Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,2,Mod(1,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1143.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.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: | \(9.12690095103\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.81509.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 5x^{3} + 3x^{2} + 5x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 381) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.21568\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1143.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21568 | 0.859612 | 0.429806 | − | 0.902921i | \(-0.358582\pi\) | ||||
0.429806 | + | 0.902921i | \(0.358582\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.522133 | −0.261067 | ||||||||
\(5\) | −1.83044 | −0.818598 | −0.409299 | − | 0.912400i | \(-0.634227\pi\) | ||||
−0.409299 | + | 0.912400i | \(0.634227\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.18527 | −0.825953 | −0.412976 | − | 0.910742i | \(-0.635511\pi\) | ||||
−0.412976 | + | 0.910742i | \(0.635511\pi\) | |||||||
\(8\) | −3.06610 | −1.08403 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.22522 | −0.703677 | ||||||||
\(11\) | 4.11261 | 1.24000 | 0.619999 | − | 0.784602i | \(-0.287133\pi\) | ||||
0.619999 | + | 0.784602i | \(0.287133\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.89879 | 0.803979 | 0.401989 | − | 0.915644i | \(-0.368319\pi\) | ||||
0.401989 | + | 0.915644i | \(0.368319\pi\) | |||||||
\(14\) | −2.65657 | −0.709999 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.68311 | −0.670778 | ||||||||
\(17\) | 2.75779 | 0.668862 | 0.334431 | − | 0.942420i | \(-0.391456\pi\) | ||||
0.334431 | + | 0.942420i | \(0.391456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.55536 | 1.04507 | 0.522536 | − | 0.852617i | \(-0.324986\pi\) | ||||
0.522536 | + | 0.852617i | \(0.324986\pi\) | |||||||
\(20\) | 0.955734 | 0.213709 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.99960 | 1.06592 | ||||||||
\(23\) | 8.48701 | 1.76966 | 0.884832 | − | 0.465909i | \(-0.154273\pi\) | ||||
0.884832 | + | 0.465909i | \(0.154273\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.64948 | −0.329897 | ||||||||
\(26\) | 3.52398 | 0.691110 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.14100 | 0.215629 | ||||||||
\(29\) | 6.07653 | 1.12838 | 0.564191 | − | 0.825644i | \(-0.309188\pi\) | ||||
0.564191 | + | 0.825644i | \(0.309188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.34154 | −1.67779 | −0.838895 | − | 0.544294i | \(-0.816798\pi\) | ||||
−0.838895 | + | 0.544294i | \(0.816798\pi\) | |||||||
\(32\) | 2.87040 | 0.507420 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.35257 | 0.574962 | ||||||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.54827 | 0.747731 | 0.373866 | − | 0.927483i | \(-0.378032\pi\) | ||||
0.373866 | + | 0.927483i | \(0.378032\pi\) | |||||||
\(38\) | 5.53784 | 0.898356 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.61231 | 0.887384 | ||||||||
\(41\) | 8.30158 | 1.29649 | 0.648244 | − | 0.761432i | \(-0.275504\pi\) | ||||
0.648244 | + | 0.761432i | \(0.275504\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.38708 | −0.211528 | −0.105764 | − | 0.994391i | \(-0.533729\pi\) | ||||
−0.105764 | + | 0.994391i | \(0.533729\pi\) | |||||||
\(44\) | −2.14733 | −0.323722 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.3175 | 1.52123 | ||||||||
\(47\) | 1.75070 | 0.255366 | 0.127683 | − | 0.991815i | \(-0.459246\pi\) | ||||
0.127683 | + | 0.991815i | \(0.459246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.22462 | −0.317802 | ||||||||
\(50\) | −2.00524 | −0.283584 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.51355 | −0.209892 | ||||||||
\(53\) | −9.57494 | −1.31522 | −0.657610 | − | 0.753359i | \(-0.728432\pi\) | ||||
−0.657610 | + | 0.753359i | \(0.728432\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.52789 | −1.01506 | ||||||||
\(56\) | 6.70023 | 0.895356 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.38708 | 0.969972 | ||||||||
\(59\) | 4.21813 | 0.549154 | 0.274577 | − | 0.961565i | \(-0.411462\pi\) | ||||
0.274577 | + | 0.961565i | \(0.411462\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.40296 | 0.307668 | 0.153834 | − | 0.988097i | \(-0.450838\pi\) | ||||
0.153834 | + | 0.988097i | \(0.450838\pi\) | |||||||
\(62\) | −11.3563 | −1.44225 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.85570 | 1.10696 | ||||||||
\(65\) | −5.30606 | −0.658136 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.62093 | 0.686705 | 0.343353 | − | 0.939207i | \(-0.388437\pi\) | ||||
0.343353 | + | 0.939207i | \(0.388437\pi\) | |||||||
\(68\) | −1.43993 | −0.174617 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.86270 | 0.581204 | ||||||||
\(71\) | −8.49454 | −1.00812 | −0.504058 | − | 0.863670i | \(-0.668160\pi\) | ||||
−0.504058 | + | 0.863670i | \(0.668160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.92994 | −0.694046 | −0.347023 | − | 0.937857i | \(-0.612807\pi\) | ||||
−0.347023 | + | 0.937857i | \(0.612807\pi\) | |||||||
\(74\) | 5.52922 | 0.642759 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.37850 | −0.272833 | ||||||||
\(77\) | −8.98715 | −1.02418 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.59193 | 0.404124 | 0.202062 | − | 0.979373i | \(-0.435236\pi\) | ||||
0.202062 | + | 0.979373i | \(0.435236\pi\) | |||||||
\(80\) | 4.91128 | 0.549097 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.0920 | 1.11448 | ||||||||
\(83\) | 15.1872 | 1.66702 | 0.833508 | − | 0.552507i | \(-0.186329\pi\) | ||||
0.833508 | + | 0.552507i | \(0.186329\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.04797 | −0.547529 | ||||||||
\(86\) | −1.68625 | −0.181832 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.6097 | −1.34419 | ||||||||
\(89\) | −1.27835 | −0.135504 | −0.0677522 | − | 0.997702i | \(-0.521583\pi\) | ||||
−0.0677522 | + | 0.997702i | \(0.521583\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.33462 | −0.664048 | ||||||||
\(92\) | −4.43135 | −0.462000 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.12828 | 0.219515 | ||||||||
\(95\) | −8.33832 | −0.855493 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.8730 | 1.81473 | 0.907363 | − | 0.420347i | \(-0.138092\pi\) | ||||
0.907363 | + | 0.420347i | \(0.138092\pi\) | |||||||
\(98\) | −2.70441 | −0.273187 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.861251 | 0.0861251 | ||||||||
\(101\) | 6.16506 | 0.613446 | 0.306723 | − | 0.951799i | \(-0.400767\pi\) | ||||
0.306723 | + | 0.951799i | \(0.400767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.09114 | −0.501645 | −0.250823 | − | 0.968033i | \(-0.580701\pi\) | ||||
−0.250823 | + | 0.968033i | \(0.580701\pi\) | |||||||
\(104\) | −8.88796 | −0.871536 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.6400 | −1.13058 | ||||||||
\(107\) | −14.0265 | −1.35599 | −0.677995 | − | 0.735066i | \(-0.737151\pi\) | ||||
−0.677995 | + | 0.735066i | \(0.737151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.5027 | −1.38911 | −0.694554 | − | 0.719440i | \(-0.744398\pi\) | ||||
−0.694554 | + | 0.719440i | \(0.744398\pi\) | |||||||
\(110\) | −9.15148 | −0.872559 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.86331 | 0.554031 | ||||||||
\(113\) | −11.1075 | −1.04491 | −0.522453 | − | 0.852668i | \(-0.674983\pi\) | ||||
−0.522453 | + | 0.852668i | \(0.674983\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.5350 | −1.44864 | ||||||||
\(116\) | −3.17276 | −0.294583 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.12788 | 0.472060 | ||||||||
\(119\) | −6.02650 | −0.552448 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.91357 | 0.537597 | ||||||||
\(122\) | 2.92122 | 0.264475 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.87752 | 0.438015 | ||||||||
\(125\) | 12.1715 | 1.08865 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 5.02485 | 0.444139 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.45045 | −0.565741 | ||||||||
\(131\) | 11.5951 | 1.01307 | 0.506536 | − | 0.862219i | \(-0.330926\pi\) | ||||
0.506536 | + | 0.862219i | \(0.330926\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.95467 | −0.863179 | ||||||||
\(134\) | 6.83322 | 0.590300 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.45564 | −0.725065 | ||||||||
\(137\) | 8.85755 | 0.756751 | 0.378376 | − | 0.925652i | \(-0.376483\pi\) | ||||
0.378376 | + | 0.925652i | \(0.376483\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.2036 | 1.37437 | 0.687184 | − | 0.726483i | \(-0.258847\pi\) | ||||
0.687184 | + | 0.726483i | \(0.258847\pi\) | |||||||
\(140\) | −2.08853 | −0.176513 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.3266 | −0.866589 | ||||||||
\(143\) | 11.9216 | 0.996933 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1227 | −0.923692 | ||||||||
\(146\) | −7.20888 | −0.596611 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.37480 | −0.195208 | ||||||||
\(149\) | 21.9339 | 1.79690 | 0.898448 | − | 0.439081i | \(-0.144696\pi\) | ||||
0.898448 | + | 0.439081i | \(0.144696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8638 | 1.37236 | 0.686180 | − | 0.727432i | \(-0.259286\pi\) | ||||
0.686180 | + | 0.727432i | \(0.259286\pi\) | |||||||
\(152\) | −13.9672 | −1.13289 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.9255 | −0.880398 | ||||||||
\(155\) | 17.0991 | 1.37344 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5711 | 1.40232 | 0.701162 | − | 0.713002i | \(-0.252665\pi\) | ||||
0.701162 | + | 0.713002i | \(0.252665\pi\) | |||||||
\(158\) | 4.36662 | 0.347390 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.25410 | −0.415373 | ||||||||
\(161\) | −18.5464 | −1.46166 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.46184 | 0.271152 | 0.135576 | − | 0.990767i | \(-0.456711\pi\) | ||||
0.135576 | + | 0.990767i | \(0.456711\pi\) | |||||||
\(164\) | −4.33453 | −0.338470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.4628 | 1.43299 | ||||||||
\(167\) | −5.79387 | −0.448343 | −0.224172 | − | 0.974550i | \(-0.571968\pi\) | ||||
−0.224172 | + | 0.974550i | \(0.571968\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.59704 | −0.353618 | ||||||||
\(170\) | −6.13669 | −0.470663 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.724243 | 0.0552230 | ||||||||
\(173\) | −14.0982 | −1.07187 | −0.535934 | − | 0.844260i | \(-0.680040\pi\) | ||||
−0.535934 | + | 0.844260i | \(0.680040\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.60456 | 0.272479 | ||||||||
\(176\) | −11.0346 | −0.831764 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.55405 | −0.116481 | ||||||||
\(179\) | 3.46373 | 0.258892 | 0.129446 | − | 0.991586i | \(-0.458680\pi\) | ||||
0.129446 | + | 0.991586i | \(0.458680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.8558 | −1.32721 | −0.663607 | − | 0.748082i | \(-0.730975\pi\) | ||||
−0.663607 | + | 0.748082i | \(0.730975\pi\) | |||||||
\(182\) | −7.70084 | −0.570824 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −26.0220 | −1.91837 | ||||||||
\(185\) | −8.32534 | −0.612091 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3417 | 0.829388 | ||||||||
\(188\) | −0.914097 | −0.0666674 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.1367 | −0.735393 | ||||||||
\(191\) | −1.22583 | −0.0886980 | −0.0443490 | − | 0.999016i | \(-0.514121\pi\) | ||||
−0.0443490 | + | 0.999016i | \(0.514121\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.74900 | 0.701748 | 0.350874 | − | 0.936423i | \(-0.385885\pi\) | ||||
0.350874 | + | 0.936423i | \(0.385885\pi\) | |||||||
\(194\) | 21.7278 | 1.55996 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.16155 | 0.0829675 | ||||||||
\(197\) | 20.1537 | 1.43589 | 0.717946 | − | 0.696099i | \(-0.245082\pi\) | ||||
0.717946 | + | 0.696099i | \(0.245082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9093 | −1.48222 | −0.741112 | − | 0.671382i | \(-0.765701\pi\) | ||||
−0.741112 | + | 0.671382i | \(0.765701\pi\) | |||||||
\(200\) | 5.05748 | 0.357618 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.49471 | 0.527326 | ||||||||
\(203\) | −13.2788 | −0.931991 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.1956 | −1.06130 | ||||||||
\(206\) | −6.18918 | −0.431220 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.77777 | −0.539291 | ||||||||
\(209\) | 18.7344 | 1.29589 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3050 | −0.984794 | −0.492397 | − | 0.870371i | \(-0.663879\pi\) | ||||
−0.492397 | + | 0.870371i | \(0.663879\pi\) | |||||||
\(212\) | 4.99939 | 0.343360 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.0516 | −1.16563 | ||||||||
\(215\) | 2.53898 | 0.173157 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.4137 | 1.38577 | ||||||||
\(218\) | −17.6306 | −1.19410 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.93056 | 0.264998 | ||||||||
\(221\) | 7.99424 | 0.537751 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.7522 | −1.32271 | −0.661354 | − | 0.750074i | \(-0.730018\pi\) | ||||
−0.661354 | + | 0.750074i | \(0.730018\pi\) | |||||||
\(224\) | −6.27258 | −0.419105 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.5031 | −0.898214 | ||||||||
\(227\) | −11.0311 | −0.732163 | −0.366082 | − | 0.930583i | \(-0.619301\pi\) | ||||
−0.366082 | + | 0.930583i | \(0.619301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.27769 | 0.613087 | 0.306543 | − | 0.951857i | \(-0.400828\pi\) | ||||
0.306543 | + | 0.951857i | \(0.400828\pi\) | |||||||
\(230\) | −18.8855 | −1.24527 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.6312 | −1.22320 | ||||||||
\(233\) | 14.1129 | 0.924564 | 0.462282 | − | 0.886733i | \(-0.347031\pi\) | ||||
0.462282 | + | 0.886733i | \(0.347031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.20455 | −0.209042 | ||||||||
\(236\) | −2.20243 | −0.143366 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.32626 | −0.474891 | ||||||||
\(239\) | −8.82209 | −0.570653 | −0.285327 | − | 0.958430i | \(-0.592102\pi\) | ||||
−0.285327 | + | 0.958430i | \(0.592102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.80699 | 0.245230 | 0.122615 | − | 0.992454i | \(-0.460872\pi\) | ||||
0.122615 | + | 0.992454i | \(0.460872\pi\) | |||||||
\(242\) | 7.18898 | 0.462125 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.25467 | −0.0803218 | ||||||||
\(245\) | 4.07203 | 0.260152 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.2050 | 0.840215 | ||||||||
\(248\) | 28.6420 | 1.81877 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.7966 | 0.935818 | ||||||||
\(251\) | −20.6019 | −1.30038 | −0.650189 | − | 0.759772i | \(-0.725310\pi\) | ||||
−0.650189 | + | 0.759772i | \(0.725310\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.9038 | 2.19438 | ||||||||
\(254\) | −1.21568 | −0.0762783 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.6028 | −0.725175 | ||||||||
\(257\) | 0.849271 | 0.0529761 | 0.0264880 | − | 0.999649i | \(-0.491568\pi\) | ||||
0.0264880 | + | 0.999649i | \(0.491568\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.93918 | −0.617591 | ||||||||
\(260\) | 2.77047 | 0.171817 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.0959 | 0.870850 | ||||||||
\(263\) | −6.26932 | −0.386583 | −0.193291 | − | 0.981141i | \(-0.561916\pi\) | ||||
−0.193291 | + | 0.981141i | \(0.561916\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.5264 | 1.07664 | ||||||||
\(266\) | −12.1016 | −0.742000 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.93487 | −0.179276 | ||||||||
\(269\) | −1.25858 | −0.0767367 | −0.0383684 | − | 0.999264i | \(-0.512216\pi\) | ||||
−0.0383684 | + | 0.999264i | \(0.512216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.95401 | −0.240189 | −0.120095 | − | 0.992762i | \(-0.538320\pi\) | ||||
−0.120095 | + | 0.992762i | \(0.538320\pi\) | |||||||
\(272\) | −7.39945 | −0.448657 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.7679 | 0.650513 | ||||||||
\(275\) | −6.78369 | −0.409072 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.3123 | 1.76121 | 0.880604 | − | 0.473853i | \(-0.157137\pi\) | ||||
0.880604 | + | 0.473853i | \(0.157137\pi\) | |||||||
\(278\) | 19.6983 | 1.18142 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.2644 | −0.732937 | ||||||||
\(281\) | −17.6591 | −1.05345 | −0.526727 | − | 0.850034i | \(-0.676581\pi\) | ||||
−0.526727 | + | 0.850034i | \(0.676581\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.33208 | −0.198071 | −0.0990357 | − | 0.995084i | \(-0.531576\pi\) | ||||
−0.0990357 | + | 0.995084i | \(0.531576\pi\) | |||||||
\(284\) | 4.43528 | 0.263185 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.4928 | 0.856976 | ||||||||
\(287\) | −18.1412 | −1.07084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.39461 | −0.552624 | ||||||||
\(290\) | −13.5216 | −0.794017 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.09622 | 0.181192 | ||||||||
\(293\) | −32.5210 | −1.89990 | −0.949949 | − | 0.312405i | \(-0.898865\pi\) | ||||
−0.949949 | + | 0.312405i | \(0.898865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.72105 | −0.449537 | ||||||||
\(296\) | −13.9454 | −0.810562 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.6645 | 1.54463 | ||||||||
\(299\) | 24.6020 | 1.42277 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.03115 | 0.174713 | ||||||||
\(302\) | 20.5010 | 1.17970 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.2225 | −0.701011 | ||||||||
\(305\) | −4.39848 | −0.251856 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6417 | 1.46345 | 0.731725 | − | 0.681600i | \(-0.238716\pi\) | ||||
0.731725 | + | 0.681600i | \(0.238716\pi\) | |||||||
\(308\) | 4.69249 | 0.267379 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.7870 | 1.18062 | ||||||||
\(311\) | 13.3964 | 0.759638 | 0.379819 | − | 0.925061i | \(-0.375986\pi\) | ||||
0.379819 | + | 0.925061i | \(0.375986\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.77451 | 0.156825 | 0.0784124 | − | 0.996921i | \(-0.475015\pi\) | ||||
0.0784124 | + | 0.996921i | \(0.475015\pi\) | |||||||
\(314\) | 21.3607 | 1.20545 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.87547 | −0.105503 | ||||||||
\(317\) | 15.2283 | 0.855307 | 0.427654 | − | 0.903943i | \(-0.359340\pi\) | ||||
0.427654 | + | 0.903943i | \(0.359340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9904 | 1.39919 | ||||||||
\(320\) | −16.2098 | −0.906157 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.5464 | −1.25646 | ||||||||
\(323\) | 12.5627 | 0.699008 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.78150 | −0.265230 | ||||||||
\(326\) | 4.20848 | 0.233086 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −25.4534 | −1.40543 | ||||||||
\(329\) | −3.82574 | −0.210920 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.5670 | −0.965568 | −0.482784 | − | 0.875739i | \(-0.660374\pi\) | ||||
−0.482784 | + | 0.875739i | \(0.660374\pi\) | |||||||
\(332\) | −7.92976 | −0.435202 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.04347 | −0.385401 | ||||||||
\(335\) | −10.2888 | −0.562136 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.8978 | 1.57416 | 0.787082 | − | 0.616848i | \(-0.211591\pi\) | ||||
0.787082 | + | 0.616848i | \(0.211591\pi\) | |||||||
\(338\) | −5.58851 | −0.303975 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.63571 | 0.142941 | ||||||||
\(341\) | −38.4181 | −2.08046 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1582 | 1.08844 | ||||||||
\(344\) | 4.25293 | 0.229303 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.1388 | −0.921390 | ||||||||
\(347\) | 4.73503 | 0.254190 | 0.127095 | − | 0.991891i | \(-0.459435\pi\) | ||||
0.127095 | + | 0.991891i | \(0.459435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.63423 | 0.248065 | 0.124032 | − | 0.992278i | \(-0.460417\pi\) | ||||
0.124032 | + | 0.992278i | \(0.460417\pi\) | |||||||
\(350\) | 4.38198 | 0.234227 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.8048 | 0.629200 | ||||||||
\(353\) | −4.42642 | −0.235594 | −0.117797 | − | 0.993038i | \(-0.537583\pi\) | ||||
−0.117797 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5488 | 0.825242 | ||||||||
\(356\) | 0.667467 | 0.0353757 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.21078 | 0.222546 | ||||||||
\(359\) | −27.5629 | −1.45472 | −0.727358 | − | 0.686258i | \(-0.759252\pi\) | ||||
−0.727358 | + | 0.686258i | \(0.759252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.75131 | 0.0921740 | ||||||||
\(362\) | −21.7069 | −1.14089 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.30751 | 0.173361 | ||||||||
\(365\) | 10.8544 | 0.568145 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.7031 | −0.924093 | −0.462046 | − | 0.886856i | \(-0.652885\pi\) | ||||
−0.462046 | + | 0.886856i | \(0.652885\pi\) | |||||||
\(368\) | −22.7716 | −1.18705 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.1209 | −0.526161 | ||||||||
\(371\) | 20.9238 | 1.08631 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.0169 | −1.19177 | −0.595885 | − | 0.803070i | \(-0.703198\pi\) | ||||
−0.595885 | + | 0.803070i | \(0.703198\pi\) | |||||||
\(374\) | 13.7878 | 0.712952 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.36781 | −0.276824 | ||||||||
\(377\) | 17.6146 | 0.907196 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0972 | −1.03232 | −0.516161 | − | 0.856492i | \(-0.672639\pi\) | ||||
−0.516161 | + | 0.856492i | \(0.672639\pi\) | |||||||
\(380\) | 4.35371 | 0.223341 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.49021 | −0.0762459 | ||||||||
\(383\) | −6.19468 | −0.316533 | −0.158267 | − | 0.987396i | \(-0.550591\pi\) | ||||
−0.158267 | + | 0.987396i | \(0.550591\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.4504 | 0.838392 | ||||||||
\(386\) | 11.8516 | 0.603231 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.33208 | −0.473764 | ||||||||
\(389\) | −27.1948 | −1.37883 | −0.689416 | − | 0.724366i | \(-0.742133\pi\) | ||||
−0.689416 | + | 0.724366i | \(0.742133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.4054 | 1.18366 | ||||||||
\(392\) | 6.82088 | 0.344507 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.5004 | 1.23431 | ||||||||
\(395\) | −6.57482 | −0.330815 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.87064 | −0.344828 | −0.172414 | − | 0.985025i | \(-0.555157\pi\) | ||||
−0.172414 | + | 0.985025i | \(0.555157\pi\) | |||||||
\(398\) | −25.4190 | −1.27414 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.42575 | 0.221288 | ||||||||
\(401\) | 6.83838 | 0.341492 | 0.170746 | − | 0.985315i | \(-0.445382\pi\) | ||||
0.170746 | + | 0.985315i | \(0.445382\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.0791 | −1.34891 | ||||||||
\(404\) | −3.21898 | −0.160150 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.1427 | −0.801151 | ||||||||
\(407\) | 18.7053 | 0.927186 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.31912 | −0.263014 | −0.131507 | − | 0.991315i | \(-0.541982\pi\) | ||||
−0.131507 | + | 0.991315i | \(0.541982\pi\) | |||||||
\(410\) | −18.4729 | −0.912309 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.65825 | 0.130963 | ||||||||
\(413\) | −9.21774 | −0.453575 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.7994 | −1.36462 | ||||||||
\(416\) | 8.32067 | 0.407955 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 22.7750 | 1.11396 | ||||||||
\(419\) | −1.00985 | −0.0493344 | −0.0246672 | − | 0.999696i | \(-0.507853\pi\) | ||||
−0.0246672 | + | 0.999696i | \(0.507853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.1506 | −1.85934 | −0.929672 | − | 0.368388i | \(-0.879910\pi\) | ||||
−0.929672 | + | 0.368388i | \(0.879910\pi\) | |||||||
\(422\) | −17.3902 | −0.846542 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29.3577 | 1.42573 | ||||||||
\(425\) | −4.54893 | −0.220655 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.25111 | −0.254119 | ||||||||
\(428\) | 7.32369 | 0.354004 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.08657 | 0.148848 | ||||||||
\(431\) | −3.70132 | −0.178287 | −0.0891433 | − | 0.996019i | \(-0.528413\pi\) | ||||
−0.0891433 | + | 0.996019i | \(0.528413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.7423 | −1.09293 | −0.546463 | − | 0.837483i | \(-0.684026\pi\) | ||||
−0.546463 | + | 0.837483i | \(0.684026\pi\) | |||||||
\(434\) | 24.8165 | 1.19123 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.57235 | 0.362650 | ||||||||
\(437\) | 38.6614 | 1.84943 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.9769 | 1.57390 | 0.786952 | − | 0.617015i | \(-0.211658\pi\) | ||||
0.786952 | + | 0.617015i | \(0.211658\pi\) | |||||||
\(440\) | 23.0812 | 1.10035 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.71840 | 0.462257 | ||||||||
\(443\) | 13.3826 | 0.635827 | 0.317913 | − | 0.948120i | \(-0.397018\pi\) | ||||
0.317913 | + | 0.948120i | \(0.397018\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.33994 | 0.110924 | ||||||||
\(446\) | −24.0123 | −1.13702 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.3520 | −0.914298 | ||||||||
\(449\) | 0.0449421 | 0.00212095 | 0.00106047 | − | 0.999999i | \(-0.499662\pi\) | ||||
0.00106047 | + | 0.999999i | \(0.499662\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.1412 | 1.60764 | ||||||||
\(452\) | 5.79960 | 0.272790 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.4103 | −0.629376 | ||||||||
\(455\) | 11.5951 | 0.543589 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.83400 | −0.179347 | −0.0896735 | − | 0.995971i | \(-0.528582\pi\) | ||||
−0.0896735 | + | 0.995971i | \(0.528582\pi\) | |||||||
\(458\) | 11.2787 | 0.527017 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.11133 | 0.378193 | ||||||||
\(461\) | 34.8667 | 1.62390 | 0.811951 | − | 0.583725i | \(-0.198405\pi\) | ||||
0.811951 | + | 0.583725i | \(0.198405\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.9857 | −1.06823 | −0.534117 | − | 0.845410i | \(-0.679356\pi\) | ||||
−0.534117 | + | 0.845410i | \(0.679356\pi\) | |||||||
\(464\) | −16.3040 | −0.756894 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.1567 | 0.794767 | ||||||||
\(467\) | 6.47557 | 0.299654 | 0.149827 | − | 0.988712i | \(-0.452128\pi\) | ||||
0.149827 | + | 0.988712i | \(0.452128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2832 | −0.567186 | ||||||||
\(470\) | −3.89569 | −0.179695 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.9332 | −0.595299 | ||||||||
\(473\) | −5.70454 | −0.262295 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.51400 | −0.344766 | ||||||||
\(476\) | 3.14663 | 0.144226 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.7248 | −0.490541 | ||||||||
\(479\) | −19.2166 | −0.878027 | −0.439013 | − | 0.898480i | \(-0.644672\pi\) | ||||
−0.439013 | + | 0.898480i | \(0.644672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.1845 | 0.601160 | ||||||||
\(482\) | 4.62806 | 0.210803 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.08767 | −0.140349 | ||||||||
\(485\) | −32.7155 | −1.48553 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.9898 | −1.63085 | −0.815426 | − | 0.578861i | \(-0.803497\pi\) | ||||
−0.815426 | + | 0.578861i | \(0.803497\pi\) | |||||||
\(488\) | −7.36771 | −0.333521 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.95026 | 0.223630 | ||||||||
\(491\) | −1.56415 | −0.0705891 | −0.0352945 | − | 0.999377i | \(-0.511237\pi\) | ||||
−0.0352945 | + | 0.999377i | \(0.511237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.7578 | 0.754732 | ||||||||
\(494\) | 16.0530 | 0.722259 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.0644 | 1.12542 | ||||||||
\(497\) | 18.5628 | 0.832656 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.2919 | −0.863626 | −0.431813 | − | 0.901963i | \(-0.642126\pi\) | ||||
−0.431813 | + | 0.901963i | \(0.642126\pi\) | |||||||
\(500\) | −6.35514 | −0.284210 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.0452 | −1.11782 | ||||||||
\(503\) | 20.4806 | 0.913184 | 0.456592 | − | 0.889676i | \(-0.349070\pi\) | ||||
0.456592 | + | 0.889676i | \(0.349070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.2848 | −0.502166 | ||||||||
\(506\) | 42.4317 | 1.88632 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.522133 | 0.0231659 | ||||||||
\(509\) | −29.1499 | −1.29205 | −0.646023 | − | 0.763318i | \(-0.723569\pi\) | ||||
−0.646023 | + | 0.763318i | \(0.723569\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9585 | 0.573250 | ||||||||
\(512\) | −24.1549 | −1.06751 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.03244 | 0.0455389 | ||||||||
\(515\) | 9.31903 | 0.410646 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.19994 | 0.316653 | ||||||||
\(518\) | −12.0828 | −0.530889 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.2689 | 0.713438 | ||||||||
\(521\) | 40.0882 | 1.75629 | 0.878147 | − | 0.478390i | \(-0.158780\pi\) | ||||
0.878147 | + | 0.478390i | \(0.158780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.957838 | 0.0418833 | 0.0209417 | − | 0.999781i | \(-0.493334\pi\) | ||||
0.0209417 | + | 0.999781i | \(0.493334\pi\) | |||||||
\(524\) | −6.05421 | −0.264479 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.62146 | −0.332311 | ||||||||
\(527\) | −25.7620 | −1.12221 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.0294 | 2.13171 | ||||||||
\(530\) | 21.3064 | 0.925490 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.19766 | 0.225347 | ||||||||
\(533\) | 24.0645 | 1.04235 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.6746 | 1.11001 | ||||||||
\(536\) | −17.2343 | −0.744408 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.53002 | −0.0659639 | ||||||||
\(539\) | −9.14898 | −0.394074 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.85408 | 0.208693 | 0.104347 | − | 0.994541i | \(-0.466725\pi\) | ||||
0.104347 | + | 0.994541i | \(0.466725\pi\) | |||||||
\(542\) | −4.80680 | −0.206470 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.91595 | 0.339393 | ||||||||
\(545\) | 26.5464 | 1.13712 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.87405 | 0.208399 | 0.104200 | − | 0.994556i | \(-0.466772\pi\) | ||||
0.104200 | + | 0.994556i | \(0.466772\pi\) | |||||||
\(548\) | −4.62482 | −0.197562 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.24677 | −0.351643 | ||||||||
\(551\) | 27.6808 | 1.17924 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.84932 | −0.333787 | ||||||||
\(554\) | 35.6343 | 1.51396 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.46041 | −0.358802 | ||||||||
\(557\) | −11.1116 | −0.470813 | −0.235407 | − | 0.971897i | \(-0.575642\pi\) | ||||
−0.235407 | + | 0.971897i | \(0.575642\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.02086 | −0.170064 | ||||||||
\(560\) | −10.7324 | −0.453529 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.4678 | −0.905562 | ||||||||
\(563\) | 41.4791 | 1.74814 | 0.874069 | − | 0.485802i | \(-0.161473\pi\) | ||||
0.874069 | + | 0.485802i | \(0.161473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.3316 | 0.855358 | ||||||||
\(566\) | −4.05073 | −0.170265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.0451 | 1.09283 | ||||||||
\(569\) | −1.35775 | −0.0569197 | −0.0284598 | − | 0.999595i | \(-0.509060\pi\) | ||||
−0.0284598 | + | 0.999595i | \(0.509060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.6021 | 0.569230 | 0.284615 | − | 0.958642i | \(-0.408134\pi\) | ||||
0.284615 | + | 0.958642i | \(0.408134\pi\) | |||||||
\(572\) | −6.22465 | −0.260266 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.0538 | −0.920506 | ||||||||
\(575\) | −13.9992 | −0.583807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.39435 | −0.349461 | −0.174731 | − | 0.984616i | \(-0.555905\pi\) | ||||
−0.174731 | + | 0.984616i | \(0.555905\pi\) | |||||||
\(578\) | −11.4208 | −0.475043 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.80754 | 0.241145 | ||||||||
\(581\) | −33.1882 | −1.37688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.3780 | −1.63087 | ||||||||
\(584\) | 18.1817 | 0.752366 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.5350 | −1.63318 | ||||||||
\(587\) | −2.56937 | −0.106049 | −0.0530247 | − | 0.998593i | \(-0.516886\pi\) | ||||
−0.0530247 | + | 0.998593i | \(0.516886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.5541 | −1.75341 | ||||||||
\(590\) | −9.38629 | −0.386427 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.2035 | −0.501561 | ||||||||
\(593\) | 30.4114 | 1.24885 | 0.624423 | − | 0.781086i | \(-0.285334\pi\) | ||||
0.624423 | + | 0.781086i | \(0.285334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0311 | 0.452233 | ||||||||
\(596\) | −11.4524 | −0.469109 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 29.9081 | 1.22303 | ||||||||
\(599\) | −34.9094 | −1.42636 | −0.713179 | − | 0.700982i | \(-0.752745\pi\) | ||||
−0.713179 | + | 0.700982i | \(0.752745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.18273 | 0.129826 | 0.0649130 | − | 0.997891i | \(-0.479323\pi\) | ||||
0.0649130 | + | 0.997891i | \(0.479323\pi\) | |||||||
\(602\) | 3.68489 | 0.150185 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.80517 | −0.358277 | ||||||||
\(605\) | −10.8244 | −0.440076 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0528 | 0.773328 | 0.386664 | − | 0.922221i | \(-0.373627\pi\) | ||||
0.386664 | + | 0.922221i | \(0.373627\pi\) | |||||||
\(608\) | 13.0757 | 0.530290 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.34713 | −0.216499 | ||||||||
\(611\) | 5.07490 | 0.205308 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.13899 | −0.369120 | −0.184560 | − | 0.982821i | \(-0.559086\pi\) | ||||
−0.184560 | + | 0.982821i | \(0.559086\pi\) | |||||||
\(614\) | 31.1720 | 1.25800 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.5555 | 1.11024 | ||||||||
\(617\) | 19.8514 | 0.799186 | 0.399593 | − | 0.916693i | \(-0.369151\pi\) | ||||
0.399593 | + | 0.916693i | \(0.369151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.0742 | −1.04801 | −0.524005 | − | 0.851715i | \(-0.675563\pi\) | ||||
−0.524005 | + | 0.851715i | \(0.675563\pi\) | |||||||
\(620\) | −8.92802 | −0.358558 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.2856 | 0.652994 | ||||||||
\(623\) | 2.79353 | 0.111920 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.0318 | −0.561271 | ||||||||
\(626\) | 3.37291 | 0.134808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.17443 | −0.366100 | ||||||||
\(629\) | 12.5432 | 0.500129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.67533 | 0.265740 | 0.132870 | − | 0.991133i | \(-0.457581\pi\) | ||||
0.132870 | + | 0.991133i | \(0.457581\pi\) | |||||||
\(632\) | −11.0132 | −0.438082 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.5127 | 0.735233 | ||||||||
\(635\) | 1.83044 | 0.0726388 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.44868 | −0.255506 | ||||||||
\(638\) | 30.3802 | 1.20276 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.19770 | −0.363571 | ||||||||
\(641\) | 28.8713 | 1.14035 | 0.570174 | − | 0.821524i | \(-0.306876\pi\) | ||||
0.570174 | + | 0.821524i | \(0.306876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5900 | −0.654245 | −0.327122 | − | 0.944982i | \(-0.606079\pi\) | ||||
−0.327122 | + | 0.944982i | \(0.606079\pi\) | |||||||
\(644\) | 9.68368 | 0.381590 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.2722 | 0.600876 | ||||||||
\(647\) | −14.2463 | −0.560078 | −0.280039 | − | 0.959989i | \(-0.590347\pi\) | ||||
−0.280039 | + | 0.959989i | \(0.590347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.3475 | 0.680951 | ||||||||
\(650\) | −5.81276 | −0.227995 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.80754 | −0.0707888 | ||||||||
\(653\) | −18.3296 | −0.717291 | −0.358645 | − | 0.933474i | \(-0.616761\pi\) | ||||
−0.358645 | + | 0.933474i | \(0.616761\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.2242 | −0.829299 | ||||||||
\(656\) | −22.2741 | −0.869656 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.65086 | −0.181309 | ||||||||
\(659\) | 3.64832 | 0.142119 | 0.0710593 | − | 0.997472i | \(-0.477362\pi\) | ||||
0.0710593 | + | 0.997472i | \(0.477362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.2032 | 1.44704 | 0.723518 | − | 0.690305i | \(-0.242524\pi\) | ||||
0.723518 | + | 0.690305i | \(0.242524\pi\) | |||||||
\(662\) | −21.3557 | −0.830015 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −46.5655 | −1.80709 | ||||||||
\(665\) | 18.2214 | 0.706597 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.5716 | 1.99686 | ||||||||
\(668\) | 3.02517 | 0.117047 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.5078 | −0.483219 | ||||||||
\(671\) | 9.88245 | 0.381508 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.1826 | 0.700887 | 0.350443 | − | 0.936584i | \(-0.386031\pi\) | ||||
0.350443 | + | 0.936584i | \(0.386031\pi\) | |||||||
\(674\) | 35.1304 | 1.35317 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.40026 | 0.0923179 | ||||||||
\(677\) | 22.8068 | 0.876536 | 0.438268 | − | 0.898844i | \(-0.355592\pi\) | ||||
0.438268 | + | 0.898844i | \(0.355592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.0572 | −1.49888 | ||||||||
\(680\) | 15.4775 | 0.593537 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −46.7039 | −1.78839 | ||||||||
\(683\) | 15.4171 | 0.589918 | 0.294959 | − | 0.955510i | \(-0.404694\pi\) | ||||
0.294959 | + | 0.955510i | \(0.404694\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.2132 | −0.619475 | ||||||||
\(686\) | 24.5059 | 0.935638 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.72170 | 0.141889 | ||||||||
\(689\) | −27.7557 | −1.05741 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.2213 | 0.426880 | 0.213440 | − | 0.976956i | \(-0.431533\pi\) | ||||
0.213440 | + | 0.976956i | \(0.431533\pi\) | |||||||
\(692\) | 7.36114 | 0.279829 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.75626 | 0.218505 | ||||||||
\(695\) | −29.6597 | −1.12506 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.8940 | 0.867172 | ||||||||
\(698\) | 5.63372 | 0.213240 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.88206 | −0.0711352 | ||||||||
\(701\) | 21.5132 | 0.812543 | 0.406272 | − | 0.913752i | \(-0.366829\pi\) | ||||
0.406272 | + | 0.913752i | \(0.366829\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.7190 | 0.781432 | ||||||||
\(704\) | 36.4200 | 1.37263 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.38108 | −0.202520 | ||||||||
\(707\) | −13.4723 | −0.506678 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.8987 | 0.709757 | 0.354878 | − | 0.934912i | \(-0.384522\pi\) | ||||
0.354878 | + | 0.934912i | \(0.384522\pi\) | |||||||
\(710\) | 18.9022 | 0.709389 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.91953 | 0.146891 | ||||||||
\(713\) | −79.2817 | −2.96912 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.8218 | −0.816087 | ||||||||
\(716\) | −1.80853 | −0.0675879 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.5076 | −1.25049 | ||||||||
\(719\) | 1.02016 | 0.0380456 | 0.0190228 | − | 0.999819i | \(-0.493944\pi\) | ||||
0.0190228 | + | 0.999819i | \(0.493944\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.1255 | 0.414335 | ||||||||
\(722\) | 2.12902 | 0.0792339 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.32312 | 0.346491 | ||||||||
\(725\) | −10.0231 | −0.372250 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.8471 | 1.40367 | 0.701836 | − | 0.712339i | \(-0.252364\pi\) | ||||
0.701836 | + | 0.712339i | \(0.252364\pi\) | |||||||
\(728\) | 19.4225 | 0.719847 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.1954 | 0.488385 | ||||||||
\(731\) | −3.82528 | −0.141483 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.4516 | 1.45718 | 0.728590 | − | 0.684951i | \(-0.240176\pi\) | ||||
0.728590 | + | 0.684951i | \(0.240176\pi\) | |||||||
\(734\) | −21.5212 | −0.794361 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.3611 | 0.897963 | ||||||||
\(737\) | 23.1167 | 0.851514 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.1429 | −0.961683 | −0.480841 | − | 0.876808i | \(-0.659669\pi\) | ||||
−0.480841 | + | 0.876808i | \(0.659669\pi\) | |||||||
\(740\) | 4.34694 | 0.159797 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.4365 | 0.933804 | ||||||||
\(743\) | −22.5099 | −0.825808 | −0.412904 | − | 0.910775i | \(-0.635485\pi\) | ||||
−0.412904 | + | 0.910775i | \(0.635485\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.1487 | −1.47094 | ||||||||
\(746\) | −27.9811 | −1.02446 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.92188 | −0.216525 | ||||||||
\(749\) | 30.6516 | 1.11998 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.9403 | −1.78586 | −0.892929 | − | 0.450198i | \(-0.851353\pi\) | ||||
−0.892929 | + | 0.450198i | \(0.851353\pi\) | |||||||
\(752\) | −4.69732 | −0.171294 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.4136 | 0.779837 | ||||||||
\(755\) | −30.8683 | −1.12341 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.02286 | 0.255250 | 0.127625 | − | 0.991822i | \(-0.459265\pi\) | ||||
0.127625 | + | 0.991822i | \(0.459265\pi\) | |||||||
\(758\) | −24.4316 | −0.887396 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 25.5661 | 0.927379 | ||||||||
\(761\) | 8.69137 | 0.315062 | 0.157531 | − | 0.987514i | \(-0.449647\pi\) | ||||
0.157531 | + | 0.987514i | \(0.449647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.6923 | 1.14734 | ||||||||
\(764\) | 0.640046 | 0.0231561 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.53072 | −0.272096 | ||||||||
\(767\) | 12.2275 | 0.441508 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.3442 | 1.41879 | 0.709394 | − | 0.704812i | \(-0.248969\pi\) | ||||
0.709394 | + | 0.704812i | \(0.248969\pi\) | |||||||
\(770\) | 19.9984 | 0.720692 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.09027 | −0.183203 | ||||||||
\(773\) | 20.4406 | 0.735197 | 0.367599 | − | 0.929985i | \(-0.380180\pi\) | ||||
0.367599 | + | 0.929985i | \(0.380180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.4087 | 0.553498 | ||||||||
\(776\) | −54.8003 | −1.96722 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.0601 | −1.18526 | ||||||||
\(779\) | 37.8167 | 1.35492 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.9347 | −1.25006 | ||||||||
\(782\) | 28.4533 | 1.01749 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.96889 | 0.213175 | ||||||||
\(785\) | −32.1628 | −1.14794 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.5314 | −0.696220 | −0.348110 | − | 0.937454i | \(-0.613176\pi\) | ||||
−0.348110 | + | 0.937454i | \(0.613176\pi\) | |||||||
\(788\) | −10.5229 | −0.374863 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.99284 | −0.284373 | ||||||||
\(791\) | 24.2728 | 0.863043 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.96568 | 0.247358 | ||||||||
\(794\) | −8.35247 | −0.296418 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.9175 | 0.386959 | ||||||||
\(797\) | 14.8843 | 0.527228 | 0.263614 | − | 0.964628i | \(-0.415085\pi\) | ||||
0.263614 | + | 0.964628i | \(0.415085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.82805 | 0.170804 | ||||||||
\(800\) | −4.73468 | −0.167396 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.31325 | 0.293551 | ||||||||
\(803\) | −24.3875 | −0.860617 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.9481 | 1.19651 | ||||||||
\(806\) | −32.9194 | −1.15954 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.9027 | −0.664993 | ||||||||
\(809\) | 31.3007 | 1.10047 | 0.550237 | − | 0.835008i | \(-0.314537\pi\) | ||||
0.550237 | + | 0.835008i | \(0.314537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.7322 | −1.50053 | −0.750266 | − | 0.661136i | \(-0.770075\pi\) | ||||
−0.750266 | + | 0.661136i | \(0.770075\pi\) | |||||||
\(812\) | 6.93331 | 0.243312 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.7395 | 0.797020 | ||||||||
\(815\) | −6.33670 | −0.221965 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.31867 | −0.221062 | ||||||||
\(818\) | −6.46633 | −0.226090 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.93410 | 0.277071 | ||||||||
\(821\) | 0.382081 | 0.0133347 | 0.00666735 | − | 0.999978i | \(-0.497878\pi\) | ||||
0.00666735 | + | 0.999978i | \(0.497878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.0612 | −1.74503 | −0.872513 | − | 0.488591i | \(-0.837511\pi\) | ||||
−0.872513 | + | 0.488591i | \(0.837511\pi\) | |||||||
\(824\) | 15.6099 | 0.543797 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.2058 | −0.389899 | ||||||||
\(827\) | −47.1956 | −1.64115 | −0.820575 | − | 0.571538i | \(-0.806347\pi\) | ||||
−0.820575 | + | 0.571538i | \(0.806347\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.61126 | 0.264350 | 0.132175 | − | 0.991226i | \(-0.457804\pi\) | ||||
0.132175 | + | 0.991226i | \(0.457804\pi\) | |||||||
\(830\) | −33.7950 | −1.17304 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.6708 | 0.889974 | ||||||||
\(833\) | −6.13501 | −0.212566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.6053 | 0.367013 | ||||||||
\(836\) | −9.78186 | −0.338313 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.22765 | −0.0424084 | ||||||||
\(839\) | 2.97972 | 0.102871 | 0.0514356 | − | 0.998676i | \(-0.483620\pi\) | ||||
0.0514356 | + | 0.998676i | \(0.483620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.92418 | 0.273248 | ||||||||
\(842\) | −46.3787 | −1.59832 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.46910 | 0.257097 | ||||||||
\(845\) | 8.41461 | 0.289471 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.9227 | −0.444030 | ||||||||
\(848\) | 25.6906 | 0.882220 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.53002 | −0.189678 | ||||||||
\(851\) | 38.6012 | 1.32323 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.1661 | −1.47798 | −0.738989 | − | 0.673718i | \(-0.764696\pi\) | ||||
−0.738989 | + | 0.673718i | \(0.764696\pi\) | |||||||
\(854\) | −6.38365 | −0.218444 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 43.0065 | 1.46993 | ||||||||
\(857\) | −33.9924 | −1.16116 | −0.580579 | − | 0.814204i | \(-0.697174\pi\) | ||||
−0.580579 | + | 0.814204i | \(0.697174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.1565 | 1.33600 | 0.668001 | − | 0.744160i | \(-0.267150\pi\) | ||||
0.668001 | + | 0.744160i | \(0.267150\pi\) | |||||||
\(860\) | −1.32568 | −0.0452055 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.49961 | −0.153257 | ||||||||
\(863\) | −27.7523 | −0.944699 | −0.472350 | − | 0.881411i | \(-0.656594\pi\) | ||||
−0.472350 | + | 0.881411i | \(0.656594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.8059 | 0.877428 | ||||||||
\(866\) | −27.6473 | −0.939493 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.6587 | −0.361779 | ||||||||
\(869\) | 14.7722 | 0.501113 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2939 | 0.552096 | ||||||||
\(872\) | 44.4667 | 1.50583 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 46.9997 | 1.58979 | ||||||||
\(875\) | −26.5979 | −0.899174 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.6321 | 0.629160 | 0.314580 | − | 0.949231i | \(-0.398136\pi\) | ||||
0.314580 | + | 0.949231i | \(0.398136\pi\) | |||||||
\(878\) | 40.0892 | 1.35295 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.1982 | 0.680880 | ||||||||
\(881\) | 31.1742 | 1.05029 | 0.525143 | − | 0.851014i | \(-0.324012\pi\) | ||||
0.525143 | + | 0.851014i | \(0.324012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.2983 | −1.72633 | −0.863163 | − | 0.504926i | \(-0.831520\pi\) | ||||
−0.863163 | + | 0.504926i | \(0.831520\pi\) | |||||||
\(884\) | −4.17405 | −0.140389 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.2689 | 0.546565 | ||||||||
\(887\) | 16.3317 | 0.548364 | 0.274182 | − | 0.961678i | \(-0.411593\pi\) | ||||
0.274182 | + | 0.961678i | \(0.411593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.18527 | 0.0732914 | ||||||||
\(890\) | 2.84461 | 0.0953514 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.3133 | 0.345315 | ||||||||
\(893\) | 7.97506 | 0.266875 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.34016 | −0.211928 | ||||||||
\(896\) | −10.9806 | −0.366837 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.0546350 | 0.00182319 | ||||||||
\(899\) | −56.7641 | −1.89319 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.4056 | −0.879700 | ||||||||
\(902\) | 41.5046 | 1.38195 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 34.0567 | 1.13271 | ||||||||
\(905\) | 32.6840 | 1.08645 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.8600 | −1.29032 | −0.645162 | − | 0.764046i | \(-0.723210\pi\) | ||||
−0.645162 | + | 0.764046i | \(0.723210\pi\) | |||||||
\(908\) | 5.75973 | 0.191143 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14.0959 | 0.467276 | ||||||||
\(911\) | −24.4819 | −0.811120 | −0.405560 | − | 0.914068i | \(-0.632923\pi\) | ||||
−0.405560 | + | 0.914068i | \(0.632923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 62.4592 | 2.06710 | ||||||||
\(914\) | −4.66090 | −0.154169 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.84419 | −0.160056 | ||||||||
\(917\) | −25.3385 | −0.836750 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.7367 | 0.552092 | 0.276046 | − | 0.961144i | \(-0.410976\pi\) | ||||
0.276046 | + | 0.961144i | \(0.410976\pi\) | |||||||
\(920\) | 47.6317 | 1.57037 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 42.3866 | 1.39593 | ||||||||
\(923\) | −24.6239 | −0.810504 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.50230 | −0.246674 | ||||||||
\(926\) | −27.9431 | −0.918268 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 17.4421 | 0.572563 | ||||||||
\(929\) | 2.51047 | 0.0823658 | 0.0411829 | − | 0.999152i | \(-0.486887\pi\) | ||||
0.0411829 | + | 0.999152i | \(0.486887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.1339 | −0.332126 | ||||||||
\(932\) | −7.36879 | −0.241373 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.87219 | 0.257586 | ||||||||
\(935\) | −20.7603 | −0.678935 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.1347 | 0.494430 | 0.247215 | − | 0.968961i | \(-0.420485\pi\) | ||||
0.247215 | + | 0.968961i | \(0.420485\pi\) | |||||||
\(938\) | −14.9324 | −0.487560 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.67320 | 0.0545738 | ||||||||
\(941\) | −12.6407 | −0.412075 | −0.206037 | − | 0.978544i | \(-0.566057\pi\) | ||||
−0.206037 | + | 0.978544i | \(0.566057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70.4556 | 2.29435 | ||||||||
\(944\) | −11.3177 | −0.368360 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.93487 | −0.225472 | ||||||||
\(947\) | 33.5547 | 1.09038 | 0.545190 | − | 0.838313i | \(-0.316458\pi\) | ||||
0.545190 | + | 0.838313i | \(0.316458\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.1896 | −0.557999 | ||||||||
\(950\) | −9.13458 | −0.296365 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.4778 | 0.598869 | ||||||||
\(953\) | 33.8876 | 1.09773 | 0.548864 | − | 0.835912i | \(-0.315061\pi\) | ||||
0.548864 | + | 0.835912i | \(0.315061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.24381 | 0.0726080 | ||||||||
\(956\) | 4.60630 | 0.148979 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.3611 | −0.754763 | ||||||||
\(959\) | −19.3561 | −0.625041 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.2643 | 1.81498 | ||||||||
\(962\) | 16.0280 | 0.516765 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.98775 | −0.0640213 | ||||||||
\(965\) | −17.8450 | −0.574450 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.6965 | 0.987131 | 0.493566 | − | 0.869709i | \(-0.335693\pi\) | ||||
0.493566 | + | 0.869709i | \(0.335693\pi\) | |||||||
\(968\) | −18.1316 | −0.582771 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −39.7714 | −1.27698 | ||||||||
\(971\) | −58.6273 | −1.88144 | −0.940719 | − | 0.339186i | \(-0.889849\pi\) | ||||
−0.940719 | + | 0.339186i | \(0.889849\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.4091 | −1.13516 | ||||||||
\(974\) | −43.7519 | −1.40190 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.44742 | −0.206377 | ||||||||
\(977\) | 26.3660 | 0.843522 | 0.421761 | − | 0.906707i | \(-0.361412\pi\) | ||||
0.421761 | + | 0.906707i | \(0.361412\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.25734 | −0.168025 | ||||||||
\(980\) | −2.12614 | −0.0679171 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.90150 | −0.0606792 | ||||||||
\(983\) | −56.2112 | −1.79286 | −0.896429 | − | 0.443187i | \(-0.853848\pi\) | ||||
−0.896429 | + | 0.443187i | \(0.853848\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.8902 | −1.17542 | ||||||||
\(986\) | 20.3720 | 0.648777 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.89478 | −0.219352 | ||||||||
\(989\) | −11.7722 | −0.374335 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.1342 | −0.607816 | −0.303908 | − | 0.952701i | \(-0.598292\pi\) | ||||
−0.303908 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(992\) | −26.8139 | −0.851343 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22.5664 | 0.715762 | ||||||||
\(995\) | 38.2733 | 1.21335 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.83584 | −0.184823 | −0.0924114 | − | 0.995721i | \(-0.529457\pi\) | ||||
−0.0924114 | + | 0.995721i | \(0.529457\pi\) | |||||||
\(998\) | −23.4527 | −0.742384 | ||||||||
\(999\) | 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 | 1143.2.a.h.1.4 | 5 | ||
3.2 | odd | 2 | 381.2.a.c.1.2 | ✓ | 5 | ||
12.11 | even | 2 | 6096.2.a.be.1.5 | 5 | |||
15.14 | odd | 2 | 9525.2.a.k.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
381.2.a.c.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
1143.2.a.h.1.4 | 5 | 1.1 | even | 1 | trivial | ||
6096.2.a.be.1.5 | 5 | 12.11 | even | 2 | |||
9525.2.a.k.1.4 | 5 | 15.14 | odd | 2 |