Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, 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("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.56155 | −1.59277 | −0.796387 | − | 0.604787i | \(-0.793258\pi\) | ||||
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.56155 | −1.34614 | −0.673070 | − | 0.739579i | \(-0.735025\pi\) | ||||
−0.673070 | + | 0.739579i | \(0.735025\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.43845 | −0.433708 | −0.216854 | − | 0.976204i | \(-0.569580\pi\) | ||||
−0.216854 | + | 0.976204i | \(0.569580\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.12311 | −1.97559 | −0.987797 | − | 0.155747i | \(-0.950222\pi\) | ||||
−0.987797 | + | 0.155747i | \(0.950222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.56155 | 1.43599 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.56155 | 1.21363 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.56155 | −0.951150 | −0.475575 | − | 0.879675i | \(-0.657760\pi\) | ||||
−0.475575 | + | 0.879675i | \(0.657760\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.68466 | 1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.56155 | 1.40415 | 0.702073 | − | 0.712105i | \(-0.252258\pi\) | ||||
0.702073 | + | 0.712105i | \(0.252258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.24621 | 1.12185 | 0.560926 | − | 0.827866i | \(-0.310445\pi\) | ||||
0.560926 | + | 0.827866i | \(0.310445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.24621 | 0.391015 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.6847 | 2.14410 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24621 | 1.35567 | 0.677834 | − | 0.735215i | \(-0.262919\pi\) | ||||
0.677834 | + | 0.735215i | \(0.262919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.1231 | 1.78112 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.6847 | −1.98101 | −0.990505 | − | 0.137474i | \(-0.956102\pi\) | ||||
−0.990505 | + | 0.137474i | \(0.956102\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.1231 | 1.62247 | 0.811236 | − | 0.584719i | \(-0.198795\pi\) | ||||
0.811236 | + | 0.584719i | \(0.198795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.68466 | 0.812094 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.56155 | −0.218661 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3693 | 1.42434 | 0.712168 | − | 0.702009i | \(-0.247714\pi\) | ||||
0.712168 | + | 0.702009i | \(0.247714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.12311 | 0.690799 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.68466 | 0.620498 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.315342 | −0.0403753 | −0.0201877 | − | 0.999796i | \(-0.506426\pi\) | ||||
−0.0201877 | + | 0.999796i | \(0.506426\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 25.3693 | 3.14668 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.87689 | 0.840146 | 0.420073 | − | 0.907490i | \(-0.362004\pi\) | ||||
0.420073 | + | 0.907490i | \(0.362004\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.12311 | 0.857521 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.8078 | −1.26495 | −0.632477 | − | 0.774580i | \(-0.717962\pi\) | ||||
−0.632477 | + | 0.774580i | \(0.717962\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.0000 | −1.38564 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.12311 | 0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.68466 | −0.752083 | −0.376041 | − | 0.926603i | \(-0.622715\pi\) | ||||
−0.376041 | + | 0.926603i | \(0.622715\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.24621 | −0.905139 | −0.452570 | − | 0.891729i | \(-0.649493\pi\) | ||||
−0.452570 | + | 0.891729i | \(0.649493\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.56155 | −0.386305 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.8078 | −1.26593 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.12311 | 0.119049 | 0.0595245 | − | 0.998227i | \(-0.481042\pi\) | ||||
0.0595245 | + | 0.998227i | \(0.481042\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.3693 | 2.65943 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.75379 | −1.01142 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.6847 | 1.09622 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.8078 | 1.50350 | 0.751750 | − | 0.659448i | \(-0.229210\pi\) | ||||
0.751750 | + | 0.659448i | \(0.229210\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.807764 | 0.0811833 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1231 | −1.10679 | −0.553395 | − | 0.832919i | \(-0.686668\pi\) | ||||
−0.553395 | + | 0.832919i | \(0.686668\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.2462 | −1.20666 | −0.603328 | − | 0.797494i | \(-0.706159\pi\) | ||||
−0.603328 | + | 0.797494i | \(0.706159\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19.8078 | −1.93304 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.438447 | −0.0423863 | −0.0211931 | − | 0.999775i | \(-0.506746\pi\) | ||||
−0.0211931 | + | 0.999775i | \(0.506746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.80776 | −0.268935 | −0.134468 | − | 0.990918i | \(-0.542932\pi\) | ||||
−0.134468 | + | 0.990918i | \(0.542932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.8769 | −1.22222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.3693 | −1.44582 | −0.722912 | − | 0.690940i | \(-0.757197\pi\) | ||||
−0.722912 | + | 0.690940i | \(0.757197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.2462 | 1.51497 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.00000 | 0.369800 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.56155 | −0.326487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.93087 | −0.811897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.8078 | 1.78601 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.56155 | −0.855211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.6847 | 1.83547 | 0.917733 | − | 0.397197i | \(-0.130017\pi\) | ||||
0.917733 | + | 0.397197i | \(0.130017\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.12311 | 0.622349 | 0.311174 | − | 0.950353i | \(-0.399278\pi\) | ||||
0.311174 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.6847 | 0.926477 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.8078 | −1.70478 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.87689 | −0.331225 | −0.165613 | − | 0.986191i | \(-0.552960\pi\) | ||||
−0.165613 | + | 0.986191i | \(0.552960\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.3693 | −1.46276 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2462 | 0.856831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.9309 | −2.23649 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.87689 | −0.732154 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.1231 | 1.40278 | 0.701390 | − | 0.712778i | \(-0.252563\pi\) | ||||
0.701390 | + | 0.712778i | \(0.252563\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.36932 | −0.436949 | −0.218474 | − | 0.975843i | \(-0.570108\pi\) | ||||
−0.218474 | + | 0.975843i | \(0.570108\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.561553 | −0.0453989 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.2462 | −1.78686 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.12311 | −0.408868 | −0.204434 | − | 0.978880i | \(-0.565535\pi\) | ||||
−0.204434 | + | 0.978880i | \(0.565535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.1922 | −1.28413 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.2462 | 1.28038 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.2462 | 1.42915 | 0.714577 | − | 0.699557i | \(-0.246619\pi\) | ||||
0.714577 | + | 0.699557i | \(0.246619\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | −0.622799 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0540 | −0.932765 | −0.466382 | − | 0.884583i | \(-0.654443\pi\) | ||||
−0.466382 | + | 0.884583i | \(0.654443\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.7386 | 2.90297 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.68466 | 0.128829 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.31534 | −0.480147 | −0.240073 | − | 0.970755i | \(-0.577171\pi\) | ||||
−0.240073 | + | 0.970755i | \(0.577171\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −27.3693 | −2.06893 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.56155 | 0.117373 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.75379 | −0.131084 | −0.0655422 | − | 0.997850i | \(-0.520878\pi\) | ||||
−0.0655422 | + | 0.997850i | \(0.520878\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.8078 | −1.17498 | −0.587491 | − | 0.809231i | \(-0.699884\pi\) | ||||
−0.587491 | + | 0.809231i | \(0.699884\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.492423 | 0.0364009 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −29.3693 | −2.15928 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.43845 | −0.105190 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.8078 | −1.44080 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3693 | 1.83566 | 0.917830 | − | 0.396974i | \(-0.129940\pi\) | ||||
0.917830 | + | 0.396974i | \(0.129940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.3153 | −0.958459 | −0.479230 | − | 0.877690i | \(-0.659084\pi\) | ||||
−0.479230 | + | 0.877690i | \(0.659084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −39.6155 | −2.83693 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3693 | 1.52250 | 0.761250 | − | 0.648458i | \(-0.224586\pi\) | ||||
0.761250 | + | 0.648458i | \(0.224586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.6847 | −1.74985 | −0.874925 | − | 0.484259i | \(-0.839089\pi\) | ||||
−0.874925 | + | 0.484259i | \(0.839089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.7386 | −0.757445 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.9309 | −1.89018 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 45.1771 | 3.15530 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.56155 | 0.178040 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.31534 | 0.298498 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.19224 | 0.495134 | 0.247567 | − | 0.968871i | \(-0.420369\pi\) | ||||
0.247567 | + | 0.968871i | \(0.420369\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.4924 | 0.855967 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.2462 | −1.51017 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.8769 | 1.14043 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.12311 | −0.479152 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.31534 | −0.288977 | −0.144488 | − | 0.989507i | \(-0.546154\pi\) | ||||
−0.144488 | + | 0.989507i | \(0.546154\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.31534 | −0.287689 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.24621 | 0.149086 | 0.0745431 | − | 0.997218i | \(-0.476250\pi\) | ||||
0.0745431 | + | 0.997218i | \(0.476250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.1231 | 1.39585 | 0.697927 | − | 0.716169i | \(-0.254106\pi\) | ||||
0.697927 | + | 0.716169i | \(0.254106\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.31534 | 0.151683 | 0.0758415 | − | 0.997120i | \(-0.475836\pi\) | ||||
0.0758415 | + | 0.997120i | \(0.475836\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39.6155 | −2.58423 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.4384 | 0.678050 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.2462 | 1.89178 | 0.945890 | − | 0.324487i | \(-0.105192\pi\) | ||||
0.945890 | + | 0.324487i | \(0.105192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.31534 | −0.471223 | −0.235611 | − | 0.971847i | \(-0.575709\pi\) | ||||
−0.235611 | + | 0.971847i | \(0.575709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.2462 | −1.29348 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.3693 | 1.35970 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.8769 | 0.816040 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.1231 | 1.27016 | 0.635080 | − | 0.772447i | \(-0.280967\pi\) | ||||
0.635080 | + | 0.772447i | \(0.280967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.56155 | 0.412521 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.56155 | 0.348278 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.2462 | −0.826276 | −0.413138 | − | 0.910668i | \(-0.635567\pi\) | ||||
−0.413138 | + | 0.910668i | \(0.635567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.3693 | −1.82492 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24621 | −0.262834 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.12311 | 0.254242 | 0.127121 | − | 0.991887i | \(-0.459426\pi\) | ||||
0.127121 | + | 0.991887i | \(0.459426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −36.9309 | −2.26865 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.75379 | −0.107330 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4384 | −0.819357 | −0.409678 | − | 0.912230i | \(-0.634359\pi\) | ||||
−0.409678 | + | 0.912230i | \(0.634359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.24621 | 0.440176 | 0.220088 | − | 0.975480i | \(-0.429366\pi\) | ||||
0.220088 | + | 0.975480i | \(0.429366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −39.6155 | −2.39764 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.0540 | −0.666580 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0540 | 1.56543 | 0.782716 | − | 0.622379i | \(-0.213834\pi\) | ||||
0.782716 | + | 0.622379i | \(0.213834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.50758 | −0.209993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.12311 | −0.365274 | −0.182637 | − | 0.983180i | \(-0.558463\pi\) | ||||
−0.182637 | + | 0.983180i | \(0.558463\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2462 | −0.609074 | −0.304537 | − | 0.952501i | \(-0.598502\pi\) | ||||
−0.304537 | + | 0.952501i | \(0.598502\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.6847 | −0.988314 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 45.1771 | 2.66672 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.1231 | −1.35550 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0000 | 0.759468 | 0.379734 | − | 0.925096i | \(-0.376015\pi\) | ||||
0.379734 | + | 0.925096i | \(0.376015\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.56155 | 0.207362 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.00000 | −0.464207 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.4924 | 1.87909 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.3693 | 0.997841 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.12311 | 0.0643088 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.2462 | 1.44088 | 0.720439 | − | 0.693519i | \(-0.243940\pi\) | ||||
0.720439 | + | 0.693519i | \(0.243940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.1231 | 1.08788 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.1771 | 1.31425 | 0.657126 | − | 0.753781i | \(-0.271772\pi\) | ||||
0.657126 | + | 0.753781i | \(0.271772\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.6155 | 0.995689 | 0.497844 | − | 0.867266i | \(-0.334125\pi\) | ||||
0.497844 | + | 0.867266i | \(0.334125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.12311 | −0.401342 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.8617 | −1.45254 | −0.726270 | − | 0.687410i | \(-0.758748\pi\) | ||||
−0.726270 | + | 0.687410i | \(0.758748\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.8769 | −0.608989 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.684658 | 0.0382139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −54.7386 | −3.03635 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.38447 | 0.242462 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −39.6155 | −2.18407 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.06913 | −0.0587647 | −0.0293824 | − | 0.999568i | \(-0.509354\pi\) | ||||
−0.0293824 | + | 0.999568i | \(0.509354\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.63068 | −0.253760 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.4924 | −1.33816 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.9309 | −0.649916 | −0.324958 | − | 0.945728i | \(-0.605350\pi\) | ||||
−0.324958 | + | 0.945728i | \(0.605350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.0000 | 1.30350 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.98485 | −0.486557 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.68466 | 0.252948 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.3693 | −1.36584 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.1771 | 1.19053 | 0.595264 | − | 0.803530i | \(-0.297047\pi\) | ||||
0.595264 | + | 0.803530i | \(0.297047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.630683 | −0.0337597 | −0.0168798 | − | 0.999858i | \(-0.505373\pi\) | ||||
−0.0168798 | + | 0.999858i | \(0.505373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −39.6155 | −2.11452 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.4924 | 1.51222 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.56155 | 0.294349 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.2462 | 0.804664 | 0.402332 | − | 0.915494i | \(-0.368200\pi\) | ||||
0.402332 | + | 0.915494i | \(0.368200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.9460 | 0.731976 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.4924 | 2.01479 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.1771 | −1.78403 | −0.892015 | − | 0.452007i | \(-0.850708\pi\) | ||||
−0.892015 | + | 0.452007i | \(0.850708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.12311 | 0.370814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.9309 | −1.91736 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.0540 | −1.29725 | −0.648623 | − | 0.761110i | \(-0.724655\pi\) | ||||
−0.648623 | + | 0.761110i | \(0.724655\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.9309 | 0.771027 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −53.8617 | −2.77402 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.68466 | −0.240635 | −0.120317 | − | 0.992735i | \(-0.538391\pi\) | ||||
−0.120317 | + | 0.992735i | \(0.538391\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.3002 | −1.65479 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.6847 | 1.00584 | 0.502920 | − | 0.864333i | \(-0.332259\pi\) | ||||
0.502920 | + | 0.864333i | \(0.332259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.2462 | −0.929913 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.4924 | −1.34322 | −0.671610 | − | 0.740905i | \(-0.734397\pi\) | ||||
−0.671610 | + | 0.740905i | \(0.734397\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.56155 | −0.230688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.1231 | −0.561086 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.8078 | 1.19790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.8078 | 1.64657 | 0.823287 | − | 0.567625i | \(-0.192138\pi\) | ||||
0.823287 | + | 0.567625i | \(0.192138\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.6847 | −0.835278 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.8078 | −1.33872 | −0.669358 | − | 0.742940i | \(-0.733431\pi\) | ||||
−0.669358 | + | 0.742940i | \(0.733431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44.4924 | −2.21633 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.9309 | 1.23882 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8617 | −0.587965 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.6155 | −1.16771 | −0.583856 | − | 0.811857i | \(-0.698457\pi\) | ||||
−0.583856 | + | 0.811857i | \(0.698457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.05398 | 0.298621 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.56155 | 0.175253 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.3693 | 1.44168 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.4924 | −0.611757 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0540 | −0.637728 | −0.318864 | − | 0.947800i | \(-0.603301\pi\) | ||||
−0.318864 | + | 0.947800i | \(0.603301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.3693 | −0.749055 | −0.374527 | − | 0.927216i | \(-0.622195\pi\) | ||||
−0.374527 | + | 0.927216i | \(0.622195\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.24621 | −0.303701 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.68466 | 0.372761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.12311 | 0.0543509 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.0000 | −0.772487 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.9309 | −0.671026 | −0.335513 | − | 0.942036i | \(-0.608910\pi\) | ||||
−0.335513 | + | 0.942036i | \(0.608910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.7386 | 1.23692 | 0.618460 | − | 0.785816i | \(-0.287757\pi\) | ||||
0.618460 | + | 0.785816i | \(0.287757\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 42.0540 | 2.01633 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.6847 | 0.654626 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.2462 | 0.870844 | 0.435422 | − | 0.900226i | \(-0.356599\pi\) | ||||
0.435422 | + | 0.900226i | \(0.356599\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.19224 | −0.152011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7538 | 0.843508 | 0.421754 | − | 0.906710i | \(-0.361415\pi\) | ||||
0.421754 | + | 0.906710i | \(0.361415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.00000 | −0.189618 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.7386 | −1.26469 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.0540 | −1.79588 | −0.897939 | − | 0.440120i | \(-0.854936\pi\) | ||||
−0.897939 | + | 0.440120i | \(0.854936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.2462 | 0.859181 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.38447 | 0.393937 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −90.3542 | −4.23587 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.7386 | 1.34434 | 0.672168 | − | 0.740398i | \(-0.265363\pi\) | ||||
0.672168 | + | 0.740398i | \(0.265363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.56155 | 0.259591 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.4384 | 0.905339 | 0.452669 | − | 0.891678i | \(-0.350472\pi\) | ||||
0.452669 | + | 0.891678i | \(0.350472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.50758 | −0.255959 | −0.127979 | − | 0.991777i | \(-0.540849\pi\) | ||||
−0.127979 | + | 0.991777i | \(0.540849\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 34.7386 | 1.61097 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.2462 | 1.30708 | 0.653539 | − | 0.756893i | \(-0.273283\pi\) | ||||
0.653539 | + | 0.756893i | \(0.273283\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.4924 | −1.13095 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.00000 | 0.368621 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.0540 | −1.05779 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.82292 | −0.266613 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.9848 | 1.87265 | 0.936323 | − | 0.351141i | \(-0.114206\pi\) | ||||
0.936323 | + | 0.351141i | \(0.114206\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −58.7386 | −2.67825 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.3693 | −1.15434 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −52.7386 | −2.39474 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.1922 | 0.643112 | 0.321556 | − | 0.946891i | \(-0.395794\pi\) | ||||
0.321556 | + | 0.946891i | \(0.395794\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.4924 | −1.28847 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.0000 | −1.66979 | −0.834893 | − | 0.550412i | \(-0.814471\pi\) | ||||
−0.834893 | + | 0.550412i | \(0.814471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.56155 | 0.340555 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.87689 | −0.129307 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.4924 | 1.27806 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.3153 | −0.864673 | −0.432337 | − | 0.901712i | \(-0.642311\pi\) | ||||
−0.432337 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.8229 | 0.840946 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.561553 | 0.0250384 | 0.0125192 | − | 0.999922i | \(-0.496015\pi\) | ||||
0.0125192 | + | 0.999922i | \(0.496015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.6155 | 1.76287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −58.9309 | −2.61721 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.8769 | 0.836704 | 0.418352 | − | 0.908285i | \(-0.362608\pi\) | ||||
0.418352 | + | 0.908285i | \(0.362608\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.4924 | 1.70280 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.6847 | −0.736646 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 43.6155 | 1.92193 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0000 | −0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.86174 | 0.432882 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.8769 | −0.564147 | −0.282073 | − | 0.959393i | \(-0.591022\pi\) | ||||
−0.282073 | + | 0.959393i | \(0.591022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.7386 | 0.950564 | 0.475282 | − | 0.879833i | \(-0.342346\pi\) | ||||
0.475282 | + | 0.879833i | \(0.342346\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 42.7386 | 1.86527 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.24621 | 0.272089 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.19224 | −0.0953146 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.561553 | 0.0243693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 90.3542 | 3.91367 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.56155 | 0.0675118 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.73863 | 0.118181 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.17708 | −0.352212 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.4924 | 0.623078 | 0.311539 | − | 0.950233i | \(-0.399156\pi\) | ||||
0.311539 | + | 0.950233i | \(0.399156\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.6847 | 1.05932 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0000 | 0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4924 | −0.705165 | −0.352583 | − | 0.935781i | \(-0.614696\pi\) | ||||
−0.352583 | + | 0.935781i | \(0.614696\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.177081 | 0.00755763 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.6847 | −0.966399 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.8078 | 1.01241 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 45.8617 | 1.94672 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.36932 | −0.354619 | −0.177310 | − | 0.984155i | \(-0.556739\pi\) | ||||
−0.177310 | + | 0.984155i | \(0.556739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.24621 | 0.0948351 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.9848 | 1.47444 | 0.737218 | − | 0.675655i | \(-0.236139\pi\) | ||||
0.737218 | + | 0.675655i | \(0.236139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54.7386 | 2.30287 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.9309 | 1.04700 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.7386 | −1.79170 | −0.895848 | − | 0.444360i | \(-0.853431\pi\) | ||||
−0.895848 | + | 0.444360i | \(0.853431\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.1231 | −0.967672 | −0.483836 | − | 0.875159i | \(-0.660757\pi\) | ||||
−0.483836 | + | 0.875159i | \(0.660757\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.6155 | −1.65496 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.0540 | −1.46185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.12311 | −0.338169 | −0.169085 | − | 0.985602i | \(-0.554081\pi\) | ||||
−0.169085 | + | 0.985602i | \(0.554081\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.7926 | 0.864111 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.3693 | 1.21844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.9157 | −0.617746 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.2462 | −0.589008 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.0000 | 0.990586 | 0.495293 | − | 0.868726i | \(-0.335061\pi\) | ||||
0.495293 | + | 0.868726i | \(0.335061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.7386 | −0.772112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.3693 | −1.37263 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.3693 | −1.08286 | −0.541429 | − | 0.840746i | \(-0.682117\pi\) | ||||
−0.541429 | + | 0.840746i | \(0.682117\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.6847 | 0.520020 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.5464 | 1.57760 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.3002 | −0.502572 | −0.251286 | − | 0.967913i | \(-0.580853\pi\) | ||||
−0.251286 | + | 0.967913i | \(0.580853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3693 | 0.626928 | 0.313464 | − | 0.949600i | \(-0.398511\pi\) | ||||
0.313464 | + | 0.949600i | \(0.398511\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.86174 | −0.157262 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.8078 | 1.29317 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.1922 | −1.14429 | −0.572144 | − | 0.820153i | \(-0.693888\pi\) | ||||
−0.572144 | + | 0.820153i | \(0.693888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 42.0540 | 1.70411 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −79.2311 | −3.20535 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.12311 | 0.0453618 | 0.0226809 | − | 0.999743i | \(-0.492780\pi\) | ||||
0.0226809 | + | 0.999743i | \(0.492780\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −70.5464 | −2.84471 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.1922 | −0.732392 | −0.366196 | − | 0.930538i | \(-0.619340\pi\) | ||||
−0.366196 | + | 0.930538i | \(0.619340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.56155 | 0.0627641 | 0.0313821 | − | 0.999507i | \(-0.490009\pi\) | ||||
0.0313821 | + | 0.999507i | \(0.490009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.3693 | −1.01804 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.00000 | −0.160257 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.73863 | −0.269115 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.24621 | 0.328798 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.6847 | 1.10211 | 0.551054 | − | 0.834469i | \(-0.314226\pi\) | ||||
0.551054 | + | 0.834469i | \(0.314226\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.2311 | −0.446394 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −73.6695 | −2.92349 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −40.4924 | −1.60437 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.49242 | 0.177717 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.6155 | 1.24874 | 0.624369 | − | 0.781129i | \(-0.285356\pi\) | ||||
0.624369 | + | 0.781129i | \(0.285356\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.5616 | 0.771432 | 0.385716 | − | 0.922617i | \(-0.373954\pi\) | ||||
0.385716 | + | 0.922617i | \(0.373954\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7538 | 0.815916 | 0.407958 | − | 0.913001i | \(-0.366241\pi\) | ||||
0.407958 | + | 0.913001i | \(0.366241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.43845 | 0.0564640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 34.7386 | 1.36151 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.56155 | 0.374172 | 0.187086 | − | 0.982343i | \(-0.440096\pi\) | ||||
0.187086 | + | 0.982343i | \(0.440096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.3693 | −0.991261 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.06913 | 0.236779 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.49242 | −0.0970910 | −0.0485455 | − | 0.998821i | \(-0.515459\pi\) | ||||
−0.0485455 | + | 0.998821i | \(0.515459\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.3153 | −0.673489 | −0.336744 | − | 0.941596i | \(-0.609326\pi\) | ||||
−0.336744 | + | 0.941596i | \(0.609326\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.1231 | 0.431986 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −38.0540 | −1.47567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.4924 | −1.33555 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.73863 | 0.260531 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.453602 | 0.0175111 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.7926 | 1.61099 | 0.805493 | − | 0.592605i | \(-0.201900\pi\) | ||||
0.805493 | + | 0.592605i | \(0.201900\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 42.7386 | 1.64501 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2462 | −0.624393 | −0.312196 | − | 0.950018i | \(-0.601065\pi\) | ||||
−0.312196 | + | 0.950018i | \(0.601065\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −52.7386 | −2.02392 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.50758 | −0.134411 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.36932 | 0.205451 | 0.102726 | − | 0.994710i | \(-0.467244\pi\) | ||||
0.102726 | + | 0.994710i | \(0.467244\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.8078 | 0.527568 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.9848 | −1.25845 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −73.8617 | −2.81391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.31534 | −0.240247 | −0.120123 | − | 0.992759i | \(-0.538329\pi\) | ||||
−0.120123 | + | 0.992759i | \(0.538329\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.87689 | −0.109284 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.4924 | −1.08078 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.6847 | −0.480466 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.61553 | −0.136752 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.50758 | 0.132479 | 0.0662397 | − | 0.997804i | \(-0.478900\pi\) | ||||
0.0662397 | + | 0.997804i | \(0.478900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.7386 | −0.933035 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 61.8617 | 2.32985 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.6155 | 1.48990 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.3153 | −0.575180 | −0.287590 | − | 0.957754i | \(-0.592854\pi\) | ||||
−0.287590 | + | 0.957754i | \(0.592854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.75379 | 0.140778 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.4924 | −1.06705 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.4924 | −1.36474 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −45.6695 | −1.70556 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.8617 | −0.815305 | −0.407653 | − | 0.913137i | \(-0.633653\pi\) | ||||
−0.407653 | + | 0.913137i | \(0.633653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.6155 | 1.62433 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.4233 | 0.424837 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 58.1080 | 2.15808 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.4233 | 1.42504 | 0.712521 | − | 0.701651i | \(-0.247554\pi\) | ||||
0.712521 | + | 0.701651i | \(0.247554\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.0691303 | −0.00255339 | −0.00127669 | − | 0.999999i | \(-0.500406\pi\) | ||||
−0.00127669 | + | 0.999999i | \(0.500406\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.6155 | 1.16616 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.89205 | −0.364378 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.7538 | 0.873797 | 0.436899 | − | 0.899511i | \(-0.356077\pi\) | ||||
0.436899 | + | 0.899511i | \(0.356077\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.3693 | −1.22585 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.4924 | 1.19203 | 0.596016 | − | 0.802973i | \(-0.296750\pi\) | ||||
0.596016 | + | 0.802973i | \(0.296750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −60.9848 | −2.23431 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.63068 | 0.169428 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.56155 | 0.0570579 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.19224 | 0.335429 | 0.167715 | − | 0.985836i | \(-0.446361\pi\) | ||||
0.167715 | + | 0.985836i | \(0.446361\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.4233 | −1.14513 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.1231 | 0.695961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.75379 | 0.245471 | 0.122735 | − | 0.992439i | \(-0.460833\pi\) | ||||
0.122735 | + | 0.992439i | \(0.460833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.2462 | −0.371914 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3693 | −0.375887 | −0.187944 | − | 0.982180i | \(-0.560182\pi\) | ||||
−0.187944 | + | 0.982180i | \(0.560182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | 0.362024 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | 0.0723102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.12311 | 0.257200 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.00000 | −0.144244 | −0.0721218 | − | 0.997396i | \(-0.522977\pi\) | ||||
−0.0721218 | + | 0.997396i | \(0.522977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.6847 | 0.744940 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.0000 | 1.29483 | 0.647415 | − | 0.762138i | \(-0.275850\pi\) | ||||
0.647415 | + | 0.762138i | \(0.275850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.0000 | 1.72421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 45.8617 | 1.64528 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.0540 | 1.36343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.5076 | 0.411773 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.0540 | 1.50289 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.2462 | 0.651235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.1080 | −1.35840 | −0.679201 | − | 0.733952i | \(-0.737673\pi\) | ||||
−0.679201 | + | 0.733952i | \(0.737673\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.43845 | −0.229215 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.7386 | 1.94628 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.24621 | 0.0797653 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 57.6695 | 2.04533 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.3693 | 1.18200 | 0.591001 | − | 0.806671i | \(-0.298733\pi\) | ||||
0.591001 | + | 0.806671i | \(0.298733\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1231 | 0.393507 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.630683 | −0.0222841 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.5464 | 0.548620 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −57.8617 | −2.03936 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.9848 | 0.738702 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.1231 | 1.44581 | 0.722906 | − | 0.690947i | \(-0.242806\pi\) | ||||
0.722906 | + | 0.690947i | \(0.242806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.5616 | −1.56477 | −0.782384 | − | 0.622796i | \(-0.785996\pi\) | ||||
−0.782384 | + | 0.622796i | \(0.785996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3153 | −0.396846 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −64.9848 | −2.27632 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.2462 | −0.497803 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.0540 | −0.664988 | −0.332494 | − | 0.943105i | \(-0.607890\pi\) | ||||
−0.332494 | + | 0.943105i | \(0.607890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.8078 | 1.42247 | 0.711235 | − | 0.702955i | \(-0.248136\pi\) | ||||
0.711235 | + | 0.702955i | \(0.248136\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.2614 | 0.600964 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.3693 | −0.951724 | −0.475862 | − | 0.879520i | \(-0.657864\pi\) | ||||
−0.475862 | + | 0.879520i | \(0.657864\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.75379 | 0.0956430 | 0.0478215 | − | 0.998856i | \(-0.484772\pi\) | ||||
0.0478215 | + | 0.998856i | \(0.484772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.6847 | −1.41134 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.68466 | 0.196962 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.9309 | 1.48568 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.7386 | 1.20074 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.1771 | −0.420400 | −0.210200 | − | 0.977658i | \(-0.567411\pi\) | ||||
−0.210200 | + | 0.977658i | \(0.567411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1771 | 0.971623 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.56155 | 0.329317 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −134.408 | −4.62378 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.8078 | 1.09293 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.0000 | 0.549119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.6155 | −1.28944 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.9309 | −1.26449 | −0.632244 | − | 0.774769i | \(-0.717866\pi\) | ||||
−0.632244 | + | 0.774769i | \(0.717866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | −0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.8078 | 0.369186 | 0.184593 | − | 0.982815i | \(-0.440903\pi\) | ||||
0.184593 | + | 0.982815i | \(0.440903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.4924 | −1.31334 | −0.656672 | − | 0.754176i | \(-0.728037\pi\) | ||||
−0.656672 | + | 0.754176i | \(0.728037\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −70.5464 | −2.40421 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.12311 | 0.106312 | 0.0531559 | − | 0.998586i | \(-0.483072\pi\) | ||||
0.0531559 | + | 0.998586i | \(0.483072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.4924 | 0.764765 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.56155 | −0.0530331 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.61553 | 0.326184 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.9848 | −1.65979 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.31534 | −0.281432 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.0540 | 1.15123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.6847 | −1.71150 | −0.855750 | − | 0.517390i | \(-0.826904\pi\) | ||||
−0.855750 | + | 0.517390i | \(0.826904\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.3002 | −0.684708 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.0540 | 0.978853 | 0.489427 | − | 0.872044i | \(-0.337206\pi\) | ||||
0.489427 | + | 0.872044i | \(0.337206\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.7538 | −1.16956 | −0.584779 | − | 0.811193i | \(-0.698819\pi\) | ||||
−0.584779 | + | 0.811193i | \(0.698819\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.56155 | −0.186950 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.61553 | 0.255704 | 0.127852 | − | 0.991793i | \(-0.459192\pi\) | ||||
0.127852 | + | 0.991793i | \(0.459192\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −73.6695 | −2.47080 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.0691 | 0.337329 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.3693 | −1.11666 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.24621 | 0.208788 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50.7386 | −1.69411 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 47.2311 | 1.57524 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3693 | 0.345452 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56.3002 | 1.87148 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.4384 | −0.944283 | −0.472142 | − | 0.881523i | \(-0.656519\pi\) | ||||
−0.472142 | + | 0.881523i | \(0.656519\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.24621 | 0.207174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.94602 | 0.130738 | 0.0653688 | − | 0.997861i | \(-0.479178\pi\) | ||||
0.0653688 | + | 0.997861i | \(0.479178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.8617 | 0.392566 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.75379 | −0.0579785 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.3693 | −0.837769 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.8617 | −1.51284 | −0.756420 | − | 0.654087i | \(-0.773053\pi\) | ||||
−0.756420 | + | 0.654087i | \(0.773053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −39.4233 | −1.29904 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 56.9848 | 1.87568 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 63.3693 | 2.08357 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.87689 | 0.225867 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.5616 | 0.740221 | 0.370110 | − | 0.928988i | \(-0.379320\pi\) | ||||
0.370110 | + | 0.928988i | \(0.379320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.0540 | −0.558921 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.1922 | −1.18488 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.12311 | 0.167543 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.3693 | −1.35148 | −0.675738 | − | 0.737142i | \(-0.736175\pi\) | ||||
−0.675738 | + | 0.737142i | \(0.736175\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.5076 | −0.897676 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.7386 | 0.936853 | 0.468426 | − | 0.883503i | \(-0.344821\pi\) | ||||
0.468426 | + | 0.883503i | \(0.344821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.8617 | 1.88424 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 70.5464 | 2.29487 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.4384 | 0.989117 | 0.494558 | − | 0.869144i | \(-0.335330\pi\) | ||||
0.494558 | + | 0.869144i | \(0.335330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 76.9848 | 2.49903 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40.3845 | 1.30956 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.5616 | 1.57306 | 0.786531 | − | 0.617550i | \(-0.211875\pi\) | ||||
0.786531 | + | 0.617550i | \(0.211875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −90.3542 | −2.92379 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.9848 | 0.549042 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.8078 | 0.445876 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.01515 | 0.258553 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.246211 | 0.00793405 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47.4233 | 1.52661 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.9848 | 0.546196 | 0.273098 | − | 0.961986i | \(-0.411952\pi\) | ||||
0.273098 | + | 0.961986i | \(0.411952\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.68466 | 0.150493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.24621 | 0.0399928 | 0.0199964 | − | 0.999800i | \(-0.493635\pi\) | ||||
0.0199964 | + | 0.999800i | \(0.493635\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.4924 | −0.913425 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 85.4773 | 2.73746 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.73863 | 0.279574 | 0.139787 | − | 0.990182i | \(-0.455358\pi\) | ||||
0.139787 | + | 0.990182i | \(0.455358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.61553 | −0.0516325 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.57671 | 0.0503404 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.0388 | 1.46841 | 0.734205 | − | 0.678928i | \(-0.237555\pi\) | ||||
0.734205 | + | 0.678928i | \(0.237555\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −76.1080 | −2.42500 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 61.8617 | 1.96908 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.68466 | 0.307643 | 0.153822 | − | 0.988099i | \(-0.450842\pi\) | ||||
0.153822 | + | 0.988099i | \(0.450842\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.66950 | 0.0529801 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 87.9157 | 2.78712 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.9460 | −0.378334 | −0.189167 | − | 0.981945i | \(-0.560579\pi\) | ||||
−0.189167 | + | 0.981945i | \(0.560579\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.8617 | 1.45100 |
(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 | 8024.2.a.p.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.p.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |