Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5760,2,Mod(1,5760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5760, 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("5760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5760 = 2^{7} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5760.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: | \(45.9938315643\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5760.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.12311 | −1.93635 | −0.968176 | − | 0.250270i | \(-0.919480\pi\) | ||||
−0.968176 | + | 0.250270i | \(0.919480\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.12311 | −1.42089 | −0.710447 | − | 0.703751i | \(-0.751507\pi\) | ||||
−0.710447 | + | 0.703751i | \(0.751507\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.12311 | 0.272393 | 0.136197 | − | 0.990682i | \(-0.456512\pi\) | ||||
0.136197 | + | 0.990682i | \(0.456512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.12311 | 1.17532 | 0.587661 | − | 0.809108i | \(-0.300049\pi\) | ||||
0.587661 | + | 0.809108i | \(0.300049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.12311 | −1.06824 | −0.534121 | − | 0.845408i | \(-0.679357\pi\) | ||||
−0.534121 | + | 0.845408i | \(0.679357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.24621 | −1.53128 | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.12311 | 1.27935 | 0.639674 | − | 0.768647i | \(-0.279069\pi\) | ||||
0.639674 | + | 0.768647i | \(0.279069\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.12311 | −0.865963 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.12311 | 0.842233 | 0.421117 | − | 0.907006i | \(-0.361638\pi\) | ||||
0.421117 | + | 0.907006i | \(0.361638\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24621 | −0.952538 | −0.476269 | − | 0.879300i | \(-0.658011\pi\) | ||||
−0.476269 | + | 0.879300i | \(0.658011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.1231 | −1.91420 | −0.957101 | − | 0.289755i | \(-0.906426\pi\) | ||||
−0.957101 | + | 0.289755i | \(0.906426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.2462 | 2.74946 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0000 | 1.37361 | 0.686803 | − | 0.726844i | \(-0.259014\pi\) | ||||
0.686803 | + | 0.726844i | \(0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.12311 | −0.635443 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.24621 | −0.763096 | −0.381548 | − | 0.924349i | \(-0.624609\pi\) | ||||
−0.381548 | + | 0.924349i | \(0.624609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.24621 | −0.496981 | −0.248491 | − | 0.968634i | \(-0.579935\pi\) | ||||
−0.248491 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.2462 | 1.16766 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.87689 | 0.548693 | 0.274347 | − | 0.961631i | \(-0.411538\pi\) | ||||
0.274347 | + | 0.961631i | \(0.411538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12311 | 0.121818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 26.2462 | 2.75135 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.12311 | 0.525620 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0000 | 1.39305 | 0.696526 | − | 0.717532i | \(-0.254728\pi\) | ||||
0.696526 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3693 | 1.12025 | 0.560126 | − | 0.828407i | \(-0.310753\pi\) | ||||
0.560126 | + | 0.828407i | \(0.310753\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.24621 | −0.217149 | −0.108575 | − | 0.994088i | \(-0.534629\pi\) | ||||
−0.108575 | + | 0.994088i | \(0.534629\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.24621 | −0.406713 | −0.203357 | − | 0.979105i | \(-0.565185\pi\) | ||||
−0.203357 | + | 0.979105i | \(0.565185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.87689 | −0.646924 | −0.323462 | − | 0.946241i | \(-0.604847\pi\) | ||||
−0.323462 | + | 0.946241i | \(0.604847\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.12311 | −0.477732 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.75379 | −0.527449 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.87689 | 0.610226 | 0.305113 | − | 0.952316i | \(-0.401306\pi\) | ||||
0.305113 | + | 0.952316i | \(0.401306\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.24621 | 0.720475 | 0.360237 | − | 0.932861i | \(-0.382696\pi\) | ||||
0.360237 | + | 0.932861i | \(0.382696\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26.2462 | −2.27584 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.87689 | 0.245790 | 0.122895 | − | 0.992420i | \(-0.460782\pi\) | ||||
0.122895 | + | 0.992420i | \(0.460782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3693 | 1.30361 | 0.651804 | − | 0.758387i | \(-0.274012\pi\) | ||||
0.651804 | + | 0.758387i | \(0.274012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2462 | 0.856831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.24621 | −0.684811 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.2462 | 1.65863 | 0.829317 | − | 0.558778i | \(-0.188730\pi\) | ||||
0.829317 | + | 0.558778i | \(0.188730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3693 | −1.41349 | −0.706747 | − | 0.707466i | \(-0.749838\pi\) | ||||
−0.706747 | + | 0.707466i | \(0.749838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.12311 | 0.572142 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.3693 | 1.54584 | 0.772920 | − | 0.634504i | \(-0.218795\pi\) | ||||
0.772920 | + | 0.634504i | \(0.218795\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.2462 | 2.06849 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.49242 | 0.665178 | 0.332589 | − | 0.943072i | \(-0.392078\pi\) | ||||
0.332589 | + | 0.943072i | \(0.392078\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.8769 | −0.841679 | −0.420840 | − | 0.907135i | \(-0.638265\pi\) | ||||
−0.420840 | + | 0.907135i | \(0.638265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.2462 | 1.01894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.12311 | −0.387270 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2462 | 0.915325 | 0.457662 | − | 0.889126i | \(-0.348687\pi\) | ||||
0.457662 | + | 0.889126i | \(0.348687\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.246211 | 0.0183007 | 0.00915037 | − | 0.999958i | \(-0.497087\pi\) | ||||
0.00915037 | + | 0.999958i | \(0.497087\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.12311 | 0.376658 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.24621 | −0.164259 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.2462 | 1.74528 | 0.872640 | − | 0.488364i | \(-0.162406\pi\) | ||||
0.872640 | + | 0.488364i | \(0.162406\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6155 | 1.39051 | 0.695254 | − | 0.718764i | \(-0.255292\pi\) | ||||
0.695254 | + | 0.718764i | \(0.255292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 42.2462 | 2.96510 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.2462 | −0.708745 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.8769 | 0.748796 | 0.374398 | − | 0.927268i | \(-0.377849\pi\) | ||||
0.374398 | + | 0.927268i | \(0.377849\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.24621 | −0.425988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −36.4924 | −2.47727 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.75379 | −0.387042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.8769 | −0.996231 | −0.498115 | − | 0.867111i | \(-0.665974\pi\) | ||||
−0.498115 | + | 0.867111i | \(0.665974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.6155 | −1.67813 | −0.839065 | − | 0.544032i | \(-0.816897\pi\) | ||||
−0.839065 | + | 0.544032i | \(0.816897\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.1231 | −0.856057 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.24621 | −0.404034 | −0.202017 | − | 0.979382i | \(-0.564750\pi\) | ||||
−0.202017 | + | 0.979382i | \(0.564750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.75379 | −0.499465 | −0.249733 | − | 0.968315i | \(-0.580343\pi\) | ||||
−0.249733 | + | 0.968315i | \(0.580343\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.2462 | 1.22960 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.2462 | −1.67001 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.24621 | 0.268018 | 0.134009 | − | 0.990980i | \(-0.457215\pi\) | ||||
0.134009 | + | 0.990980i | \(0.457215\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.2462 | 0.644174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.8617 | −1.98748 | −0.993740 | − | 0.111714i | \(-0.964366\pi\) | ||||
−0.993740 | + | 0.111714i | \(0.964366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.2462 | −1.63086 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3693 | 0.947713 | 0.473856 | − | 0.880602i | \(-0.342862\pi\) | ||||
0.473856 | + | 0.880602i | \(0.342862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000 | 0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.24621 | −0.502780 | −0.251390 | − | 0.967886i | \(-0.580888\pi\) | ||||
−0.251390 | + | 0.967886i | \(0.580888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.12311 | 0.432698 | 0.216349 | − | 0.976316i | \(-0.430585\pi\) | ||||
0.216349 | + | 0.976316i | \(0.430585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8769 | 0.893866 | 0.446933 | − | 0.894567i | \(-0.352516\pi\) | ||||
0.446933 | + | 0.894567i | \(0.352516\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.246211 | −0.0146877 | −0.00734387 | − | 0.999973i | \(-0.502338\pi\) | ||||
−0.00734387 | + | 0.999973i | \(0.502338\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.2462 | 1.79795 | 0.898975 | − | 0.437999i | \(-0.144313\pi\) | ||||
0.898975 | + | 0.437999i | \(0.144313\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.2462 | −0.604815 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7386 | −0.925802 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.7386 | −1.67893 | −0.839464 | − | 0.543415i | \(-0.817131\pi\) | ||||
−0.839464 | + | 0.543415i | \(0.817131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.2462 | 1.51786 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.0000 | 1.84445 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.2462 | 0.813074 | 0.406537 | − | 0.913634i | \(-0.366736\pi\) | ||||
0.406537 | + | 0.913634i | \(0.366736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.2462 | −1.71511 | −0.857553 | − | 0.514396i | \(-0.828016\pi\) | ||||
−0.857553 | + | 0.514396i | \(0.828016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.7386 | 1.17222 | 0.586108 | − | 0.810233i | \(-0.300659\pi\) | ||||
0.586108 | + | 0.810233i | \(0.300659\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.00000 | 0.112331 | 0.0561656 | − | 0.998421i | \(-0.482113\pi\) | ||||
0.0561656 | + | 0.998421i | \(0.482113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.4924 | 0.923398 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.75379 | 0.320149 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.12311 | −0.284179 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 67.2311 | 3.70657 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.12311 | −0.0617315 | −0.0308657 | − | 0.999524i | \(-0.509826\pi\) | ||||
−0.0308657 | + | 0.999524i | \(0.509826\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.24621 | −0.341267 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7386 | −1.34760 | −0.673800 | − | 0.738914i | \(-0.735339\pi\) | ||||
−0.673800 | + | 0.738914i | \(0.735339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.2462 | −0.771476 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −62.7386 | −3.38757 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.2462 | −0.550045 | −0.275023 | − | 0.961438i | \(-0.588685\pi\) | ||||
−0.275023 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4924 | −0.561646 | −0.280823 | − | 0.959760i | \(-0.590607\pi\) | ||||
−0.280823 | + | 0.959760i | \(0.590607\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.8617 | 1.48293 | 0.741465 | − | 0.670991i | \(-0.234131\pi\) | ||||
0.741465 | + | 0.670991i | \(0.234131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000 | 0.211112 | 0.105556 | − | 0.994413i | \(-0.466338\pi\) | ||||
0.105556 | + | 0.994413i | \(0.466338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.24621 | −0.222257 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.36932 | −0.384675 | −0.192338 | − | 0.981329i | \(-0.561607\pi\) | ||||
−0.192338 | + | 0.981329i | \(0.561607\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −51.2311 | −2.65978 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1231 | −0.886601 | −0.443300 | − | 0.896373i | \(-0.646193\pi\) | ||||
−0.443300 | + | 0.896373i | \(0.646193\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 42.2462 | 2.17579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.36932 | −0.173070 | −0.0865351 | − | 0.996249i | \(-0.527579\pi\) | ||||
−0.0865351 | + | 0.996249i | \(0.527579\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.12311 | 0.261778 | 0.130889 | − | 0.991397i | \(-0.458217\pi\) | ||||
0.130889 | + | 0.991397i | \(0.458217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.2462 | 0.522195 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.4924 | 0.531987 | 0.265993 | − | 0.963975i | \(-0.414300\pi\) | ||||
0.265993 | + | 0.963975i | \(0.414300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.75379 | −0.290982 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.87689 | 0.245383 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.3693 | 0.771364 | 0.385682 | − | 0.922632i | \(-0.373966\pi\) | ||||
0.385682 | + | 0.922632i | \(0.373966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7538 | 0.586956 | 0.293478 | − | 0.955966i | \(-0.405187\pi\) | ||||
0.293478 | + | 0.955966i | \(0.405187\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.4924 | −1.81782 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2462 | −0.507886 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4924 | 0.914391 | 0.457196 | − | 0.889366i | \(-0.348854\pi\) | ||||
0.457196 | + | 0.889366i | \(0.348854\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.7386 | 1.51255 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.246211 | −0.0120282 | −0.00601410 | − | 0.999982i | \(-0.501914\pi\) | ||||
−0.00601410 | + | 0.999982i | \(0.501914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.9848 | −1.51011 | −0.755054 | − | 0.655662i | \(-0.772390\pi\) | ||||
−0.755054 | + | 0.655662i | \(0.772390\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.12311 | 0.0544786 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2462 | −0.495849 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.4924 | 0.794412 | 0.397206 | − | 0.917729i | \(-0.369980\pi\) | ||||
0.397206 | + | 0.917729i | \(0.369980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.246211 | 0.0118322 | 0.00591608 | − | 0.999982i | \(-0.498117\pi\) | ||||
0.00591608 | + | 0.999982i | \(0.498117\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.2462 | −1.25553 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.63068 | 0.125556 | 0.0627778 | − | 0.998028i | \(-0.480004\pi\) | ||||
0.0627778 | + | 0.998028i | \(0.480004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.50758 | 0.166650 | 0.0833250 | − | 0.996522i | \(-0.473446\pi\) | ||||
0.0833250 | + | 0.996522i | \(0.473446\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | 0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.0000 | 0.660701 | 0.330350 | − | 0.943858i | \(-0.392833\pi\) | ||||
0.330350 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.00000 | −0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.2462 | 1.23044 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.49242 | 0.303703 | 0.151851 | − | 0.988403i | \(-0.451476\pi\) | ||||
0.151851 | + | 0.988403i | \(0.451476\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.2462 | −1.87445 | −0.937226 | − | 0.348721i | \(-0.886616\pi\) | ||||
−0.937226 | + | 0.348721i | \(0.886616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.1231 | −1.72526 | −0.862629 | − | 0.505838i | \(-0.831183\pi\) | ||||
−0.862629 | + | 0.505838i | \(0.831183\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.7386 | 0.867121 | 0.433560 | − | 0.901125i | \(-0.357257\pi\) | ||||
0.433560 | + | 0.901125i | \(0.357257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0000 | 1.47762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.4924 | 0.574402 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.12311 | 0.235064 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.4924 | 1.66738 | 0.833691 | − | 0.552232i | \(-0.186224\pi\) | ||||
0.833691 | + | 0.552232i | \(0.186224\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.2462 | −1.19672 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0000 | 0.454077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6155 | 0.616978 | 0.308489 | − | 0.951228i | \(-0.400177\pi\) | ||||
0.308489 | + | 0.951228i | \(0.400177\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.50758 | 0.0680360 | 0.0340180 | − | 0.999421i | \(-0.489170\pi\) | ||||
0.0340180 | + | 0.999421i | \(0.489170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.26137 | −0.417111 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.9848 | 1.83842 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.63068 | −0.207298 | −0.103649 | − | 0.994614i | \(-0.533052\pi\) | ||||
−0.103649 | + | 0.994614i | \(0.533052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.61553 | −0.0720328 | −0.0360164 | − | 0.999351i | \(-0.511467\pi\) | ||||
−0.0360164 | + | 0.999351i | \(0.511467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | 0.620539 | 0.310270 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.7538 | 0.962331 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.3693 | 0.500992 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.2462 | 1.15431 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7386 | 0.819383 | 0.409692 | − | 0.912224i | \(-0.365636\pi\) | ||||
0.409692 | + | 0.912224i | \(0.365636\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000 | 0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.2462 | −0.443813 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.24621 | −0.0971122 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38.4924 | −1.65799 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.24621 | 0.354532 | 0.177266 | − | 0.984163i | \(-0.443275\pi\) | ||||
0.177266 | + | 0.984163i | \(0.443275\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.24621 | −0.181888 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.75379 | −0.417042 | −0.208521 | − | 0.978018i | \(-0.566865\pi\) | ||||
−0.208521 | + | 0.978018i | \(0.566865\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.2462 | −1.79975 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.9848 | −1.06246 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.50758 | 0.0638781 | 0.0319391 | − | 0.999490i | \(-0.489832\pi\) | ||||
0.0319391 | + | 0.999490i | \(0.489832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.0000 | 1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.7386 | 0.958319 | 0.479160 | − | 0.877728i | \(-0.340942\pi\) | ||||
0.479160 | + | 0.877728i | \(0.340942\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.87689 | −0.289313 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.7386 | −1.03710 | −0.518549 | − | 0.855048i | \(-0.673528\pi\) | ||||
−0.518549 | + | 0.855048i | \(0.673528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.38447 | 0.0997870 | 0.0498935 | − | 0.998755i | \(-0.484112\pi\) | ||||
0.0498935 | + | 0.998755i | \(0.484112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.12311 | −0.213648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.9848 | 1.78948 | 0.894741 | − | 0.446585i | \(-0.147360\pi\) | ||||
0.894741 | + | 0.446585i | \(0.147360\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.4924 | −0.850169 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.0000 | −0.828315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 46.7386 | 1.92911 | 0.964555 | − | 0.263882i | \(-0.0850030\pi\) | ||||
0.964555 | + | 0.263882i | \(0.0850030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.4924 | 1.50364 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.8617 | −1.63693 | −0.818463 | − | 0.574560i | \(-0.805173\pi\) | ||||
−0.818463 | + | 0.574560i | \(0.805173\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.75379 | −0.235882 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.4924 | −1.00073 | −0.500367 | − | 0.865814i | \(-0.666801\pi\) | ||||
−0.500367 | + | 0.865814i | \(0.666801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.9848 | −1.26390 | −0.631949 | − | 0.775010i | \(-0.717745\pi\) | ||||
−0.631949 | + | 0.775010i | \(0.717745\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1231 | 0.532650 | 0.266325 | − | 0.963883i | \(-0.414190\pi\) | ||||
0.266325 | + | 0.963883i | \(0.414190\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 67.2311 | 2.71988 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.36932 | 0.297644 | 0.148822 | − | 0.988864i | \(-0.452452\pi\) | ||||
0.148822 | + | 0.988864i | \(0.452452\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.61553 | −0.387107 | −0.193553 | − | 0.981090i | \(-0.562001\pi\) | ||||
−0.193553 | + | 0.981090i | \(0.562001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.1231 | −0.849009 | −0.424505 | − | 0.905426i | \(-0.639552\pi\) | ||||
−0.424505 | + | 0.905426i | \(0.639552\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −51.2311 | −2.05253 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.75379 | 0.229419 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8617 | 0.551827 | 0.275914 | − | 0.961182i | \(-0.411020\pi\) | ||||
0.275914 | + | 0.961182i | \(0.411020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.87689 | 0.272901 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −98.6004 | −3.90669 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.2462 | 1.43164 | 0.715820 | − | 0.698285i | \(-0.246053\pi\) | ||||
0.715820 | + | 0.698285i | \(0.246053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.4924 | −1.28138 | −0.640688 | − | 0.767801i | \(-0.721351\pi\) | ||||
−0.640688 | + | 0.767801i | \(0.721351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.1231 | 0.515923 | 0.257961 | − | 0.966155i | \(-0.416949\pi\) | ||||
0.257961 | + | 0.966155i | \(0.416949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.7386 | 1.75076 | 0.875379 | − | 0.483437i | \(-0.160612\pi\) | ||||
0.875379 | + | 0.483437i | \(0.160612\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.24621 | 0.322206 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.0000 | −1.01282 | −0.506408 | − | 0.862294i | \(-0.669027\pi\) | ||||
−0.506408 | + | 0.862294i | \(0.669027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00000 | 0.0777910 | 0.0388955 | − | 0.999243i | \(-0.487616\pi\) | ||||
0.0388955 | + | 0.999243i | \(0.487616\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.2462 | −1.01778 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.2462 | 1.63578 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.2462 | −0.780434 | −0.390217 | − | 0.920723i | \(-0.627600\pi\) | ||||
−0.390217 | + | 0.920723i | \(0.627600\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.73863 | 0.182120 | 0.0910602 | − | 0.995845i | \(-0.470974\pi\) | ||||
0.0910602 | + | 0.995845i | \(0.470974\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −51.2311 | −1.96607 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.75379 | 0.373218 | 0.186609 | − | 0.982434i | \(-0.440250\pi\) | ||||
0.186609 | + | 0.982434i | \(0.440250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.87689 | 0.109920 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −51.2311 | −1.95175 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.1231 | −0.499226 | −0.249613 | − | 0.968346i | \(-0.580303\pi\) | ||||
−0.249613 | + | 0.968346i | \(0.580303\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.3693 | 0.582991 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.24621 | 0.0850813 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.2462 | 0.989895 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −71.7235 | −2.69744 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.9848 | 1.91478 | 0.957388 | − | 0.288805i | \(-0.0932578\pi\) | ||||
0.957388 | + | 0.288805i | \(0.0932578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.4924 | −1.36665 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.2462 | 0.383187 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.2462 | 0.829644 | 0.414822 | − | 0.909903i | \(-0.363844\pi\) | ||||
0.414822 | + | 0.909903i | \(0.363844\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −58.2462 | −2.16920 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.24621 | −0.306257 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.6155 | 1.09838 | 0.549190 | − | 0.835698i | \(-0.314936\pi\) | ||||
0.549190 | + | 0.835698i | \(0.314936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.01515 | −0.259465 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.6155 | −1.38936 | −0.694681 | − | 0.719318i | \(-0.744454\pi\) | ||||
−0.694681 | + | 0.719318i | \(0.744454\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.4924 | 0.460164 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.1231 | −1.21845 | −0.609227 | − | 0.792996i | \(-0.708520\pi\) | ||||
−0.609227 | + | 0.792996i | \(0.708520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.8617 | 0.728657 | 0.364328 | − | 0.931271i | \(-0.381299\pi\) | ||||
0.364328 | + | 0.931271i | \(0.381299\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.2462 | 0.741764 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.5076 | 0.420478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.63068 | 0.0959950 | 0.0479975 | − | 0.998847i | \(-0.484716\pi\) | ||||
0.0479975 | + | 0.998847i | \(0.484716\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.3693 | −0.632134 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6155 | −0.494865 | −0.247432 | − | 0.968905i | \(-0.579587\pi\) | ||||
−0.247432 | + | 0.968905i | \(0.579587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.0000 | −1.52250 | −0.761249 | − | 0.648459i | \(-0.775414\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.7538 | 0.787540 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.7386 | 1.10991 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.7538 | 1.14507 | 0.572535 | − | 0.819880i | \(-0.305960\pi\) | ||||
0.572535 | + | 0.819880i | \(0.305960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.4773 | 1.70764 | 0.853819 | − | 0.520569i | \(-0.174280\pi\) | ||||
0.853819 | + | 0.520569i | \(0.174280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.12311 | 0.255870 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.2462 | 0.367109 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.3693 | 0.691321 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.2462 | 1.36333 | 0.681665 | − | 0.731664i | \(-0.261256\pi\) | ||||
0.681665 | + | 0.731664i | \(0.261256\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.2311 | 1.25267 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2462 | −0.363854 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.7538 | 0.416341 | 0.208170 | − | 0.978093i | \(-0.433249\pi\) | ||||
0.208170 | + | 0.978093i | \(0.433249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7386 | −0.521415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.49242 | 0.299691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.2462 | 0.925057 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.2462 | 0.430554 | 0.215277 | − | 0.976553i | \(-0.430935\pi\) | ||||
0.215277 | + | 0.976553i | \(0.430935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.1231 | −0.601274 | −0.300637 | − | 0.953739i | \(-0.597199\pi\) | ||||
−0.300637 | + | 0.953739i | \(0.597199\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.49242 | 0.297477 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.7386 | 0.863384 | 0.431692 | − | 0.902021i | \(-0.357917\pi\) | ||||
0.431692 | + | 0.902021i | \(0.357917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.6307 | −0.719140 | −0.359570 | − | 0.933118i | \(-0.617077\pi\) | ||||
−0.359570 | + | 0.933118i | \(0.617077\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.5076 | −0.817439 | −0.408719 | − | 0.912660i | \(-0.634024\pi\) | ||||
−0.408719 | + | 0.912660i | \(0.634024\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7386 | 0.720283 | 0.360141 | − | 0.932898i | \(-0.382728\pi\) | ||||
0.360141 | + | 0.932898i | \(0.382728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.6155 | 0.748934 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.8769 | −0.376410 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.0000 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.2462 | 0.455684 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.8617 | 1.23222 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.2462 | −0.899709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1231 | −0.723241 | −0.361621 | − | 0.932325i | \(-0.617776\pi\) | ||||
−0.361621 | + | 0.932325i | \(0.617776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.8769 | −1.05473 | −0.527367 | − | 0.849637i | \(-0.676821\pi\) | ||||
−0.527367 | + | 0.849637i | \(0.676821\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.1231 | 0.857189 | 0.428595 | − | 0.903497i | \(-0.359009\pi\) | ||||
0.428595 | + | 0.903497i | \(0.359009\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.3693 | −1.61247 | −0.806235 | − | 0.591595i | \(-0.798498\pi\) | ||||
−0.806235 | + | 0.591595i | \(0.798498\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | 0.476014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.75379 | −0.330875 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0000 | 1.08428 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.12311 | −0.173193 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.6155 | −1.81047 | −0.905234 | − | 0.424914i | \(-0.860304\pi\) | ||||
−0.905234 | + | 0.424914i | \(0.860304\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.4924 | 0.488262 | 0.244131 | − | 0.969742i | \(-0.421497\pi\) | ||||
0.244131 | + | 0.969742i | \(0.421497\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.492423 | −0.0165713 | −0.00828567 | − | 0.999966i | \(-0.502637\pi\) | ||||
−0.00828567 | + | 0.999966i | \(0.502637\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.38447 | −0.214370 | −0.107185 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107185 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.2311 | −1.18161 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −67.2311 | −2.24980 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.2462 | 0.409346 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.7386 | −1.95904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.2311 | 0.374161 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.246211 | 0.00818434 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.9848 | 0.962426 | 0.481213 | − | 0.876604i | \(-0.340196\pi\) | ||||
0.481213 | + | 0.876604i | \(0.340196\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.26137 | 0.306843 | 0.153421 | − | 0.988161i | \(-0.450971\pi\) | ||||
0.153421 | + | 0.988161i | \(0.450971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | −0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42.2462 | −1.39509 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.1231 | 1.29055 | 0.645276 | − | 0.763949i | \(-0.276742\pi\) | ||||
0.645276 | + | 0.763949i | \(0.276742\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.9848 | 1.34903 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.12311 | 0.168447 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.4924 | −0.475481 | −0.237740 | − | 0.971329i | \(-0.576407\pi\) | ||||
−0.237740 | + | 0.971329i | \(0.576407\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 98.6004 | 3.23150 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.24621 | −0.0734590 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0000 | −0.457360 | −0.228680 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228680 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.4773 | 1.41732 | 0.708659 | − | 0.705551i | \(-0.249300\pi\) | ||||
0.708659 | + | 0.705551i | \(0.249300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.2462 | −0.333663 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.7386 | 0.868889 | 0.434444 | − | 0.900699i | \(-0.356945\pi\) | ||||
0.434444 | + | 0.900699i | \(0.356945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.7538 | 0.706158 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.1231 | −1.46168 | −0.730840 | − | 0.682548i | \(-0.760872\pi\) | ||||
−0.730840 | + | 0.682548i | \(0.760872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | −0.129437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.7386 | −0.475935 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7386 | 0.636730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.2462 | 0.780513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.3693 | −1.65193 | −0.825963 | − | 0.563724i | \(-0.809368\pi\) | ||||
−0.825963 | + | 0.563724i | \(0.809368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.2462 | −1.03483 | −0.517415 | − | 0.855735i | \(-0.673106\pi\) | ||||
−0.517415 | + | 0.855735i | \(0.673106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −78.7386 | −2.52424 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.8769 | −0.987839 | −0.493920 | − | 0.869508i | \(-0.664436\pi\) | ||||
−0.493920 | + | 0.869508i | \(0.664436\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.0000 | −0.639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.3693 | 1.51085 | 0.755423 | − | 0.655237i | \(-0.227431\pi\) | ||||
0.755423 | + | 0.655237i | \(0.227431\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.00000 | 0.0637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0000 | 1.01754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.1231 | −0.480401 | −0.240201 | − | 0.970723i | \(-0.577213\pi\) | ||||
−0.240201 | + | 0.970723i | \(0.577213\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.6155 | 0.621854 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.61553 | 0.177846 | 0.0889228 | − | 0.996039i | \(-0.471658\pi\) | ||||
0.0889228 | + | 0.996039i | \(0.471658\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5760.2.a.cg.1.1 | 2 | ||
3.2 | odd | 2 | 1920.2.a.ba.1.1 | yes | 2 | ||
4.3 | odd | 2 | 5760.2.a.cj.1.2 | 2 | |||
8.3 | odd | 2 | 5760.2.a.cc.1.2 | 2 | |||
8.5 | even | 2 | 5760.2.a.bx.1.1 | 2 | |||
12.11 | even | 2 | 1920.2.a.y.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 9600.2.a.ct.1.2 | 2 | |||
24.5 | odd | 2 | 1920.2.a.z.1.1 | yes | 2 | ||
24.11 | even | 2 | 1920.2.a.bb.1.2 | yes | 2 | ||
48.5 | odd | 4 | 3840.2.k.bd.1921.2 | 4 | |||
48.11 | even | 4 | 3840.2.k.bc.1921.3 | 4 | |||
48.29 | odd | 4 | 3840.2.k.bd.1921.4 | 4 | |||
48.35 | even | 4 | 3840.2.k.bc.1921.1 | 4 | |||
60.59 | even | 2 | 9600.2.a.cw.1.1 | 2 | |||
120.29 | odd | 2 | 9600.2.a.dg.1.2 | 2 | |||
120.59 | even | 2 | 9600.2.a.cl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1920.2.a.y.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
1920.2.a.z.1.1 | yes | 2 | 24.5 | odd | 2 | ||
1920.2.a.ba.1.1 | yes | 2 | 3.2 | odd | 2 | ||
1920.2.a.bb.1.2 | yes | 2 | 24.11 | even | 2 | ||
3840.2.k.bc.1921.1 | 4 | 48.35 | even | 4 | |||
3840.2.k.bc.1921.3 | 4 | 48.11 | even | 4 | |||
3840.2.k.bd.1921.2 | 4 | 48.5 | odd | 4 | |||
3840.2.k.bd.1921.4 | 4 | 48.29 | odd | 4 | |||
5760.2.a.bx.1.1 | 2 | 8.5 | even | 2 | |||
5760.2.a.cc.1.2 | 2 | 8.3 | odd | 2 | |||
5760.2.a.cg.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5760.2.a.cj.1.2 | 2 | 4.3 | odd | 2 | |||
9600.2.a.cl.1.1 | 2 | 120.59 | even | 2 | |||
9600.2.a.ct.1.2 | 2 | 15.14 | odd | 2 | |||
9600.2.a.cw.1.1 | 2 | 60.59 | even | 2 | |||
9600.2.a.dg.1.2 | 2 | 120.29 | odd | 2 |