\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 88.4674 | 3.43062 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.2651 | −0.978267 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.85307 | −0.0715369 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.3505 | −1.09283 | −0.546416 | − | 0.837514i | \(-0.684008\pi\) | ||||
−0.546416 | + | 0.837514i | \(0.684008\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.3505 | −1.93513 | −0.967564 | − | 0.252626i | \(-0.918706\pi\) | ||||
−0.967564 | + | 0.252626i | \(0.918706\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.3257 | −1.62431 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.73160 | 0.372369 | 0.186185 | − | 0.982515i | \(-0.440388\pi\) | ||||
0.186185 | + | 0.982515i | \(0.440388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.3723 | 1.35151 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.48913 | −0.209119 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2619 | −0.694716 | −0.347358 | − | 0.937733i | \(-0.612921\pi\) | ||||
−0.347358 | + | 0.937733i | \(0.612921\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −66.3895 | −2.51830 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.37228 | −0.0898566 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2554 | 0.878346 | 0.439173 | − | 0.898403i | \(-0.355272\pi\) | ||||
0.439173 | + | 0.898403i | \(0.355272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.3130 | −0.841550 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.95521 | −0.374404 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.6060 | −1.03676 | −0.518382 | − | 0.855149i | \(-0.673465\pi\) | ||||
−0.518382 | + | 0.855149i | \(0.673465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.3505 | 1.13664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.05107 | 0.151501 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.3098 | −0.570961 | −0.285481 | − | 0.958385i | \(-0.592153\pi\) | ||||
−0.285481 | + | 0.958385i | \(0.592153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.1168 | −0.823674 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.2337 | −1.27141 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0127 | 0.742230 | 0.371115 | − | 0.928587i | \(-0.378976\pi\) | ||||
0.371115 | + | 0.928587i | \(0.378976\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.07668 | −0.0768087 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.1168 | −1.48175 | −0.740875 | − | 0.671643i | \(-0.765589\pi\) | ||||
−0.740875 | + | 0.671643i | \(0.765589\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.46738 | 0.275064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.32903 | −0.269603 | −0.134801 | − | 0.990873i | \(-0.543040\pi\) | ||||
−0.134801 | + | 0.990873i | \(0.543040\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.3288 | −1.80970 | −0.904850 | − | 0.425731i | \(-0.860017\pi\) | ||||
−0.904850 | + | 0.425731i | \(0.860017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 58.5842 | 2.14636 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.2337 | 0.958558 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.7635 | −0.794161 | −0.397081 | − | 0.917784i | \(-0.629977\pi\) | ||||
−0.397081 | + | 0.917784i | \(0.629977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.8593 | −0.577181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.4674 | −1.25274 | −0.626369 | − | 0.779527i | \(-0.715460\pi\) | ||||
−0.626369 | + | 0.779527i | \(0.715460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.6277 | −0.530254 | −0.265127 | − | 0.964213i | \(-0.585414\pi\) | ||||
−0.265127 | + | 0.964213i | \(0.585414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.8146 | −0.934550 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.7060 | −0.422679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.1168 | −1.15816 | −0.579082 | − | 0.815270i | \(-0.696589\pi\) | ||||
−0.579082 | + | 0.815270i | \(0.696589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.25544 | −0.260960 | −0.130480 | − | 0.991451i | \(-0.541652\pi\) | ||||
−0.130480 | + | 0.991451i | \(0.541652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.1244 | 1.47723 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.57825 | −0.199861 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.23369 | −0.294625 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.6060 | 1.69913 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.85621 | −0.315690 | −0.157845 | − | 0.987464i | \(-0.550455\pi\) | ||||
−0.157845 | + | 0.987464i | \(0.550455\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 81.6993 | 2.90489 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.90491 | 0.103156 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0951 | −0.605539 | −0.302770 | − | 0.953064i | \(-0.597911\pi\) | ||||
−0.302770 | + | 0.953064i | \(0.597911\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1565 | 0.394688 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.07982 | −0.320420 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 74.5842 | 2.62875 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.3723 | 0.645935 | 0.322968 | − | 0.946410i | \(-0.395320\pi\) | ||||
0.322968 | + | 0.946410i | \(0.395320\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.2042 | −1.76291 | −0.881454 | − | 0.472269i | \(-0.843435\pi\) | ||||
−0.881454 | + | 0.472269i | \(0.843435\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −63.4374 | −2.22212 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.88316 | −0.170840 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.62772 | 0.0917080 | 0.0458540 | − | 0.998948i | \(-0.485399\pi\) | ||||
0.0458540 | + | 0.998948i | \(0.485399\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.7635 | 0.758628 | 0.379314 | − | 0.925268i | \(-0.376160\pi\) | ||||
0.379314 | + | 0.925268i | \(0.376160\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.8114 | −0.654137 | −0.327069 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327069 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.2337 | −0.911134 | −0.455567 | − | 0.890202i | \(-0.650563\pi\) | ||||
−0.455567 | + | 0.890202i | \(0.650563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.8614 | 1.24252 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.7635 | −0.753157 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.45364 | −0.222804 | −0.111402 | − | 0.993775i | \(-0.535534\pi\) | ||||
−0.111402 | + | 0.993775i | \(0.535534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.138593 | −0.00477908 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.4891 | 1.28967 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.1275 | 1.65368 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.8114 | −0.644847 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.88316 | 0.132957 | 0.0664784 | − | 0.997788i | \(-0.478824\pi\) | ||||
0.0664784 | + | 0.997788i | \(0.478824\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.0951 | −0.652276 | −0.326138 | − | 0.945322i | \(-0.605747\pi\) | ||||
−0.326138 | + | 0.945322i | \(0.605747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.62618 | 0.0896040 | 0.0448020 | − | 0.998996i | \(-0.485734\pi\) | ||||
0.0448020 | + | 0.998996i | \(0.485734\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.6228 | 1.28070 | 0.640348 | − | 0.768085i | \(-0.278790\pi\) | ||||
0.640348 | + | 0.768085i | \(0.278790\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.1168 | −0.615991 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.64947 | 0.191645 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.7060 | −0.396643 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.7635 | 0.735740 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.3505 | −1.29501 | −0.647503 | − | 0.762063i | \(-0.724187\pi\) | ||||
−0.647503 | + | 0.762063i | \(0.724187\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.2337 | 1.01860 | 0.509299 | − | 0.860589i | \(-0.329905\pi\) | ||||
0.509299 | + | 0.860589i | \(0.329905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0446 | 1.07839 | 0.539193 | − | 0.842182i | \(-0.318729\pi\) | ||||
0.539193 | + | 0.842182i | \(0.318729\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.7635 | −0.730746 | −0.365373 | − | 0.930861i | \(-0.619059\pi\) | ||||
−0.365373 | + | 0.930861i | \(0.619059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.4674 | −1.75970 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.2337 | 0.877877 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.4374 | 2.12048 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.6708 | −1.15633 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.48913 | −0.316129 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 88.4674 | 2.94076 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.3449 | −1.14040 | −0.570201 | − | 0.821505i | \(-0.693135\pi\) | ||||
−0.570201 | + | 0.821505i | \(0.693135\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8625 | −0.757468 | −0.378734 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378734 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.58422 | −0.0855252 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.3505 | 1.00226 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4663 | 0.873044 | 0.436522 | − | 0.899694i | \(-0.356210\pi\) | ||||
0.436522 | + | 0.899694i | \(0.356210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.9073 | 0.424848 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.4891 | −0.838077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.6277 | −1.00486 | −0.502431 | − | 0.864617i | \(-0.667561\pi\) | ||||
−0.502431 | + | 0.864617i | \(0.667561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 84.3255 | 2.76366 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.00314 | 0.229027 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.2337 | −0.726343 | −0.363171 | − | 0.931722i | \(-0.618306\pi\) | ||||
−0.363171 | + | 0.931722i | \(0.618306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.0951 | 0.557284 | 0.278642 | − | 0.960395i | \(-0.410116\pi\) | ||||
0.278642 | + | 0.960395i | \(0.410116\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.70285 | −0.153146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.02875 | −0.163412 | −0.0817062 | − | 0.996656i | \(-0.526037\pi\) | ||||
−0.0817062 | + | 0.996656i | \(0.526037\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.2337 | 0.462045 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.60597 | −0.278775 | −0.139387 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139387 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 59.3863 | 1.92170 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.3288 | 1.59291 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6495 | 0.343531 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.37228 | −0.108558 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.3288 | −1.58631 | −0.793154 | − | 0.609021i | \(-0.791563\pi\) | ||||
−0.793154 | + | 0.609021i | \(0.791563\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.5333 | 1.84633 | 0.923165 | − | 0.384404i | \(-0.125593\pi\) | ||||
0.923165 | + | 0.384404i | \(0.125593\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −92.5842 | −2.96811 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.2337 | −1.44715 | −0.723577 | − | 0.690244i | \(-0.757503\pi\) | ||||
−0.723577 | + | 0.690244i | \(0.757503\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.1565 | 0.356563 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.3863 | 1.89413 | 0.947065 | − | 0.321042i | \(-0.104033\pi\) | ||||
0.947065 | + | 0.321042i | \(0.104033\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.2337 | 1.15450 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.11684 | −0.130908 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.00314 | −0.222462 | −0.111231 | − | 0.993795i | \(-0.535479\pi\) | ||||
−0.111231 | + | 0.993795i | \(0.535479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57.5333 | 1.82393 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3505 | 0.327805 | 0.163902 | − | 0.986477i | \(-0.447592\pi\) | ||||
0.163902 | + | 0.986477i | \(0.447592\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5184.2.a.cc.1.1 | 4 | ||
3.2 | odd | 2 | 5184.2.a.cf.1.3 | 4 | |||
4.3 | odd | 2 | inner | 5184.2.a.cc.1.2 | 4 | ||
8.3 | odd | 2 | 2592.2.a.x.1.4 | 4 | |||
8.5 | even | 2 | 2592.2.a.x.1.3 | 4 | |||
9.2 | odd | 6 | 576.2.i.n.193.2 | 8 | |||
9.4 | even | 3 | 1728.2.i.n.1153.4 | 8 | |||
9.5 | odd | 6 | 576.2.i.n.385.2 | 8 | |||
9.7 | even | 3 | 1728.2.i.n.577.4 | 8 | |||
12.11 | even | 2 | 5184.2.a.cf.1.4 | 4 | |||
24.5 | odd | 2 | 2592.2.a.u.1.1 | 4 | |||
24.11 | even | 2 | 2592.2.a.u.1.2 | 4 | |||
36.7 | odd | 6 | 1728.2.i.n.577.3 | 8 | |||
36.11 | even | 6 | 576.2.i.n.193.3 | 8 | |||
36.23 | even | 6 | 576.2.i.n.385.3 | 8 | |||
36.31 | odd | 6 | 1728.2.i.n.1153.3 | 8 | |||
72.5 | odd | 6 | 288.2.i.f.97.3 | yes | 8 | ||
72.11 | even | 6 | 288.2.i.f.193.2 | yes | 8 | ||
72.13 | even | 6 | 864.2.i.f.289.2 | 8 | |||
72.29 | odd | 6 | 288.2.i.f.193.3 | yes | 8 | ||
72.43 | odd | 6 | 864.2.i.f.577.1 | 8 | |||
72.59 | even | 6 | 288.2.i.f.97.2 | ✓ | 8 | ||
72.61 | even | 6 | 864.2.i.f.577.2 | 8 | |||
72.67 | odd | 6 | 864.2.i.f.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.f.97.2 | ✓ | 8 | 72.59 | even | 6 | ||
288.2.i.f.97.3 | yes | 8 | 72.5 | odd | 6 | ||
288.2.i.f.193.2 | yes | 8 | 72.11 | even | 6 | ||
288.2.i.f.193.3 | yes | 8 | 72.29 | odd | 6 | ||
576.2.i.n.193.2 | 8 | 9.2 | odd | 6 | |||
576.2.i.n.193.3 | 8 | 36.11 | even | 6 | |||
576.2.i.n.385.2 | 8 | 9.5 | odd | 6 | |||
576.2.i.n.385.3 | 8 | 36.23 | even | 6 | |||
864.2.i.f.289.1 | 8 | 72.67 | odd | 6 | |||
864.2.i.f.289.2 | 8 | 72.13 | even | 6 | |||
864.2.i.f.577.1 | 8 | 72.43 | odd | 6 | |||
864.2.i.f.577.2 | 8 | 72.61 | even | 6 | |||
1728.2.i.n.577.3 | 8 | 36.7 | odd | 6 | |||
1728.2.i.n.577.4 | 8 | 9.7 | even | 3 | |||
1728.2.i.n.1153.3 | 8 | 36.31 | odd | 6 | |||
1728.2.i.n.1153.4 | 8 | 9.4 | even | 3 | |||
2592.2.a.u.1.1 | 4 | 24.5 | odd | 2 | |||
2592.2.a.u.1.2 | 4 | 24.11 | even | 2 | |||
2592.2.a.x.1.3 | 4 | 8.5 | even | 2 | |||
2592.2.a.x.1.4 | 4 | 8.3 | odd | 2 | |||
5184.2.a.cc.1.1 | 4 | 1.1 | even | 1 | trivial | ||
5184.2.a.cc.1.2 | 4 | 4.3 | odd | 2 | inner | ||
5184.2.a.cf.1.3 | 4 | 3.2 | odd | 2 | |||
5184.2.a.cf.1.4 | 4 | 12.11 | even | 2 |