Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, 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("2736.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.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: | \(21.8470699930\) |
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 | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1 |
$q$-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 | ||||||||
\(5\) | −2.70156 | −1.20818 | −0.604088 | − | 0.796918i | \(-0.706462\pi\) | ||||
−0.604088 | + | 0.796918i | \(0.706462\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.70156 | 1.77702 | 0.888512 | − | 0.458854i | \(-0.151740\pi\) | ||||
0.888512 | + | 0.458854i | \(0.151740\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.70156 | 1.41757 | 0.708787 | − | 0.705422i | \(-0.249243\pi\) | ||||
0.708787 | + | 0.705422i | \(0.249243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.70156 | 0.655225 | 0.327613 | − | 0.944812i | \(-0.393756\pi\) | ||||
0.327613 | + | 0.944812i | \(0.393756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.29844 | 0.459688 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.40312 | −1.68885 | −0.844425 | − | 0.535673i | \(-0.820058\pi\) | ||||
−0.844425 | + | 0.535673i | \(0.820058\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.7016 | −2.14696 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.40312 | −0.559470 | −0.279735 | − | 0.960077i | \(-0.590247\pi\) | ||||
−0.279735 | + | 0.960077i | \(0.590247\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.40312 | 0.531479 | 0.265739 | − | 0.964045i | \(-0.414384\pi\) | ||||
0.265739 | + | 0.964045i | \(0.414384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1047 | −1.54095 | −0.770475 | − | 0.637470i | \(-0.779981\pi\) | ||||
−0.770475 | + | 0.637470i | \(0.779981\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.701562 | −0.102333 | −0.0511667 | − | 0.998690i | \(-0.516294\pi\) | ||||
−0.0511667 | + | 0.998690i | \(0.516294\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.1047 | 2.15781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.7016 | −1.71268 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.29844 | 0.166248 | 0.0831240 | − | 0.996539i | \(-0.473510\pi\) | ||||
0.0831240 | + | 0.996539i | \(0.473510\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.2094 | −2.01053 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.70156 | 0.784359 | 0.392179 | − | 0.919889i | \(-0.371721\pi\) | ||||
0.392179 | + | 0.919889i | \(0.371721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.1047 | 2.51906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8062 | 1.21580 | 0.607899 | − | 0.794014i | \(-0.292013\pi\) | ||||
0.607899 | + | 0.794014i | \(0.292013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8062 | −1.18614 | −0.593070 | − | 0.805151i | \(-0.702084\pi\) | ||||
−0.593070 | + | 0.805151i | \(0.702084\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.29844 | −0.791627 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8062 | 1.35746 | 0.678730 | − | 0.734388i | \(-0.262531\pi\) | ||||
0.678730 | + | 0.734388i | \(0.262531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28.2094 | 2.95715 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.70156 | 0.277174 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.8062 | −1.67228 | −0.836142 | − | 0.548513i | \(-0.815194\pi\) | ||||
−0.836142 | + | 0.548513i | \(0.815194\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.40312 | 0.926517 | 0.463259 | − | 0.886223i | \(-0.346680\pi\) | ||||
0.463259 | + | 0.886223i | \(0.346680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.40312 | 0.522340 | 0.261170 | − | 0.965293i | \(-0.415892\pi\) | ||||
0.261170 | + | 0.965293i | \(0.415892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.40312 | −0.325960 | −0.162980 | − | 0.986629i | \(-0.552111\pi\) | ||||
−0.162980 | + | 0.986629i | \(0.552111\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.8062 | −1.00769 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.7016 | 1.16435 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.1047 | 1.00952 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.29844 | 0.652792 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.40312 | −0.834392 | −0.417196 | − | 0.908816i | \(-0.636987\pi\) | ||||
−0.417196 | + | 0.908816i | \(0.636987\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7016 | −1.10974 | −0.554870 | − | 0.831937i | \(-0.687232\pi\) | ||||
−0.554870 | + | 0.831937i | \(0.687232\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.70156 | −0.407677 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7016 | 0.914296 | 0.457148 | − | 0.889391i | \(-0.348871\pi\) | ||||
0.457148 | + | 0.889391i | \(0.348871\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2984 | −1.29760 | −0.648798 | − | 0.760960i | \(-0.724728\pi\) | ||||
−0.648798 | + | 0.760960i | \(0.724728\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 28.2094 | 2.35899 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.40312 | 0.448705 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.1047 | −1.64704 | −0.823520 | − | 0.567287i | \(-0.807993\pi\) | ||||
−0.823520 | + | 0.567287i | \(0.807993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.80625 | −0.228369 | −0.114185 | − | 0.993460i | \(-0.536426\pi\) | ||||
−0.114185 | + | 0.993460i | \(0.536426\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.4031 | 2.04043 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.8062 | 1.48214 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8062 | 1.15971 | 0.579857 | − | 0.814718i | \(-0.303108\pi\) | ||||
0.579857 | + | 0.814718i | \(0.303108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.2094 | 1.56385 | 0.781924 | − | 0.623374i | \(-0.214238\pi\) | ||||
0.781924 | + | 0.623374i | \(0.214238\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.80625 | 0.669527 | 0.334763 | − | 0.942302i | \(-0.391344\pi\) | ||||
0.334763 | + | 0.942302i | \(0.391344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.8062 | 0.816876 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.40312 | −0.403848 | −0.201924 | − | 0.979401i | \(-0.564719\pi\) | ||||
−0.201924 | + | 0.979401i | \(0.564719\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.80625 | −0.357246 | −0.178623 | − | 0.983918i | \(-0.557164\pi\) | ||||
−0.178623 | + | 0.983918i | \(0.557164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.19375 | 0.675938 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.7016 | 0.928830 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.9109 | −1.51306 | −0.756531 | − | 0.653958i | \(-0.773107\pi\) | ||||
−0.756531 | + | 0.653958i | \(0.773107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4031 | 0.820815 | 0.410407 | − | 0.911902i | \(-0.365386\pi\) | ||||
0.410407 | + | 0.911902i | \(0.365386\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.29844 | −0.233820 | −0.116910 | − | 0.993143i | \(-0.537299\pi\) | ||||
−0.116910 | + | 0.993143i | \(0.537299\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.40312 | −0.659970 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.19375 | −0.642119 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.70156 | −0.325214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.80625 | −0.468561 | −0.234281 | − | 0.972169i | \(-0.575273\pi\) | ||||
−0.234281 | + | 0.972169i | \(0.575273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.2984 | 1.86174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44.2094 | −3.00113 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.2094 | 1.09036 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8062 | −1.79508 | −0.897540 | − | 0.440934i | \(-0.854647\pi\) | ||||
−0.897540 | + | 0.440934i | \(0.854647\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5969 | −0.703339 | −0.351670 | − | 0.936124i | \(-0.614386\pi\) | ||||
−0.351670 | + | 0.936124i | \(0.614386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.50781 | 0.363966 | 0.181983 | − | 0.983302i | \(-0.441748\pi\) | ||||
0.181983 | + | 0.983302i | \(0.441748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1047 | 0.793004 | 0.396502 | − | 0.918034i | \(-0.370224\pi\) | ||||
0.396502 | + | 0.918034i | \(0.370224\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.89531 | 0.123637 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.10469 | −0.136141 | −0.0680704 | − | 0.997681i | \(-0.521684\pi\) | ||||
−0.0680704 | + | 0.997681i | \(0.521684\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.4031 | −0.992202 | −0.496101 | − | 0.868265i | \(-0.665236\pi\) | ||||
−0.496101 | + | 0.868265i | \(0.665236\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −40.8062 | −2.60702 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.2984 | 1.21811 | 0.609053 | − | 0.793129i | \(-0.291550\pi\) | ||||
0.609053 | + | 0.793129i | \(0.291550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.8062 | 1.18234 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.4031 | 1.21033 | 0.605167 | − | 0.796099i | \(-0.293106\pi\) | ||||
0.605167 | + | 0.796099i | \(0.293106\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.701562 | −0.0432602 | −0.0216301 | − | 0.999766i | \(-0.506886\pi\) | ||||
−0.0216301 | + | 0.999766i | \(0.506886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.2094 | −0.995734 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8062 | −0.656433 | −0.328216 | − | 0.944603i | \(-0.606448\pi\) | ||||
−0.328216 | + | 0.944603i | \(0.606448\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.8062 | 0.651641 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.70156 | 0.162321 | 0.0811606 | − | 0.996701i | \(-0.474137\pi\) | ||||
0.0811606 | + | 0.996701i | \(0.474137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.806248 | −0.0480968 | −0.0240484 | − | 0.999711i | \(-0.507656\pi\) | ||||
−0.0240484 | + | 0.999711i | \(0.507656\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.70156 | 0.517254 | 0.258627 | − | 0.965977i | \(-0.416730\pi\) | ||||
0.258627 | + | 0.965977i | \(0.416730\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.0000 | 0.944450 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.70156 | −0.570680 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4031 | 1.36723 | 0.683613 | − | 0.729845i | \(-0.260408\pi\) | ||||
0.683613 | + | 0.729845i | \(0.260408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8062 | 0.629164 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.0000 | 1.38796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −47.5078 | −2.73830 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.50781 | −0.200857 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.19375 | 0.0681310 | 0.0340655 | − | 0.999420i | \(-0.489155\pi\) | ||||
0.0340655 | + | 0.999420i | \(0.489155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.5078 | −1.55982 | −0.779912 | − | 0.625889i | \(-0.784736\pi\) | ||||
−0.779912 | + | 0.625889i | \(0.784736\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.8062 | 1.62823 | 0.814113 | − | 0.580707i | \(-0.197224\pi\) | ||||
0.814113 | + | 0.580707i | \(0.197224\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.40312 | −0.191138 | −0.0955692 | − | 0.995423i | \(-0.530467\pi\) | ||||
−0.0955692 | + | 0.995423i | \(0.530467\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.40312 | −0.526474 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.70156 | −0.150319 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.7906 | 0.764966 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.29844 | −0.181849 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.8062 | 1.69326 | 0.846632 | − | 0.532178i | \(-0.178626\pi\) | ||||
0.846632 | + | 0.532178i | \(0.178626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −32.4187 | −1.77123 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8062 | 0.697601 | 0.348800 | − | 0.937197i | \(-0.386589\pi\) | ||||
0.348800 | + | 0.937197i | \(0.386589\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.2094 | −2.39407 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 38.1047 | 2.05746 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.7016 | −1.11132 | −0.555659 | − | 0.831410i | \(-0.687534\pi\) | ||||
−0.555659 | + | 0.831410i | \(0.687534\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.1047 | −1.29029 | −0.645147 | − | 0.764058i | \(-0.723204\pi\) | ||||
−0.645147 | + | 0.764058i | \(0.723204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.19375 | −0.382885 | −0.191442 | − | 0.981504i | \(-0.561317\pi\) | ||||
−0.191442 | + | 0.981504i | \(0.561317\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.49219 | −0.237089 | −0.118544 | − | 0.992949i | \(-0.537823\pi\) | ||||
−0.118544 | + | 0.992949i | \(0.537823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.1047 | −0.947643 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.2094 | 1.46456 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.40312 | −0.176207 | −0.0881035 | − | 0.996111i | \(-0.528081\pi\) | ||||
−0.0881035 | + | 0.996111i | \(0.528081\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4031 | 1.09940 | 0.549702 | − | 0.835361i | \(-0.314741\pi\) | ||||
0.549702 | + | 0.835361i | \(0.314741\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.2094 | 1.03265 | 0.516325 | − | 0.856393i | \(-0.327300\pi\) | ||||
0.516325 | + | 0.856393i | \(0.327300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −59.7172 | −3.04347 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.9109 | 1.77005 | 0.885027 | − | 0.465539i | \(-0.154140\pi\) | ||||
0.885027 | + | 0.465539i | \(0.154140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8062 | 0.546495 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.1938 | −1.46890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.5078 | 1.48095 | 0.740477 | − | 0.672081i | \(-0.234600\pi\) | ||||
0.740477 | + | 0.672081i | \(0.234600\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.2094 | −0.509832 | −0.254916 | − | 0.966963i | \(-0.582048\pi\) | ||||
−0.254916 | + | 0.966963i | \(0.582048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −56.4187 | −2.81042 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.8062 | −0.925395 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.1938 | 1.43306 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.8062 | 0.918745 | 0.459373 | − | 0.888244i | \(-0.348074\pi\) | ||||
0.459373 | + | 0.888244i | \(0.348074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.806248 | 0.0392941 | 0.0196471 | − | 0.999807i | \(-0.493746\pi\) | ||||
0.0196471 | + | 0.999807i | \(0.493746\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.20937 | 0.301199 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.10469 | 0.295426 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.5969 | −0.703107 | −0.351553 | − | 0.936168i | \(-0.614346\pi\) | ||||
−0.351553 | + | 0.936168i | \(0.614346\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.6125 | 1.13474 | 0.567372 | − | 0.823462i | \(-0.307960\pi\) | ||||
0.567372 | + | 0.823462i | \(0.307960\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.00000 | −0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.59688 | −0.314852 | −0.157426 | − | 0.987531i | \(-0.550320\pi\) | ||||
−0.157426 | + | 0.987531i | \(0.550320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.50781 | −0.356707 | −0.178353 | − | 0.983966i | \(-0.557077\pi\) | ||||
−0.178353 | + | 0.983966i | \(0.557077\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.5969 | −1.64005 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.596876 | 0.0281683 | 0.0140842 | − | 0.999901i | \(-0.495517\pi\) | ||||
0.0140842 | + | 0.999901i | \(0.495517\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000 | 0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −76.2094 | −3.57275 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.8953 | −0.743551 | −0.371776 | − | 0.928323i | \(-0.621251\pi\) | ||||
−0.371776 | + | 0.928323i | \(0.621251\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.1047 | −1.30897 | −0.654483 | − | 0.756077i | \(-0.727114\pi\) | ||||
−0.654483 | + | 0.756077i | \(0.727114\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.50781 | −0.348918 | −0.174459 | − | 0.984664i | \(-0.555818\pi\) | ||||
−0.174459 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.8953 | −0.828096 | −0.414048 | − | 0.910255i | \(-0.635886\pi\) | ||||
−0.414048 | + | 0.910255i | \(0.635886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 56.4187 | 2.60518 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −47.5078 | −2.18441 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.29844 | −0.105460 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.8062 | 1.04204 | 0.521022 | − | 0.853543i | \(-0.325551\pi\) | ||||
0.521022 | + | 0.853543i | \(0.325551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.4187 | −0.931015 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.2094 | 0.736030 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.19375 | −0.235351 | −0.117676 | − | 0.993052i | \(-0.537544\pi\) | ||||
−0.117676 | + | 0.993052i | \(0.537544\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00000 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.40312 | −0.243344 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.9109 | 0.936102 | 0.468051 | − | 0.883701i | \(-0.344956\pi\) | ||||
0.468051 | + | 0.883701i | \(0.344956\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.8062 | −1.73029 | −0.865143 | − | 0.501526i | \(-0.832772\pi\) | ||||
−0.865143 | + | 0.501526i | \(0.832772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.4031 | 2.02041 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.6125 | 1.93309 | 0.966545 | − | 0.256497i | \(-0.0825684\pi\) | ||||
0.966545 | + | 0.256497i | \(0.0825684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.5078 | 1.39382 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.4031 | −1.11940 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.29844 | −0.145065 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5969 | −0.551879 | −0.275940 | − | 0.961175i | \(-0.588989\pi\) | ||||
−0.275940 | + | 0.961175i | \(0.588989\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.2094 | 0.708786 | 0.354393 | − | 0.935097i | \(-0.384687\pi\) | ||||
0.354393 | + | 0.935097i | \(0.384687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.4031 | −1.10658 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.4187 | 0.884434 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.5969 | −0.631078 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 71.0156 | 3.05886 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.7172 | 1.10567 | 0.552834 | − | 0.833291i | \(-0.313546\pi\) | ||||
0.552834 | + | 0.833291i | \(0.313546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.19375 | 0.393817 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0156 | 0.813049 | 0.406525 | − | 0.913640i | \(-0.366741\pi\) | ||||
0.406525 | + | 0.913640i | \(0.366741\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.8062 | 2.16050 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.7016 | 1.63984 | 0.819919 | − | 0.572480i | \(-0.194018\pi\) | ||||
0.819919 | + | 0.572480i | \(0.194018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −60.6281 | −2.56430 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −48.6281 | −2.04580 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.806248 | −0.0337997 | −0.0168998 | − | 0.999857i | \(-0.505380\pi\) | ||||
−0.0168998 | + | 0.999857i | \(0.505380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.19375 | −0.0499569 | −0.0249785 | − | 0.999688i | \(-0.507952\pi\) | ||||
−0.0249785 | + | 0.999688i | \(0.507952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.19375 | 0.383406 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.49219 | 0.103751 | 0.0518756 | − | 0.998654i | \(-0.483480\pi\) | ||||
0.0518756 | + | 0.998654i | \(0.483480\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50.8062 | −2.10780 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.2094 | 1.16831 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.29844 | 0.136141 | 0.0680706 | − | 0.997681i | \(-0.478316\pi\) | ||||
0.0680706 | + | 0.997681i | \(0.478316\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.40312 | 0.387449 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.00000 | −0.0821302 | −0.0410651 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410651 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.3141 | −1.40674 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.8062 | −0.441531 | −0.220766 | − | 0.975327i | \(-0.570856\pi\) | ||||
−0.220766 | + | 0.975327i | \(0.570856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.2094 | 0.905939 | 0.452970 | − | 0.891526i | \(-0.350365\pi\) | ||||
0.452970 | + | 0.891526i | \(0.350365\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.0000 | −1.21967 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.2094 | −1.14498 | −0.572492 | − | 0.819911i | \(-0.694023\pi\) | ||||
−0.572492 | + | 0.819911i | \(0.694023\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.20937 | −0.170293 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4922 | −0.423776 | −0.211888 | − | 0.977294i | \(-0.567961\pi\) | ||||
−0.211888 | + | 0.977294i | \(0.567961\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.5078 | 1.18794 | 0.593970 | − | 0.804487i | \(-0.297560\pi\) | ||||
0.593970 | + | 0.804487i | \(0.297560\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0000 | −0.482321 | −0.241160 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 60.2094 | 2.41224 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2094 | −1.24837 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.19375 | −0.366579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.49219 | −0.338069 | −0.169034 | − | 0.985610i | \(-0.554065\pi\) | ||||
−0.169034 | + | 0.985610i | \(0.554065\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.4031 | 1.00809 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 90.6281 | 3.59082 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.5078 | 0.769313 | 0.384656 | − | 0.923060i | \(-0.374320\pi\) | ||||
0.384656 | + | 0.923060i | \(0.374320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.2984 | −1.23047 | −0.615234 | − | 0.788344i | \(-0.710939\pi\) | ||||
−0.615234 | + | 0.788344i | \(0.710939\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.8062 | −0.738210 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.1047 | −1.09982 | −0.549911 | − | 0.835223i | \(-0.685338\pi\) | ||||
−0.549911 | + | 0.835223i | \(0.685338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.3141 | 1.34076 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.5969 | 0.724431 | 0.362216 | − | 0.932094i | \(-0.382020\pi\) | ||||
0.362216 | + | 0.932094i | \(0.382020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.2094 | −1.48617 | −0.743086 | − | 0.669196i | \(-0.766639\pi\) | ||||
−0.743086 | + | 0.669196i | \(0.766639\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.7016 | 0.492545 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.10469 | 0.235669 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.40312 | −0.285369 | −0.142685 | − | 0.989768i | \(-0.545574\pi\) | ||||
−0.142685 | + | 0.989768i | \(0.545574\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.8062 | −0.492184 | −0.246092 | − | 0.969246i | \(-0.579147\pi\) | ||||
−0.246092 | + | 0.969246i | \(0.579147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.2094 | −1.08258 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −48.2094 | −1.84468 | −0.922340 | − | 0.386379i | \(-0.873726\pi\) | ||||
−0.922340 | + | 0.386379i | \(0.873726\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.9109 | −1.10463 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.0000 | 1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5078 | −0.437778 | −0.218889 | − | 0.975750i | \(-0.570243\pi\) | ||||
−0.218889 | + | 0.975750i | \(0.570243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.3297 | 1.56772 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.19375 | 0.348238 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.19375 | −0.120626 | −0.0603132 | − | 0.998180i | \(-0.519210\pi\) | ||||
−0.0603132 | + | 0.998180i | \(0.519210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.40312 | 0.128351 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −79.0156 | −2.97169 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.6125 | 1.03701 | 0.518505 | − | 0.855075i | \(-0.326489\pi\) | ||||
0.518505 | + | 0.855075i | \(0.326489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.6125 | −1.40860 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −76.2094 | −2.85007 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.7016 | 0.921213 | 0.460606 | − | 0.887604i | \(-0.347632\pi\) | ||||
0.460606 | + | 0.887604i | \(0.347632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.2094 | 1.64644 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.59688 | −0.170724 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.5078 | −0.575153 | −0.287576 | − | 0.957758i | \(-0.592850\pi\) | ||||
−0.287576 | + | 0.957758i | \(0.592850\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.2984 | −1.00967 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.8062 | −0.768496 | −0.384248 | − | 0.923230i | \(-0.625539\pi\) | ||||
−0.384248 | + | 0.923230i | \(0.625539\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 56.4187 | 2.07821 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.2984 | −0.857047 | −0.428523 | − | 0.903531i | \(-0.640966\pi\) | ||||
−0.428523 | + | 0.903531i | \(0.640966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.80625 | 0.102951 | 0.0514756 | − | 0.998674i | \(-0.483608\pi\) | ||||
0.0514756 | + | 0.998674i | \(0.483608\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.3141 | 1.98991 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.4031 | 0.928210 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.6125 | −1.08058 | −0.540288 | − | 0.841480i | \(-0.681685\pi\) | ||||
−0.540288 | + | 0.841480i | \(0.681685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.58125 | 0.275910 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.2984 | 0.919487 | 0.459744 | − | 0.888052i | \(-0.347941\pi\) | ||||
0.459744 | + | 0.888052i | \(0.347941\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.9109 | −0.975521 | −0.487760 | − | 0.872978i | \(-0.662186\pi\) | ||||
−0.487760 | + | 0.872978i | \(0.662186\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | −0.579239 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.0000 | −0.866590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.1203 | −1.26647 | −0.633235 | − | 0.773959i | \(-0.718273\pi\) | ||||
−0.633235 | + | 0.773959i | \(0.718273\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.0156 | −1.18749 | −0.593745 | − | 0.804654i | \(-0.702351\pi\) | ||||
−0.593745 | + | 0.804654i | \(0.702351\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.6125 | −0.776344 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.40312 | −0.121930 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.40312 | 0.192846 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.8062 | −1.38329 | −0.691647 | − | 0.722236i | \(-0.743114\pi\) | ||||
−0.691647 | + | 0.722236i | \(0.743114\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 84.6281 | 3.00903 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.79063 | 0.276653 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.5969 | 0.446204 | 0.223102 | − | 0.974795i | \(-0.428382\pi\) | ||||
0.223102 | + | 0.974795i | \(0.428382\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.89531 | −0.0670514 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.5078 | 1.11189 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −50.8062 | −1.79068 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.7172 | 1.74796 | 0.873982 | − | 0.485959i | \(-0.161530\pi\) | ||||
0.873982 | + | 0.485959i | \(0.161530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.59688 | 0.0911886 | 0.0455943 | − | 0.998960i | \(-0.485482\pi\) | ||||
0.0455943 | + | 0.998960i | \(0.485482\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.0000 | −1.40114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.1047 | 0.353518 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.4922 | −0.505781 | −0.252890 | − | 0.967495i | \(-0.581381\pi\) | ||||
−0.252890 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3141 | 0.359525 | 0.179763 | − | 0.983710i | \(-0.442467\pi\) | ||||
0.179763 | + | 0.983710i | \(0.442467\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.4187 | −1.54459 | −0.772296 | − | 0.635263i | \(-0.780892\pi\) | ||||
−0.772296 | + | 0.635263i | \(0.780892\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2094 | −0.771363 | −0.385682 | − | 0.922632i | \(-0.626034\pi\) | ||||
−0.385682 | + | 0.922632i | \(0.626034\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.8062 | 1.41385 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54.5969 | −1.88940 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.0156 | −1.07078 | −0.535389 | − | 0.844606i | \(-0.679835\pi\) | ||||
−0.535389 | + | 0.844606i | \(0.679835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −62.1359 | −2.13754 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 52.2094 | 1.79394 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.6125 | −0.466630 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.19375 | 0.109352 | 0.0546760 | − | 0.998504i | \(-0.482587\pi\) | ||||
0.0546760 | + | 0.998504i | \(0.482587\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.0156 | −1.81098 | −0.905490 | − | 0.424369i | \(-0.860496\pi\) | ||||
−0.905490 | + | 0.424369i | \(0.860496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.2984 | −1.06789 | −0.533944 | − | 0.845520i | \(-0.679291\pi\) | ||||
−0.533944 | + | 0.845520i | \(0.679291\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.8062 | −0.912495 | −0.456248 | − | 0.889853i | \(-0.650807\pi\) | ||||
−0.456248 | + | 0.889853i | \(0.650807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.7906 | −0.808906 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.8062 | 1.72348 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 72.0000 | 2.43963 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.3141 | 1.16003 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.8062 | −1.78314 | −0.891570 | − | 0.452883i | \(-0.850396\pi\) | ||||
−0.891570 | + | 0.452883i | \(0.850396\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.1047 | −1.08163 | −0.540817 | − | 0.841140i | \(-0.681885\pi\) | ||||
−0.540817 | + | 0.841140i | \(0.681885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.9109 | −1.51137 | −0.755687 | − | 0.654933i | \(-0.772697\pi\) | ||||
−0.755687 | + | 0.654933i | \(0.772697\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.6125 | −0.994290 | −0.497145 | − | 0.867667i | \(-0.665618\pi\) | ||||
−0.497145 | + | 0.867667i | \(0.665618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.2094 | −1.48273 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.701562 | 0.0234769 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.5969 | 0.487920 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.8062 | 0.627224 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.2094 | 0.540013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.9844 | 0.431615 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0156 | −0.897039 | −0.448519 | − | 0.893773i | \(-0.648049\pi\) | ||||
−0.448519 | + | 0.893773i | \(0.648049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.2094 | −0.934618 | −0.467309 | − | 0.884094i | \(-0.654776\pi\) | ||||
−0.467309 | + | 0.884094i | \(0.654776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.8062 | −1.68144 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −59.7172 | −1.97204 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.6125 | 0.976826 | 0.488413 | − | 0.872613i | \(-0.337576\pi\) | ||||
0.488413 | + | 0.872613i | \(0.337576\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.82187 | −0.257181 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.8062 | −1.20757 | −0.603787 | − | 0.797146i | \(-0.706342\pi\) | ||||
−0.603787 | + | 0.797146i | \(0.706342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.1047 | −0.495036 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −34.3141 | −1.12219 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.70156 | 0.218930 | 0.109465 | − | 0.993991i | \(-0.465086\pi\) | ||||
0.109465 | + | 0.993991i | \(0.465086\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0000 | −0.325991 | −0.162995 | − | 0.986627i | \(-0.552116\pi\) | ||||
−0.162995 | + | 0.986627i | \(0.552116\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.6125 | 0.443284 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.8062 | 0.611121 | 0.305560 | − | 0.952173i | \(-0.401156\pi\) | ||||
0.305560 | + | 0.952173i | \(0.401156\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.2094 | 1.30525 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.40312 | −0.239811 | −0.119905 | − | 0.992785i | \(-0.538259\pi\) | ||||
−0.119905 | + | 0.992785i | \(0.538259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 56.4922 | 1.82804 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.3141 | 1.62473 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.4187 | 1.85222 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.8062 | −0.991688 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.0000 | −1.28631 | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −71.9266 | −2.30586 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60.2094 | 1.92430 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.4187 | 1.03400 | 0.516999 | − | 0.855986i | \(-0.327049\pi\) | ||||
0.516999 | + | 0.855986i | \(0.327049\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.4344 | 1.89374 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.4187 | −1.28524 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0000 | 1.52477 | 0.762385 | − | 0.647124i | \(-0.224028\pi\) | ||||
0.762385 | + | 0.647124i | \(0.224028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.91093 | 0.282496 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.8953 | 0.503410 | 0.251705 | − | 0.967804i | \(-0.419009\pi\) | ||||
0.251705 | + | 0.967804i | \(0.419009\pi\) | |||||||
\(998\) | 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 | 2736.2.a.bb.1.1 | 2 | ||
3.2 | odd | 2 | 912.2.a.o.1.2 | 2 | |||
4.3 | odd | 2 | 1368.2.a.l.1.1 | 2 | |||
12.11 | even | 2 | 456.2.a.e.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 3648.2.a.bn.1.1 | 2 | |||
24.11 | even | 2 | 3648.2.a.bs.1.1 | 2 | |||
228.227 | odd | 2 | 8664.2.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.a.e.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
912.2.a.o.1.2 | 2 | 3.2 | odd | 2 | |||
1368.2.a.l.1.1 | 2 | 4.3 | odd | 2 | |||
2736.2.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial | ||
3648.2.a.bn.1.1 | 2 | 24.5 | odd | 2 | |||
3648.2.a.bs.1.1 | 2 | 24.11 | even | 2 | |||
8664.2.a.v.1.2 | 2 | 228.227 | odd | 2 |