Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 29x^{7} - 7x^{6} + 266x^{5} + 69x^{4} - 901x^{3} - 199x^{2} + 875x + 391 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.529979\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.52998 | 0.684227 | 0.342114 | − | 0.939659i | \(-0.388857\pi\) | ||||
0.342114 | + | 0.939659i | \(0.388857\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.05249 | 0.397806 | 0.198903 | − | 0.980019i | \(-0.436262\pi\) | ||||
0.198903 | + | 0.980019i | \(0.436262\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.162063 | −0.0488637 | −0.0244318 | − | 0.999701i | \(-0.507778\pi\) | ||||
−0.0244318 | + | 0.999701i | \(0.507778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.63900 | 1.00928 | 0.504638 | − | 0.863331i | \(-0.331626\pi\) | ||||
0.504638 | + | 0.863331i | \(0.331626\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52998 | −0.395039 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.89726 | 1.18776 | 0.593880 | − | 0.804553i | \(-0.297595\pi\) | ||||
0.593880 | + | 0.804553i | \(0.297595\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.02632 | −0.235455 | −0.117727 | − | 0.993046i | \(-0.537561\pi\) | ||||
−0.117727 | + | 0.993046i | \(0.537561\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.05249 | −0.229673 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.59021 | 1.58267 | 0.791334 | − | 0.611384i | \(-0.209387\pi\) | ||||
0.791334 | + | 0.611384i | \(0.209387\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.65917 | −0.531833 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.59787 | 1.78228 | 0.891140 | − | 0.453729i | \(-0.149906\pi\) | ||||
0.891140 | + | 0.453729i | \(0.149906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.68185 | −0.481675 | −0.240837 | − | 0.970565i | \(-0.577422\pi\) | ||||
−0.240837 | + | 0.970565i | \(0.577422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.162063 | 0.0282115 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61029 | 0.272189 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.12252 | 0.677738 | 0.338869 | − | 0.940834i | \(-0.389956\pi\) | ||||
0.338869 | + | 0.940834i | \(0.389956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.63900 | −0.582706 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.08012 | −0.168687 | −0.0843433 | − | 0.996437i | \(-0.526879\pi\) | ||||
−0.0843433 | + | 0.996437i | \(0.526879\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.77829 | −0.423686 | −0.211843 | − | 0.977304i | \(-0.567946\pi\) | ||||
−0.211843 | + | 0.977304i | \(0.567946\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.52998 | 0.228076 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.50274 | 1.38612 | 0.693059 | − | 0.720881i | \(-0.256263\pi\) | ||||
0.693059 | + | 0.720881i | \(0.256263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.89226 | −0.841751 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.89726 | −0.685754 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.80545 | 0.660080 | 0.330040 | − | 0.943967i | \(-0.392938\pi\) | ||||
0.330040 | + | 0.943967i | \(0.392938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.247952 | −0.0334339 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.02632 | 0.135940 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.22708 | −1.07107 | −0.535537 | − | 0.844512i | \(-0.679891\pi\) | ||||
−0.535537 | + | 0.844512i | \(0.679891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.510754 | 0.0653953 | 0.0326976 | − | 0.999465i | \(-0.489590\pi\) | ||||
0.0326976 | + | 0.999465i | \(0.489590\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.05249 | 0.132602 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.56759 | 0.690575 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.317219 | 0.0387544 | 0.0193772 | − | 0.999812i | \(-0.493832\pi\) | ||||
0.0193772 | + | 0.999812i | \(0.493832\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.59021 | −0.913754 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.83623 | −0.692633 | −0.346316 | − | 0.938118i | \(-0.612568\pi\) | ||||
−0.346316 | + | 0.938118i | \(0.612568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2379 | 1.31529 | 0.657647 | − | 0.753326i | \(-0.271552\pi\) | ||||
0.657647 | + | 0.753326i | \(0.271552\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.65917 | 0.307054 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.170570 | −0.0194382 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.59029 | −0.628957 | −0.314478 | − | 0.949265i | \(-0.601830\pi\) | ||||
−0.314478 | + | 0.949265i | \(0.601830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.98299 | −0.546954 | −0.273477 | − | 0.961879i | \(-0.588174\pi\) | ||||
−0.273477 | + | 0.961879i | \(0.588174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.49271 | 0.812698 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.59787 | −1.02900 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.199333 | −0.0211292 | −0.0105646 | − | 0.999944i | \(-0.503363\pi\) | ||||
−0.0105646 | + | 0.999944i | \(0.503363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.83003 | 0.401496 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.68185 | 0.278095 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.57025 | −0.161104 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.9371 | −1.11049 | −0.555247 | − | 0.831686i | \(-0.687376\pi\) | ||||
−0.555247 | + | 0.831686i | \(0.687376\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.162063 | −0.0162879 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8811 | 1.18221 | 0.591107 | − | 0.806593i | \(-0.298691\pi\) | ||||
0.591107 | + | 0.806593i | \(0.298691\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.54707 | 0.152437 | 0.0762187 | − | 0.997091i | \(-0.475715\pi\) | ||||
0.0762187 | + | 0.997091i | \(0.475715\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.61029 | −0.157149 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.89728 | 0.280091 | 0.140045 | − | 0.990145i | \(-0.455275\pi\) | ||||
0.140045 | + | 0.990145i | \(0.455275\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.16825 | 0.782377 | 0.391188 | − | 0.920311i | \(-0.372064\pi\) | ||||
0.391188 | + | 0.920311i | \(0.372064\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.12252 | −0.391292 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.73714 | −0.633777 | −0.316889 | − | 0.948463i | \(-0.602638\pi\) | ||||
−0.316889 | + | 0.948463i | \(0.602638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.6129 | 1.08290 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.63900 | 0.336426 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.15434 | 0.472498 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9737 | −0.997612 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.08012 | 0.0973912 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7184 | −1.04812 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8812 | 1.40923 | 0.704616 | − | 0.709588i | \(-0.251119\pi\) | ||||
0.704616 | + | 0.709588i | \(0.251119\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.77829 | 0.244615 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.81474 | −0.857517 | −0.428759 | − | 0.903419i | \(-0.641049\pi\) | ||||
−0.428759 | + | 0.903419i | \(0.641049\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.08020 | −0.0936651 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.52998 | −0.131680 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.22904 | −0.190440 | −0.0952199 | − | 0.995456i | \(-0.530355\pi\) | ||||
−0.0952199 | + | 0.995456i | \(0.530355\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.71321 | 0.654226 | 0.327113 | − | 0.944985i | \(-0.393924\pi\) | ||||
0.327113 | + | 0.944985i | \(0.393924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.50274 | −0.800275 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.589745 | −0.0493170 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.6845 | 1.21948 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.89226 | 0.485985 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.1731 | −1.57072 | −0.785360 | − | 0.619039i | \(-0.787522\pi\) | ||||
−0.785360 | + | 0.619039i | \(0.787522\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.05210 | 0.655271 | 0.327635 | − | 0.944804i | \(-0.393748\pi\) | ||||
0.327635 | + | 0.944804i | \(0.393748\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.89726 | 0.395920 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.10318 | −0.329575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1858 | 0.812914 | 0.406457 | − | 0.913670i | \(-0.366764\pi\) | ||||
0.406457 | + | 0.913670i | \(0.366764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.80545 | −0.381097 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.98866 | 0.629594 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.432916 | −0.0339086 | −0.0169543 | − | 0.999856i | \(-0.505397\pi\) | ||||
−0.0169543 | + | 0.999856i | \(0.505397\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.247952 | 0.0193031 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.242320 | 0.0186400 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.02632 | −0.0784848 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.2653 | 1.31266 | 0.656329 | − | 0.754475i | \(-0.272108\pi\) | ||||
0.656329 | + | 0.754475i | \(0.272108\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.79876 | −0.211566 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.22708 | 0.618385 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.05820 | −0.527554 | −0.263777 | − | 0.964584i | \(-0.584968\pi\) | ||||
−0.263777 | + | 0.964584i | \(0.584968\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7420 | −1.09577 | −0.547883 | − | 0.836555i | \(-0.684566\pi\) | ||||
−0.547883 | + | 0.836555i | \(0.684566\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.510754 | −0.0377560 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.30737 | 0.463727 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.793663 | −0.0580384 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.05249 | −0.0765577 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.5477 | −1.63149 | −0.815747 | − | 0.578409i | \(-0.803674\pi\) | ||||
−0.815747 | + | 0.578409i | \(0.803674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.60996 | 0.259850 | 0.129925 | − | 0.991524i | \(-0.458526\pi\) | ||||
0.129925 | + | 0.991524i | \(0.458526\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.56759 | −0.398704 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.4286 | 0.885502 | 0.442751 | − | 0.896645i | \(-0.354003\pi\) | ||||
0.442751 | + | 0.896645i | \(0.354003\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.92918 | −0.491197 | −0.245598 | − | 0.969372i | \(-0.578984\pi\) | ||||
−0.245598 | + | 0.969372i | \(0.578984\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.317219 | −0.0223749 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.1017 | 0.709001 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.65256 | −0.115420 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.59021 | 0.527556 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.166328 | 0.0115052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.3772 | 1.40283 | 0.701414 | − | 0.712754i | \(-0.252553\pi\) | ||||
0.701414 | + | 0.712754i | \(0.252553\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.83623 | 0.399892 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.25073 | −0.289897 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.82264 | −0.191613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.2379 | −0.759385 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.8211 | 1.19878 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.2826 | 1.35823 | 0.679113 | − | 0.734033i | \(-0.262364\pi\) | ||||
0.679113 | + | 0.734033i | \(0.262364\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.65917 | −0.177278 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.39895 | −0.491085 | −0.245543 | − | 0.969386i | \(-0.578966\pi\) | ||||
−0.245543 | + | 0.969386i | \(0.578966\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7782 | −0.712247 | −0.356123 | − | 0.934439i | \(-0.615902\pi\) | ||||
−0.356123 | + | 0.934439i | \(0.615902\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.170570 | 0.0112227 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.03570 | −0.460924 | −0.230462 | − | 0.973081i | \(-0.574024\pi\) | ||||
−0.230462 | + | 0.973081i | \(0.574024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.5390 | 0.948420 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.59029 | 0.363128 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.21369 | −0.466615 | −0.233307 | − | 0.972403i | \(-0.574955\pi\) | ||||
−0.233307 | + | 0.972403i | \(0.574955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.07039 | −0.391028 | −0.195514 | − | 0.980701i | \(-0.562638\pi\) | ||||
−0.195514 | + | 0.980701i | \(0.562638\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.01502 | −0.575949 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.73479 | −0.237639 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.98299 | 0.315784 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.20193 | 0.0758652 | 0.0379326 | − | 0.999280i | \(-0.487923\pi\) | ||||
0.0379326 | + | 0.999280i | \(0.487923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.23009 | −0.0773350 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.49271 | −0.469212 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.5799 | −0.909471 | −0.454735 | − | 0.890627i | \(-0.650266\pi\) | ||||
−0.454735 | + | 0.890627i | \(0.650266\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.33893 | 0.269608 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.59787 | 0.594093 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.6235 | −1.02505 | −0.512524 | − | 0.858673i | \(-0.671289\pi\) | ||||
−0.512524 | + | 0.858673i | \(0.671289\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.35224 | 0.451644 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.199333 | 0.0121990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.32925 | −0.507843 | −0.253922 | − | 0.967225i | \(-0.581721\pi\) | ||||
−0.253922 | + | 0.967225i | \(0.581721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.8577 | 1.63149 | 0.815744 | − | 0.578414i | \(-0.196328\pi\) | ||||
0.815744 | + | 0.578414i | \(0.196328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.83003 | −0.231804 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.430951 | 0.0259873 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.42647 | 0.446213 | 0.223107 | − | 0.974794i | \(-0.428380\pi\) | ||||
0.223107 | + | 0.974794i | \(0.428380\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.68185 | −0.160558 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.07711 | 0.123910 | 0.0619551 | − | 0.998079i | \(-0.480266\pi\) | ||||
0.0619551 | + | 0.998079i | \(0.480266\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.8081 | 1.35580 | 0.677900 | − | 0.735154i | \(-0.262890\pi\) | ||||
0.677900 | + | 0.735154i | \(0.262890\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.57025 | 0.0930137 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.13682 | −0.0671044 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.98318 | 0.410775 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.9371 | 0.641144 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.3193 | −1.12864 | −0.564322 | − | 0.825555i | \(-0.690862\pi\) | ||||
−0.564322 | + | 0.825555i | \(0.690862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.5873 | −0.732858 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.162063 | 0.00940382 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.6208 | 1.59735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.92414 | −0.168544 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.8811 | −0.682552 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.781442 | 0.0447452 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.57084 | 0.546237 | 0.273118 | − | 0.961980i | \(-0.411945\pi\) | ||||
0.273118 | + | 0.961980i | \(0.411945\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.54707 | −0.0880097 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.69478 | 0.493036 | 0.246518 | − | 0.969138i | \(-0.420714\pi\) | ||||
0.246518 | + | 0.969138i | \(0.420714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.7334 | −1.39802 | −0.699009 | − | 0.715113i | \(-0.746375\pi\) | ||||
−0.699009 | + | 0.715113i | \(0.746375\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.61029 | 0.0907298 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.3559 | 1.70496 | 0.852479 | − | 0.522762i | \(-0.175098\pi\) | ||||
0.852479 | + | 0.522762i | \(0.175098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.55546 | −0.0870888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.89728 | −0.161710 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.02617 | −0.279664 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.67670 | −0.536767 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.16825 | −0.451705 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0016 | 0.551405 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.2944 | −1.66513 | −0.832566 | − | 0.553926i | \(-0.813129\pi\) | ||||
−0.832566 | + | 0.553926i | \(0.813129\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.12252 | 0.225913 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.485338 | 0.0265168 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.467044 | −0.0254415 | −0.0127208 | − | 0.999919i | \(-0.504049\pi\) | ||||
−0.0127208 | + | 0.999919i | \(0.504049\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.73714 | 0.365911 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.434628 | 0.0235364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.5690 | −0.732659 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.6129 | −0.625215 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.81839 | 0.151299 | 0.0756496 | − | 0.997134i | \(-0.475897\pi\) | ||||
0.0756496 | + | 0.997134i | \(0.475897\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 37.0275 | 1.98204 | 0.991018 | − | 0.133726i | \(-0.0426943\pi\) | ||||
0.991018 | + | 0.133726i | \(0.0426943\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.63900 | −0.194235 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.85955 | −0.258648 | −0.129324 | − | 0.991602i | \(-0.541281\pi\) | ||||
−0.129324 | + | 0.991602i | \(0.541281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.92930 | −0.473918 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.15434 | −0.272797 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.0868793 | 0.00458531 | 0.00229266 | − | 0.999997i | \(-0.499270\pi\) | ||||
0.00229266 | + | 0.999997i | \(0.499270\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9467 | −0.944561 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9737 | 0.575972 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.1937 | 0.899960 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3217 | 0.799787 | 0.399894 | − | 0.916562i | \(-0.369047\pi\) | ||||
0.399894 | + | 0.916562i | \(0.369047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.08012 | −0.0562288 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.05771 | 0.262583 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.349987 | 0.0181216 | 0.00906081 | − | 0.999959i | \(-0.497116\pi\) | ||||
0.00906081 | + | 0.999959i | \(0.497116\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.7184 | 0.605133 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.9267 | 1.79881 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6312 | 1.52206 | 0.761028 | − | 0.648720i | \(-0.224695\pi\) | ||||
0.761028 | + | 0.648720i | \(0.224695\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8812 | −0.813621 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.4092 | 1.45164 | 0.725821 | − | 0.687884i | \(-0.241460\pi\) | ||||
0.725821 | + | 0.687884i | \(0.241460\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.260968 | −0.0133002 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.77829 | −0.141229 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.4318 | 0.934530 | 0.467265 | − | 0.884117i | \(-0.345239\pi\) | ||||
0.467265 | + | 0.884117i | \(0.345239\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.1713 | 1.87983 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.81474 | 0.495088 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.55302 | −0.430349 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.947842 | 0.0475708 | 0.0237854 | − | 0.999717i | \(-0.492428\pi\) | ||||
0.0237854 | + | 0.999717i | \(0.492428\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.08020 | 0.0540776 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.29454 | 0.0646464 | 0.0323232 | − | 0.999477i | \(-0.489709\pi\) | ||||
0.0323232 | + | 0.999477i | \(0.489709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.75926 | −0.486143 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.52998 | 0.0760253 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.668106 | −0.0331168 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.1328 | −1.44053 | −0.720263 | − | 0.693701i | \(-0.755979\pi\) | ||||
−0.720263 | + | 0.693701i | \(0.755979\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.22904 | 0.109951 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.65896 | −0.426079 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.62386 | −0.374241 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.71321 | −0.377717 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.3595 | −0.750362 | −0.375181 | − | 0.926952i | \(-0.622419\pi\) | ||||
−0.375181 | + | 0.926952i | \(0.622419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.9588 | −1.11894 | −0.559472 | − | 0.828849i | \(-0.688996\pi\) | ||||
−0.559472 | + | 0.828849i | \(0.688996\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.50274 | 0.462039 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.0226 | −0.631690 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.537565 | 0.0260146 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.589745 | 0.0284732 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.4208 | 1.12814 | 0.564070 | − | 0.825727i | \(-0.309235\pi\) | ||||
0.564070 | + | 0.825727i | \(0.309235\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.2786 | −1.45510 | −0.727549 | − | 0.686056i | \(-0.759340\pi\) | ||||
−0.727549 | + | 0.686056i | \(0.759340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.6845 | −0.704070 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.79000 | −0.372646 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.4125 | 0.974236 | 0.487118 | − | 0.873336i | \(-0.338048\pi\) | ||||
0.487118 | + | 0.873336i | \(0.338048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.89226 | −0.280584 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.1725 | 1.43354 | 0.716770 | − | 0.697310i | \(-0.245620\pi\) | ||||
0.716770 | + | 0.697310i | \(0.245620\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.304975 | −0.0144572 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.1731 | 0.906856 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.7721 | −0.697137 | −0.348568 | − | 0.937283i | \(-0.613332\pi\) | ||||
−0.348568 | + | 0.937283i | \(0.613332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.175047 | 0.00824265 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.05210 | −0.378321 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.85986 | 0.274715 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.0643 | 1.54668 | 0.773342 | − | 0.633989i | \(-0.218583\pi\) | ||||
0.773342 | + | 0.633989i | \(0.218583\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.89726 | −0.228585 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.9924 | −0.977714 | −0.488857 | − | 0.872364i | \(-0.662586\pi\) | ||||
−0.488857 | + | 0.872364i | \(0.662586\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.8607 | 1.80601 | 0.903005 | − | 0.429631i | \(-0.141356\pi\) | ||||
0.903005 | + | 0.429631i | \(0.141356\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.10318 | 0.190280 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.7010 | −1.42067 | −0.710335 | − | 0.703863i | \(-0.751457\pi\) | ||||
−0.710335 | + | 0.703863i | \(0.751457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.333871 | 0.0154167 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.1858 | −0.469336 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.450257 | 0.0207028 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.72916 | 0.125222 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.80545 | 0.220027 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.10481 | 0.187554 | 0.0937768 | − | 0.995593i | \(-0.470106\pi\) | ||||
0.0937768 | + | 0.995593i | \(0.470106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.0019 | 0.684026 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.98866 | −0.363496 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.7335 | −0.759830 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0473 | −0.455289 | −0.227644 | − | 0.973744i | \(-0.573102\pi\) | ||||
−0.227644 | + | 0.973744i | \(0.573102\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.432916 | 0.0195771 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4195 | 0.741001 | 0.370500 | − | 0.928832i | \(-0.379186\pi\) | ||||
0.370500 | + | 0.928832i | \(0.379186\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 47.0033 | 2.11692 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.247952 | −0.0111446 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.14260 | −0.275533 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.1636 | −0.499753 | −0.249877 | − | 0.968278i | \(-0.580390\pi\) | ||||
−0.249877 | + | 0.968278i | \(0.580390\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.6818 | 1.01133 | 0.505666 | − | 0.862729i | \(-0.331247\pi\) | ||||
0.505666 | + | 0.862729i | \(0.331247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.1778 | 0.808903 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.242320 | −0.0107618 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.92089 | −0.129466 | −0.0647331 | − | 0.997903i | \(-0.520620\pi\) | ||||
−0.0647331 | + | 0.997903i | \(0.520620\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.8278 | 0.523231 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.02632 | 0.0453132 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.36698 | 0.104302 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.54004 | −0.0677308 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.2653 | −0.757864 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.6454 | 1.25498 | 0.627490 | − | 0.778625i | \(-0.284082\pi\) | ||||
0.627490 | + | 0.778625i | \(0.284082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.60009 | 0.244875 | 0.122437 | − | 0.992476i | \(-0.460929\pi\) | ||||
0.122437 | + | 0.992476i | \(0.460929\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.79876 | 0.122148 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.1337 | −0.572114 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.6113 | 1.50484 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.22708 | −0.357025 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.93056 | −0.170251 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.43278 | 0.191646 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.05820 | 0.304584 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.954914 | 0.0411310 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.7504 | −1.62302 | −0.811509 | − | 0.584341i | \(-0.801353\pi\) | ||||
−0.811509 | + | 0.584341i | \(0.801353\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.7420 | 0.632641 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.4973 | 0.535323 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.04129 | 0.343821 | 0.171910 | − | 0.985113i | \(-0.445006\pi\) | ||||
0.171910 | + | 0.985113i | \(0.445006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.510754 | 0.0217984 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.85051 | −0.419646 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.88375 | −0.250202 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.30737 | −0.267733 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.6075 | 0.746052 | 0.373026 | − | 0.927821i | \(-0.378320\pi\) | ||||
0.373026 | + | 0.927821i | \(0.378320\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1102 | −0.427616 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.793663 | 0.0335085 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.8654 | 1.72227 | 0.861135 | − | 0.508376i | \(-0.169754\pi\) | ||||
0.861135 | + | 0.508376i | \(0.169754\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.3077 | −0.433648 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.05249 | 0.0442006 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.5716 | −1.19779 | −0.598893 | − | 0.800829i | \(-0.704392\pi\) | ||||
−0.598893 | + | 0.800829i | \(0.704392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.5883 | 0.652352 | 0.326176 | − | 0.945309i | \(-0.394240\pi\) | ||||
0.326176 | + | 0.945309i | \(0.394240\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.5477 | 0.941943 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.1836 | −0.841715 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.1993 | −1.00743 | −0.503715 | − | 0.863870i | \(-0.668034\pi\) | ||||
−0.503715 | + | 0.863870i | \(0.668034\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.60996 | −0.150025 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.24457 | −0.217581 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.778784 | −0.0322539 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.56759 | 0.230192 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.3193 | 1.21014 | 0.605069 | − | 0.796173i | \(-0.293145\pi\) | ||||
0.605069 | + | 0.796173i | \(0.293145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.75245 | 0.113413 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4286 | −0.511245 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.3422 | −0.876418 | −0.438209 | − | 0.898873i | \(-0.644387\pi\) | ||||
−0.438209 | + | 0.898873i | \(0.644387\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.88603 | 0.323296 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.92918 | 0.283593 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.3543 | 0.913373 | 0.456686 | − | 0.889628i | \(-0.349036\pi\) | ||||
0.456686 | + | 0.889628i | \(0.349036\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.2799 | 1.68384 | 0.841921 | − | 0.539602i | \(-0.181425\pi\) | ||||
0.841921 | + | 0.539602i | \(0.181425\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.317219 | 0.0129181 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.7896 | −0.682594 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.06522 | −0.246180 | −0.123090 | − | 0.992396i | \(-0.539280\pi\) | ||||
−0.123090 | + | 0.992396i | \(0.539280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.1017 | −0.409342 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.5805 | 1.39898 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.1383 | −0.449871 | −0.224935 | − | 0.974374i | \(-0.572217\pi\) | ||||
−0.224935 | + | 0.974374i | \(0.572217\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.65256 | 0.0666377 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.1170 | 0.769621 | 0.384810 | − | 0.922996i | \(-0.374267\pi\) | ||||
0.384810 | + | 0.922996i | \(0.374267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.9654 | −1.24460 | −0.622302 | − | 0.782777i | \(-0.713803\pi\) | ||||
−0.622302 | + | 0.782777i | \(0.713803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.59021 | −0.304585 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.209797 | −0.00840533 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.63301 | −0.185321 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.166328 | −0.00664252 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.1891 | 0.804991 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.1070 | −0.959686 | −0.479843 | − | 0.877354i | \(-0.659306\pi\) | ||||
−0.479843 | + | 0.877354i | \(0.659306\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.3772 | −0.809923 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.2980 | 0.964235 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.4419 | −0.849560 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.83623 | −0.230878 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.5154 | −1.28428 | −0.642141 | − | 0.766586i | \(-0.721954\pi\) | ||||
−0.642141 | + | 0.766586i | \(0.721954\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.8759 | 0.626085 | 0.313042 | − | 0.949739i | \(-0.398652\pi\) | ||||
0.313042 | + | 0.949739i | \(0.398652\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.25073 | 0.167372 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.0625 | −0.985310 | −0.492655 | − | 0.870225i | \(-0.663974\pi\) | ||||
−0.492655 | + | 0.870225i | \(0.663974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.33330 | 0.0523366 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.82264 | 0.110628 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.74801 | −0.224937 | −0.112469 | − | 0.993655i | \(-0.535876\pi\) | ||||
−0.112469 | + | 0.993655i | \(0.535876\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.0163 | −0.586737 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.2379 | 0.438431 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.0446 | −0.430238 | −0.215119 | − | 0.976588i | \(-0.569014\pi\) | ||||
−0.215119 | + | 0.976588i | \(0.569014\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.4709 | 1.06849 | 0.534247 | − | 0.845329i | \(-0.320595\pi\) | ||||
0.534247 | + | 0.845329i | \(0.320595\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.8211 | −0.692116 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.65268 | −0.0640882 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 72.8499 | 2.82076 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.2826 | −0.784172 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0827740 | −0.00319545 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.7360 | 0.529485 | 0.264743 | − | 0.964319i | \(-0.414713\pi\) | ||||
0.264743 | + | 0.964319i | \(0.414713\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.65917 | 0.102351 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.5759 | 1.36729 | 0.683646 | − | 0.729814i | \(-0.260393\pi\) | ||||
0.683646 | + | 0.729814i | \(0.260393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.5112 | −0.441760 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.39895 | 0.283528 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.58516 | −0.175446 | −0.0877231 | − | 0.996145i | \(-0.527959\pi\) | ||||
−0.0877231 | + | 0.996145i | \(0.527959\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.41039 | −0.130304 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.7782 | 0.411216 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.4870 | 0.666203 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.54129 | −0.324926 | −0.162463 | − | 0.986715i | \(-0.551944\pi\) | ||||
−0.162463 | + | 0.986715i | \(0.551944\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.170570 | −0.00647942 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.8010 | 0.447639 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.28964 | −0.200359 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.03570 | 0.266115 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.3748 | 1.75155 | 0.875776 | − | 0.482718i | \(-0.160350\pi\) | ||||
0.875776 | + | 0.482718i | \(0.160350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.23104 | −0.159577 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.5390 | −0.547570 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.5048 | 0.470292 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.4820 | 1.74567 | 0.872835 | − | 0.488016i | \(-0.162279\pi\) | ||||
0.872835 | + | 0.488016i | \(0.162279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.59029 | −0.209652 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.3558 | −0.762332 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.902298 | −0.0337440 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.21369 | 0.269400 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.2461 | −1.01611 | −0.508053 | − | 0.861326i | \(-0.669635\pi\) | ||||
−0.508053 | + | 0.861326i | \(0.669635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.62828 | 0.0606404 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.07039 | 0.225760 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.5223 | −0.947875 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.9595 | 0.814432 | 0.407216 | − | 0.913332i | \(-0.366500\pi\) | ||||
0.407216 | + | 0.913332i | \(0.366500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6060 | −0.503237 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3357 | −0.640309 | −0.320154 | − | 0.947365i | \(-0.603735\pi\) | ||||
−0.320154 | + | 0.947365i | \(0.603735\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.01502 | 0.332524 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0514092 | −0.00189368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.7105 | −0.541135 | −0.270568 | − | 0.962701i | \(-0.587211\pi\) | ||||
−0.270568 | + | 0.962701i | \(0.587211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.73479 | 0.137201 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0012 | −0.587029 | −0.293514 | − | 0.955955i | \(-0.594825\pi\) | ||||
−0.293514 | + | 0.955955i | \(0.594825\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.3344 | −1.07473 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.98299 | −0.182318 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.04937 | 0.111422 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.2600 | −1.57858 | −0.789289 | − | 0.614022i | \(-0.789551\pi\) | ||||
−0.789289 | + | 0.614022i | \(0.789551\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.20193 | −0.0438008 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.3195 | 0.448354 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.81138 | −0.356601 | −0.178300 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178300 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.23009 | 0.0446494 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.1070 | 0.547627 | 0.273814 | − | 0.961783i | \(-0.411715\pi\) | ||||
0.273814 | + | 0.961783i | \(0.411715\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.59704 | 0.311234 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.49271 | 0.270899 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.9383 | −1.08101 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.1675 | 0.727258 | 0.363629 | − | 0.931544i | \(-0.381538\pi\) | ||||
0.363629 | + | 0.931544i | \(0.381538\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.5799 | 0.525083 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.4289 | 0.950582 | 0.475291 | − | 0.879829i | \(-0.342343\pi\) | ||||
0.475291 | + | 0.879829i | \(0.342343\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.13149 | 0.256171 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.33893 | −0.155658 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.10855 | 0.0397180 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.945833 | 0.0338446 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.59787 | −0.343000 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.5840 | 0.556218 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.9094 | 0.852280 | 0.426140 | − | 0.904657i | \(-0.359873\pi\) | ||||
0.426140 | + | 0.904657i | \(0.359873\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.6235 | 0.591811 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.09081 | −0.252120 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.85863 | 0.0660020 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.35224 | −0.260757 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.2713 | 0.930578 | 0.465289 | − | 0.885159i | \(-0.345950\pi\) | ||||
0.465289 | + | 0.885159i | \(0.345950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.5374 | 1.64638 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.199333 | −0.00704308 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.82124 | −0.0642701 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.2225 | 0.430786 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.32925 | 0.293203 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.70973 | −0.306218 | −0.153109 | − | 0.988209i | \(-0.548929\pi\) | ||||
−0.153109 | + | 0.988209i | \(0.548929\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.7512 | 0.939363 | 0.469682 | − | 0.882836i | \(-0.344369\pi\) | ||||
0.469682 | + | 0.882836i | \(0.344369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.8577 | −0.941940 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.662352 | −0.0232012 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.85142 | 0.0997587 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.83003 | 0.133832 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.36277 | 0.152262 | 0.0761309 | − | 0.997098i | \(-0.475743\pi\) | ||||
0.0761309 | + | 0.997098i | \(0.475743\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.76960 | 0.305689 | 0.152844 | − | 0.988250i | \(-0.451157\pi\) | ||||
0.152844 | + | 0.988250i | \(0.451157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.430951 | −0.0150038 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.60546 | 0.0906009 | 0.0453004 | − | 0.998973i | \(-0.485575\pi\) | ||||
0.0453004 | + | 0.998973i | \(0.485575\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.2663 | −0.738608 | −0.369304 | − | 0.929309i | \(-0.620404\pi\) | ||||
−0.369304 | + | 0.929309i | \(0.620404\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.42647 | −0.257621 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.8559 | −0.999798 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.52998 | −0.0529471 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.68185 | 0.0926984 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.8458 | 1.03039 | 0.515195 | − | 0.857073i | \(-0.327719\pi\) | ||||
0.515195 | + | 0.857073i | \(0.327719\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63.1191 | 2.17652 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.07711 | −0.0715396 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.370744 | 0.0127540 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.5498 | −0.396856 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.8081 | −0.782771 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.2908 | 1.07263 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.85903 | 0.269088 | 0.134544 | − | 0.990908i | \(-0.457043\pi\) | ||||
0.134544 | + | 0.990908i | \(0.457043\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.57025 | −0.0537015 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.2600 | −0.931183 | −0.465591 | − | 0.885000i | \(-0.654158\pi\) | ||||
−0.465591 | + | 0.885000i | \(0.654158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.16871 | −0.0398758 | −0.0199379 | − | 0.999801i | \(-0.506347\pi\) | ||||
−0.0199379 | + | 0.999801i | \(0.506347\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.13682 | 0.0387428 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −57.0280 | −1.94126 | −0.970628 | − | 0.240587i | \(-0.922660\pi\) | ||||
−0.970628 | + | 0.240587i | \(0.922660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.4156 | 0.898157 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.98318 | −0.237161 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.905976 | 0.0307331 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.15436 | 0.0391139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.9371 | −0.370164 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.3335 | −0.416949 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.3813 | 0.857065 | 0.428533 | − | 0.903526i | \(-0.359031\pi\) | ||||
0.428533 | + | 0.903526i | \(0.359031\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.3193 | 0.651623 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.2777 | −0.750554 | −0.375277 | − | 0.926913i | \(-0.622452\pi\) | ||||
−0.375277 | + | 0.926913i | \(0.622452\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8081 | −0.733900 | −0.366950 | − | 0.930241i | \(-0.619598\pi\) | ||||
−0.366950 | + | 0.930241i | \(0.619598\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.5873 | 0.423116 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.0024 | −1.04096 | −0.520480 | − | 0.853874i | \(-0.674247\pi\) | ||||
−0.520480 | + | 0.853874i | \(0.674247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.7149 | 0.560601 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.162063 | −0.00542930 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.75288 | −0.326368 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.7989 | −0.360967 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.6208 | −0.922231 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.7401 | −0.858479 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.5336 | 0.784017 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.92414 | 0.0973092 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.5550 | −0.749753 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.9506 | 1.65858 | 0.829291 | − | 0.558817i | \(-0.188745\pi\) | ||||
0.829291 | + | 0.558817i | \(0.188745\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.8811 | 0.394072 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.1409 | −1.03174 | −0.515872 | − | 0.856666i | \(-0.672532\pi\) | ||||
−0.515872 | + | 0.856666i | \(0.672532\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.807555 | 0.0267262 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.781442 | −0.0258337 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3300 | −0.341125 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.0648 | 1.65149 | 0.825743 | − | 0.564046i | \(-0.190756\pi\) | ||||
0.825743 | + | 0.564046i | \(0.190756\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.57084 | −0.315370 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.2380 | −0.699058 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.9625 | −0.360444 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.54707 | 0.0508124 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.2739 | 0.927638 | 0.463819 | − | 0.885930i | \(-0.346479\pi\) | ||||
0.463819 | + | 0.885930i | \(0.346479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.04735 | 0.198194 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.69478 | −0.284654 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.21429 | −0.0397114 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.8173 | 1.26811 | 0.634053 | − | 0.773290i | \(-0.281390\pi\) | ||||
0.634053 | + | 0.773290i | \(0.281390\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.7334 | 0.807146 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.4498 | −0.927437 | −0.463719 | − | 0.885983i | \(-0.653485\pi\) | ||||
−0.463719 | + | 0.885983i | \(0.653485\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.19834 | −0.266975 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.61029 | −0.0523829 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.80156 | −0.286012 | −0.143006 | − | 0.989722i | \(-0.545677\pi\) | ||||
−0.143006 | + | 0.989722i | \(0.545677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.8946 | 1.32750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.3559 | −0.984358 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.0564 | −0.358151 | −0.179075 | − | 0.983835i | \(-0.557311\pi\) | ||||
−0.179075 | + | 0.983835i | \(0.557311\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.4975 | −1.11631 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.55546 | 0.0502807 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.34605 | −0.0757581 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.8077 | −0.767989 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.89728 | 0.0933636 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.52316 | 0.177797 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.2114 | −0.778586 | −0.389293 | − | 0.921114i | \(-0.627281\pi\) | ||||
−0.389293 | + | 0.921114i | \(0.627281\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.02617 | 0.161464 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.68129 | −0.246504 | −0.123252 | − | 0.992375i | \(-0.539332\pi\) | ||||
−0.123252 | + | 0.992375i | \(0.539332\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.11811 | 0.260255 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.67670 | 0.309902 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.4901 | −1.16742 | −0.583711 | − | 0.811961i | \(-0.698400\pi\) | ||||
−0.583711 | + | 0.811961i | \(0.698400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0323044 | 0.00103245 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.16825 | 0.260792 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.9487 | 0.891424 | 0.445712 | − | 0.895176i | \(-0.352951\pi\) | ||||
0.445712 | + | 0.895176i | \(0.352951\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.0155 | 0.605885 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.0016 | −0.318354 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.0878 | −0.670554 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.69672 | −0.0538980 | −0.0269490 | − | 0.999637i | \(-0.508579\pi\) | ||||
−0.0269490 | + | 0.999637i | \(0.508579\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.2944 | 0.961365 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.6015 | −0.336090 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.9519 | 0.663553 | 0.331777 | − | 0.943358i | \(-0.392352\pi\) | ||||
0.331777 | + | 0.943358i | \(0.392352\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.12252 | −0.130431 |
(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 | 8016.2.a.bb.1.5 | 9 | ||
4.3 | odd | 2 | 2004.2.a.d.1.5 | ✓ | 9 | ||
12.11 | even | 2 | 6012.2.a.h.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.d.1.5 | ✓ | 9 | 4.3 | odd | 2 | ||
6012.2.a.h.1.5 | 9 | 12.11 | even | 2 | |||
8016.2.a.bb.1.5 | 9 | 1.1 | even | 1 | trivial |