Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 825) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | 5.23607 | 1.97905 | 0.989524 | − | 0.144370i | \(-0.0461154\pi\) | ||||
0.989524 | + | 0.144370i | \(0.0461154\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | −3.23607 | −0.897524 | −0.448762 | − | 0.893651i | \(-0.648135\pi\) | ||||
−0.448762 | + | 0.893651i | \(0.648135\pi\) | |||||||
\(14\) | 8.47214 | 2.26427 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 1.61803 | 0.381374 | ||||||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.23607 | 1.14260 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.61803 | −0.962927 | −0.481463 | − | 0.876466i | \(-0.659895\pi\) | ||||
−0.481463 | + | 0.876466i | \(0.659895\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.23607 | −1.02688 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.23607 | 0.611559 | ||||||||
\(29\) | 0.854102 | 0.158603 | 0.0793014 | − | 0.996851i | \(-0.474731\pi\) | ||||
0.0793014 | + | 0.996851i | \(0.474731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.23607 | −0.554981 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | −1.47214 | −0.242018 | −0.121009 | − | 0.992651i | \(-0.538613\pi\) | ||||
−0.121009 | + | 0.992651i | \(0.538613\pi\) | |||||||
\(38\) | 8.09017 | 1.31240 | ||||||||
\(39\) | −3.23607 | −0.518186 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4721 | 1.79165 | 0.895823 | − | 0.444410i | \(-0.146587\pi\) | ||||
0.895823 | + | 0.444410i | \(0.146587\pi\) | |||||||
\(42\) | 8.47214 | 1.30728 | ||||||||
\(43\) | −9.09017 | −1.38624 | −0.693119 | − | 0.720823i | \(-0.743764\pi\) | ||||
−0.693119 | + | 0.720823i | \(0.743764\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.47214 | −1.10171 | ||||||||
\(47\) | 6.09017 | 0.888343 | 0.444171 | − | 0.895942i | \(-0.353498\pi\) | ||||
0.444171 | + | 0.895942i | \(0.353498\pi\) | |||||||
\(48\) | −4.85410 | −0.700629 | ||||||||
\(49\) | 20.4164 | 2.91663 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | 5.38197 | 0.739270 | 0.369635 | − | 0.929177i | \(-0.379483\pi\) | ||||
0.369635 | + | 0.929177i | \(0.379483\pi\) | |||||||
\(54\) | 1.61803 | 0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.7082 | −1.56457 | ||||||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | 1.38197 | 0.181461 | ||||||||
\(59\) | 6.70820 | 0.873334 | 0.436667 | − | 0.899623i | \(-0.356159\pi\) | ||||
0.436667 | + | 0.899623i | \(0.356159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | 0.896258 | 0.448129 | − | 0.893969i | \(-0.352090\pi\) | ||||
0.448129 | + | 0.893969i | \(0.352090\pi\) | |||||||
\(62\) | 11.3262 | 1.43843 | ||||||||
\(63\) | 5.23607 | 0.659683 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6180 | 1.41937 | 0.709684 | − | 0.704520i | \(-0.248838\pi\) | ||||
0.709684 | + | 0.704520i | \(0.248838\pi\) | |||||||
\(68\) | −1.23607 | −0.149895 | ||||||||
\(69\) | −4.61803 | −0.555946 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −2.23607 | −0.263523 | ||||||||
\(73\) | 4.52786 | 0.529946 | 0.264973 | − | 0.964256i | \(-0.414637\pi\) | ||||
0.264973 | + | 0.964256i | \(0.414637\pi\) | |||||||
\(74\) | −2.38197 | −0.276898 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.09017 | 0.354467 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.23607 | −0.592868 | ||||||||
\(79\) | 3.09017 | 0.347671 | 0.173836 | − | 0.984775i | \(-0.444384\pi\) | ||||
0.173836 | + | 0.984775i | \(0.444384\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 18.5623 | 2.04986 | ||||||||
\(83\) | −7.70820 | −0.846085 | −0.423043 | − | 0.906110i | \(-0.639038\pi\) | ||||
−0.423043 | + | 0.906110i | \(0.639038\pi\) | |||||||
\(84\) | 3.23607 | 0.353084 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.7082 | −1.58603 | ||||||||
\(87\) | 0.854102 | 0.0915693 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.14590 | 0.439464 | 0.219732 | − | 0.975560i | \(-0.429482\pi\) | ||||
0.219732 | + | 0.975560i | \(0.429482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.9443 | −1.77624 | ||||||||
\(92\) | −2.85410 | −0.297561 | ||||||||
\(93\) | 7.00000 | 0.725866 | ||||||||
\(94\) | 9.85410 | 1.01637 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.38197 | −0.345170 | ||||||||
\(97\) | −2.52786 | −0.256666 | −0.128333 | − | 0.991731i | \(-0.540963\pi\) | ||||
−0.128333 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(98\) | 33.0344 | 3.33698 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.5623 | 1.94652 | 0.973261 | − | 0.229702i | \(-0.0737750\pi\) | ||||
0.973261 | + | 0.229702i | \(0.0737750\pi\) | |||||||
\(102\) | −3.23607 | −0.320418 | ||||||||
\(103\) | −4.61803 | −0.455028 | −0.227514 | − | 0.973775i | \(-0.573060\pi\) | ||||
−0.227514 | + | 0.973775i | \(0.573060\pi\) | |||||||
\(104\) | 7.23607 | 0.709555 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.70820 | 0.845816 | ||||||||
\(107\) | 3.85410 | 0.372590 | 0.186295 | − | 0.982494i | \(-0.440352\pi\) | ||||
0.186295 | + | 0.982494i | \(0.440352\pi\) | |||||||
\(108\) | 0.618034 | 0.0594703 | ||||||||
\(109\) | 10.8541 | 1.03963 | 0.519817 | − | 0.854278i | \(-0.326000\pi\) | ||||
0.519817 | + | 0.854278i | \(0.326000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.47214 | −0.139729 | ||||||||
\(112\) | −25.4164 | −2.40162 | ||||||||
\(113\) | 3.47214 | 0.326631 | 0.163316 | − | 0.986574i | \(-0.447781\pi\) | ||||
0.163316 | + | 0.986574i | \(0.447781\pi\) | |||||||
\(114\) | 8.09017 | 0.757714 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.527864 | 0.0490109 | ||||||||
\(117\) | −3.23607 | −0.299175 | ||||||||
\(118\) | 10.8541 | 0.999201 | ||||||||
\(119\) | −10.4721 | −0.959979 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 11.3262 | 1.02543 | ||||||||
\(123\) | 11.4721 | 1.03441 | ||||||||
\(124\) | 4.32624 | 0.388508 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.47214 | 0.754758 | ||||||||
\(127\) | 1.94427 | 0.172526 | 0.0862631 | − | 0.996272i | \(-0.472507\pi\) | ||||
0.0862631 | + | 0.996272i | \(0.472507\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | −9.09017 | −0.800345 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.18034 | −0.802090 | −0.401045 | − | 0.916058i | \(-0.631353\pi\) | ||||
−0.401045 | + | 0.916058i | \(0.631353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.1803 | 2.27012 | ||||||||
\(134\) | 18.7984 | 1.62393 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.47214 | 0.383482 | ||||||||
\(137\) | −5.29180 | −0.452109 | −0.226054 | − | 0.974115i | \(-0.572583\pi\) | ||||
−0.226054 | + | 0.974115i | \(0.572583\pi\) | |||||||
\(138\) | −7.47214 | −0.636070 | ||||||||
\(139\) | −1.18034 | −0.100115 | −0.0500576 | − | 0.998746i | \(-0.515940\pi\) | ||||
−0.0500576 | + | 0.998746i | \(0.515940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.09017 | 0.512885 | ||||||||
\(142\) | −12.9443 | −1.08626 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.32624 | 0.606324 | ||||||||
\(147\) | 20.4164 | 1.68392 | ||||||||
\(148\) | −0.909830 | −0.0747876 | ||||||||
\(149\) | −20.1246 | −1.64867 | −0.824336 | − | 0.566101i | \(-0.808451\pi\) | ||||
−0.824336 | + | 0.566101i | \(0.808451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2361 | −1.23989 | −0.619947 | − | 0.784644i | \(-0.712846\pi\) | ||||
−0.619947 | + | 0.784644i | \(0.712846\pi\) | |||||||
\(152\) | −11.1803 | −0.906845 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | −12.3262 | −0.983741 | −0.491870 | − | 0.870668i | \(-0.663687\pi\) | ||||
−0.491870 | + | 0.870668i | \(0.663687\pi\) | |||||||
\(158\) | 5.00000 | 0.397779 | ||||||||
\(159\) | 5.38197 | 0.426818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.1803 | −1.90568 | ||||||||
\(162\) | 1.61803 | 0.127125 | ||||||||
\(163\) | 6.56231 | 0.513999 | 0.257000 | − | 0.966411i | \(-0.417266\pi\) | ||||
0.257000 | + | 0.966411i | \(0.417266\pi\) | |||||||
\(164\) | 7.09017 | 0.553649 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.4721 | −0.968025 | ||||||||
\(167\) | −9.03444 | −0.699106 | −0.349553 | − | 0.936917i | \(-0.613667\pi\) | ||||
−0.349553 | + | 0.936917i | \(0.613667\pi\) | |||||||
\(168\) | −11.7082 | −0.903308 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.00000 | 0.382360 | ||||||||
\(172\) | −5.61803 | −0.428371 | ||||||||
\(173\) | 16.5623 | 1.25921 | 0.629604 | − | 0.776916i | \(-0.283217\pi\) | ||||
0.629604 | + | 0.776916i | \(0.283217\pi\) | |||||||
\(174\) | 1.38197 | 0.104767 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.70820 | 0.504219 | ||||||||
\(178\) | 6.70820 | 0.502801 | ||||||||
\(179\) | −10.5279 | −0.786890 | −0.393445 | − | 0.919348i | \(-0.628717\pi\) | ||||
−0.393445 | + | 0.919348i | \(0.628717\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.763932 | −0.0567826 | −0.0283913 | − | 0.999597i | \(-0.509038\pi\) | ||||
−0.0283913 | + | 0.999597i | \(0.509038\pi\) | |||||||
\(182\) | −27.4164 | −2.03224 | ||||||||
\(183\) | 7.00000 | 0.517455 | ||||||||
\(184\) | 10.3262 | 0.761260 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.3262 | 0.830480 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.76393 | 0.274513 | ||||||||
\(189\) | 5.23607 | 0.380868 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.4164 | −1.18785 | −0.593925 | − | 0.804521i | \(-0.702422\pi\) | ||||
−0.593925 | + | 0.804521i | \(0.702422\pi\) | |||||||
\(192\) | 4.23607 | 0.305712 | ||||||||
\(193\) | −8.03444 | −0.578332 | −0.289166 | − | 0.957279i | \(-0.593378\pi\) | ||||
−0.289166 | + | 0.957279i | \(0.593378\pi\) | |||||||
\(194\) | −4.09017 | −0.293657 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.6180 | 0.901288 | ||||||||
\(197\) | −9.76393 | −0.695651 | −0.347826 | − | 0.937559i | \(-0.613080\pi\) | ||||
−0.347826 | + | 0.937559i | \(0.613080\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.79837 | −0.340148 | −0.170074 | − | 0.985431i | \(-0.554401\pi\) | ||||
−0.170074 | + | 0.985431i | \(0.554401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6180 | 0.819473 | ||||||||
\(202\) | 31.6525 | 2.22706 | ||||||||
\(203\) | 4.47214 | 0.313882 | ||||||||
\(204\) | −1.23607 | −0.0865421 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.47214 | −0.520608 | ||||||||
\(207\) | −4.61803 | −0.320976 | ||||||||
\(208\) | 15.7082 | 1.08917 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.85410 | 0.196484 | 0.0982422 | − | 0.995163i | \(-0.468678\pi\) | ||||
0.0982422 | + | 0.995163i | \(0.468678\pi\) | |||||||
\(212\) | 3.32624 | 0.228447 | ||||||||
\(213\) | −8.00000 | −0.548151 | ||||||||
\(214\) | 6.23607 | 0.426289 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 36.6525 | 2.48813 | ||||||||
\(218\) | 17.5623 | 1.18947 | ||||||||
\(219\) | 4.52786 | 0.305965 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.47214 | 0.435363 | ||||||||
\(222\) | −2.38197 | −0.159867 | ||||||||
\(223\) | 21.0344 | 1.40857 | 0.704285 | − | 0.709917i | \(-0.251268\pi\) | ||||
0.704285 | + | 0.709917i | \(0.251268\pi\) | |||||||
\(224\) | −17.7082 | −1.18318 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.61803 | 0.373706 | ||||||||
\(227\) | −8.05573 | −0.534677 | −0.267339 | − | 0.963603i | \(-0.586144\pi\) | ||||
−0.267339 | + | 0.963603i | \(0.586144\pi\) | |||||||
\(228\) | 3.09017 | 0.204652 | ||||||||
\(229\) | 6.90983 | 0.456614 | 0.228307 | − | 0.973589i | \(-0.426681\pi\) | ||||
0.228307 | + | 0.973589i | \(0.426681\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.90983 | −0.125386 | ||||||||
\(233\) | −10.2705 | −0.672843 | −0.336422 | − | 0.941711i | \(-0.609217\pi\) | ||||
−0.336422 | + | 0.941711i | \(0.609217\pi\) | |||||||
\(234\) | −5.23607 | −0.342292 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.14590 | 0.269875 | ||||||||
\(237\) | 3.09017 | 0.200728 | ||||||||
\(238\) | −16.9443 | −1.09833 | ||||||||
\(239\) | 22.0344 | 1.42529 | 0.712645 | − | 0.701525i | \(-0.247497\pi\) | ||||
0.712645 | + | 0.701525i | \(0.247497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.618034 | 0.0398111 | 0.0199055 | − | 0.999802i | \(-0.493663\pi\) | ||||
0.0199055 | + | 0.999802i | \(0.493663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.32624 | 0.276959 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.5623 | 1.18349 | ||||||||
\(247\) | −16.1803 | −1.02953 | ||||||||
\(248\) | −15.6525 | −0.993933 | ||||||||
\(249\) | −7.70820 | −0.488488 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.4721 | 1.03971 | 0.519856 | − | 0.854254i | \(-0.325986\pi\) | ||||
0.519856 | + | 0.854254i | \(0.325986\pi\) | |||||||
\(252\) | 3.23607 | 0.203853 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.14590 | 0.197391 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −9.56231 | −0.596480 | −0.298240 | − | 0.954491i | \(-0.596400\pi\) | ||||
−0.298240 | + | 0.954491i | \(0.596400\pi\) | |||||||
\(258\) | −14.7082 | −0.915693 | ||||||||
\(259\) | −7.70820 | −0.478964 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.854102 | 0.0528676 | ||||||||
\(262\) | −14.8541 | −0.917689 | ||||||||
\(263\) | −24.2148 | −1.49315 | −0.746574 | − | 0.665303i | \(-0.768302\pi\) | ||||
−0.746574 | + | 0.665303i | \(0.768302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 42.3607 | 2.59730 | ||||||||
\(267\) | 4.14590 | 0.253725 | ||||||||
\(268\) | 7.18034 | 0.438609 | ||||||||
\(269\) | 0.854102 | 0.0520755 | 0.0260378 | − | 0.999661i | \(-0.491711\pi\) | ||||
0.0260378 | + | 0.999661i | \(0.491711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.3820 | 1.11662 | 0.558312 | − | 0.829631i | \(-0.311449\pi\) | ||||
0.558312 | + | 0.829631i | \(0.311449\pi\) | |||||||
\(272\) | 9.70820 | 0.588646 | ||||||||
\(273\) | −16.9443 | −1.02551 | ||||||||
\(274\) | −8.56231 | −0.517268 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.85410 | −0.171797 | ||||||||
\(277\) | −22.6525 | −1.36106 | −0.680528 | − | 0.732722i | \(-0.738249\pi\) | ||||
−0.680528 | + | 0.732722i | \(0.738249\pi\) | |||||||
\(278\) | −1.90983 | −0.114544 | ||||||||
\(279\) | 7.00000 | 0.419079 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.09017 | −0.0650341 | −0.0325170 | − | 0.999471i | \(-0.510352\pi\) | ||||
−0.0325170 | + | 0.999471i | \(0.510352\pi\) | |||||||
\(282\) | 9.85410 | 0.586803 | ||||||||
\(283\) | 16.0344 | 0.953149 | 0.476574 | − | 0.879134i | \(-0.341878\pi\) | ||||
0.476574 | + | 0.879134i | \(0.341878\pi\) | |||||||
\(284\) | −4.94427 | −0.293389 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 60.0689 | 3.54575 | ||||||||
\(288\) | −3.38197 | −0.199284 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.52786 | −0.148186 | ||||||||
\(292\) | 2.79837 | 0.163762 | ||||||||
\(293\) | −25.4721 | −1.48810 | −0.744049 | − | 0.668125i | \(-0.767097\pi\) | ||||
−0.744049 | + | 0.668125i | \(0.767097\pi\) | |||||||
\(294\) | 33.0344 | 1.92661 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.29180 | 0.191332 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −32.5623 | −1.88628 | ||||||||
\(299\) | 14.9443 | 0.864250 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −47.5967 | −2.74343 | ||||||||
\(302\) | −24.6525 | −1.41859 | ||||||||
\(303\) | 19.5623 | 1.12383 | ||||||||
\(304\) | −24.2705 | −1.39201 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.23607 | −0.184994 | ||||||||
\(307\) | 28.1246 | 1.60516 | 0.802578 | − | 0.596547i | \(-0.203461\pi\) | ||||
0.802578 | + | 0.596547i | \(0.203461\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.61803 | −0.262711 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.5279 | 0.710390 | 0.355195 | − | 0.934792i | \(-0.384414\pi\) | ||||
0.355195 | + | 0.934792i | \(0.384414\pi\) | |||||||
\(312\) | 7.23607 | 0.409662 | ||||||||
\(313\) | 8.47214 | 0.478873 | 0.239437 | − | 0.970912i | \(-0.423037\pi\) | ||||
0.239437 | + | 0.970912i | \(0.423037\pi\) | |||||||
\(314\) | −19.9443 | −1.12552 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.90983 | 0.107436 | ||||||||
\(317\) | −3.58359 | −0.201275 | −0.100637 | − | 0.994923i | \(-0.532088\pi\) | ||||
−0.100637 | + | 0.994923i | \(0.532088\pi\) | |||||||
\(318\) | 8.70820 | 0.488332 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.85410 | 0.215115 | ||||||||
\(322\) | −39.1246 | −2.18033 | ||||||||
\(323\) | −10.0000 | −0.556415 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.6180 | 0.588079 | ||||||||
\(327\) | 10.8541 | 0.600233 | ||||||||
\(328\) | −25.6525 | −1.41642 | ||||||||
\(329\) | 31.8885 | 1.75807 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.5967 | −1.51685 | −0.758427 | − | 0.651758i | \(-0.774032\pi\) | ||||
−0.758427 | + | 0.651758i | \(0.774032\pi\) | |||||||
\(332\) | −4.76393 | −0.261455 | ||||||||
\(333\) | −1.47214 | −0.0806726 | ||||||||
\(334\) | −14.6180 | −0.799863 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −25.4164 | −1.38658 | ||||||||
\(337\) | 28.8541 | 1.57178 | 0.785892 | − | 0.618364i | \(-0.212204\pi\) | ||||
0.785892 | + | 0.618364i | \(0.212204\pi\) | |||||||
\(338\) | −4.09017 | −0.222476 | ||||||||
\(339\) | 3.47214 | 0.188581 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 8.09017 | 0.437466 | ||||||||
\(343\) | 70.2492 | 3.79310 | ||||||||
\(344\) | 20.3262 | 1.09592 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26.7984 | 1.44069 | ||||||||
\(347\) | −28.1803 | −1.51280 | −0.756400 | − | 0.654109i | \(-0.773044\pi\) | ||||
−0.756400 | + | 0.654109i | \(0.773044\pi\) | |||||||
\(348\) | 0.527864 | 0.0282965 | ||||||||
\(349\) | 32.2361 | 1.72556 | 0.862779 | − | 0.505582i | \(-0.168722\pi\) | ||||
0.862779 | + | 0.505582i | \(0.168722\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.23607 | −0.172729 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.8328 | −0.949145 | −0.474573 | − | 0.880216i | \(-0.657397\pi\) | ||||
−0.474573 | + | 0.880216i | \(0.657397\pi\) | |||||||
\(354\) | 10.8541 | 0.576889 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.56231 | 0.135802 | ||||||||
\(357\) | −10.4721 | −0.554244 | ||||||||
\(358\) | −17.0344 | −0.900298 | ||||||||
\(359\) | 3.29180 | 0.173734 | 0.0868672 | − | 0.996220i | \(-0.472314\pi\) | ||||
0.0868672 | + | 0.996220i | \(0.472314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | −1.23607 | −0.0649663 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.4721 | −0.548889 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.3262 | 0.592032 | ||||||||
\(367\) | −22.1246 | −1.15490 | −0.577448 | − | 0.816428i | \(-0.695951\pi\) | ||||
−0.577448 | + | 0.816428i | \(0.695951\pi\) | |||||||
\(368\) | 22.4164 | 1.16854 | ||||||||
\(369\) | 11.4721 | 0.597216 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.1803 | 1.46305 | ||||||||
\(372\) | 4.32624 | 0.224305 | ||||||||
\(373\) | 32.7426 | 1.69535 | 0.847675 | − | 0.530516i | \(-0.178002\pi\) | ||||
0.847675 | + | 0.530516i | \(0.178002\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.6180 | −0.702296 | ||||||||
\(377\) | −2.76393 | −0.142350 | ||||||||
\(378\) | 8.47214 | 0.435760 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.94427 | 0.0996081 | ||||||||
\(382\) | −26.5623 | −1.35905 | ||||||||
\(383\) | −13.3607 | −0.682699 | −0.341349 | − | 0.939936i | \(-0.610884\pi\) | ||||
−0.341349 | + | 0.939936i | \(0.610884\pi\) | |||||||
\(384\) | 13.6180 | 0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | −9.09017 | −0.462079 | ||||||||
\(388\) | −1.56231 | −0.0793141 | ||||||||
\(389\) | −21.0557 | −1.06757 | −0.533784 | − | 0.845621i | \(-0.679230\pi\) | ||||
−0.533784 | + | 0.845621i | \(0.679230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.23607 | 0.467088 | ||||||||
\(392\) | −45.6525 | −2.30580 | ||||||||
\(393\) | −9.18034 | −0.463087 | ||||||||
\(394\) | −15.7984 | −0.795911 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.72949 | −0.136989 | −0.0684946 | − | 0.997651i | \(-0.521820\pi\) | ||||
−0.0684946 | + | 0.997651i | \(0.521820\pi\) | |||||||
\(398\) | −7.76393 | −0.389171 | ||||||||
\(399\) | 26.1803 | 1.31066 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.8885 | −1.54250 | −0.771250 | − | 0.636532i | \(-0.780368\pi\) | ||||
−0.771250 | + | 0.636532i | \(0.780368\pi\) | |||||||
\(402\) | 18.7984 | 0.937578 | ||||||||
\(403\) | −22.6525 | −1.12840 | ||||||||
\(404\) | 12.0902 | 0.601508 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.23607 | 0.359120 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.47214 | 0.221404 | ||||||||
\(409\) | −26.3050 | −1.30070 | −0.650348 | − | 0.759636i | \(-0.725377\pi\) | ||||
−0.650348 | + | 0.759636i | \(0.725377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.29180 | −0.261025 | ||||||||
\(412\) | −2.85410 | −0.140612 | ||||||||
\(413\) | 35.1246 | 1.72837 | ||||||||
\(414\) | −7.47214 | −0.367235 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.9443 | 0.536587 | ||||||||
\(417\) | −1.18034 | −0.0578015 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.5967 | −1.20163 | −0.600815 | − | 0.799388i | \(-0.705157\pi\) | ||||
−0.600815 | + | 0.799388i | \(0.705157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.85410 | −0.187837 | −0.0939187 | − | 0.995580i | \(-0.529939\pi\) | ||||
−0.0939187 | + | 0.995580i | \(0.529939\pi\) | |||||||
\(422\) | 4.61803 | 0.224802 | ||||||||
\(423\) | 6.09017 | 0.296114 | ||||||||
\(424\) | −12.0344 | −0.584444 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.9443 | −0.627152 | ||||||||
\(427\) | 36.6525 | 1.77374 | ||||||||
\(428\) | 2.38197 | 0.115137 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.8885 | −0.765324 | −0.382662 | − | 0.923888i | \(-0.624993\pi\) | ||||
−0.382662 | + | 0.923888i | \(0.624993\pi\) | |||||||
\(432\) | −4.85410 | −0.233543 | ||||||||
\(433\) | 1.03444 | 0.0497121 | 0.0248561 | − | 0.999691i | \(-0.492087\pi\) | ||||
0.0248561 | + | 0.999691i | \(0.492087\pi\) | |||||||
\(434\) | 59.3050 | 2.84673 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.70820 | 0.321265 | ||||||||
\(437\) | −23.0902 | −1.10455 | ||||||||
\(438\) | 7.32624 | 0.350061 | ||||||||
\(439\) | 25.3262 | 1.20876 | 0.604378 | − | 0.796698i | \(-0.293422\pi\) | ||||
0.604378 | + | 0.796698i | \(0.293422\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.4164 | 0.972210 | ||||||||
\(442\) | 10.4721 | 0.498109 | ||||||||
\(443\) | 8.27051 | 0.392944 | 0.196472 | − | 0.980509i | \(-0.437052\pi\) | ||||
0.196472 | + | 0.980509i | \(0.437052\pi\) | |||||||
\(444\) | −0.909830 | −0.0431786 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 34.0344 | 1.61158 | ||||||||
\(447\) | −20.1246 | −0.951861 | ||||||||
\(448\) | 22.1803 | 1.04792 | ||||||||
\(449\) | −34.2705 | −1.61733 | −0.808663 | − | 0.588273i | \(-0.799808\pi\) | ||||
−0.808663 | + | 0.588273i | \(0.799808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.14590 | 0.100935 | ||||||||
\(453\) | −15.2361 | −0.715853 | ||||||||
\(454\) | −13.0344 | −0.611737 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.1803 | −0.523567 | ||||||||
\(457\) | 7.47214 | 0.349532 | 0.174766 | − | 0.984610i | \(-0.444083\pi\) | ||||
0.174766 | + | 0.984610i | \(0.444083\pi\) | |||||||
\(458\) | 11.1803 | 0.522423 | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.05573 | 0.375193 | 0.187596 | − | 0.982246i | \(-0.439930\pi\) | ||||
0.187596 | + | 0.982246i | \(0.439930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.270510 | −0.0125717 | −0.00628583 | − | 0.999980i | \(-0.502001\pi\) | ||||
−0.00628583 | + | 0.999980i | \(0.502001\pi\) | |||||||
\(464\) | −4.14590 | −0.192468 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.6180 | −0.769816 | ||||||||
\(467\) | 30.8885 | 1.42935 | 0.714676 | − | 0.699456i | \(-0.246574\pi\) | ||||
0.714676 | + | 0.699456i | \(0.246574\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 60.8328 | 2.80900 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.3262 | −0.567963 | ||||||||
\(472\) | −15.0000 | −0.690431 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 5.00000 | 0.229658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.47214 | −0.296650 | ||||||||
\(477\) | 5.38197 | 0.246423 | ||||||||
\(478\) | 35.6525 | 1.63071 | ||||||||
\(479\) | 6.58359 | 0.300812 | 0.150406 | − | 0.988624i | \(-0.451942\pi\) | ||||
0.150406 | + | 0.988624i | \(0.451942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.76393 | 0.217217 | ||||||||
\(482\) | 1.00000 | 0.0455488 | ||||||||
\(483\) | −24.1803 | −1.10024 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.61803 | 0.0733955 | ||||||||
\(487\) | −8.18034 | −0.370687 | −0.185343 | − | 0.982674i | \(-0.559340\pi\) | ||||
−0.185343 | + | 0.982674i | \(0.559340\pi\) | |||||||
\(488\) | −15.6525 | −0.708554 | ||||||||
\(489\) | 6.56231 | 0.296758 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.20163 | 0.325005 | 0.162502 | − | 0.986708i | \(-0.448043\pi\) | ||||
0.162502 | + | 0.986708i | \(0.448043\pi\) | |||||||
\(492\) | 7.09017 | 0.319650 | ||||||||
\(493\) | −1.70820 | −0.0769336 | ||||||||
\(494\) | −26.1803 | −1.17791 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −33.9787 | −1.52569 | ||||||||
\(497\) | −41.8885 | −1.87896 | ||||||||
\(498\) | −12.4721 | −0.558890 | ||||||||
\(499\) | 11.1803 | 0.500501 | 0.250250 | − | 0.968181i | \(-0.419487\pi\) | ||||
0.250250 | + | 0.968181i | \(0.419487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.03444 | −0.403629 | ||||||||
\(502\) | 26.6525 | 1.18956 | ||||||||
\(503\) | −13.8885 | −0.619260 | −0.309630 | − | 0.950857i | \(-0.600205\pi\) | ||||
−0.309630 | + | 0.950857i | \(0.600205\pi\) | |||||||
\(504\) | −11.7082 | −0.521525 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.52786 | −0.112266 | ||||||||
\(508\) | 1.20163 | 0.0533135 | ||||||||
\(509\) | 9.47214 | 0.419845 | 0.209923 | − | 0.977718i | \(-0.432679\pi\) | ||||
0.209923 | + | 0.977718i | \(0.432679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.7082 | 1.04879 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 5.00000 | 0.220755 | ||||||||
\(514\) | −15.4721 | −0.682447 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.61803 | −0.247320 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −12.4721 | −0.547994 | ||||||||
\(519\) | 16.5623 | 0.727005 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3607 | 1.28631 | 0.643157 | − | 0.765734i | \(-0.277624\pi\) | ||||
0.643157 | + | 0.765734i | \(0.277624\pi\) | |||||||
\(522\) | 1.38197 | 0.0604870 | ||||||||
\(523\) | −3.76393 | −0.164585 | −0.0822926 | − | 0.996608i | \(-0.526224\pi\) | ||||
−0.0822926 | + | 0.996608i | \(0.526224\pi\) | |||||||
\(524\) | −5.67376 | −0.247859 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.1803 | −1.70834 | ||||||||
\(527\) | −14.0000 | −0.609850 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.67376 | −0.0727723 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.70820 | 0.291111 | ||||||||
\(532\) | 16.1803 | 0.701507 | ||||||||
\(533\) | −37.1246 | −1.60805 | ||||||||
\(534\) | 6.70820 | 0.290292 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.9787 | −1.12211 | ||||||||
\(537\) | −10.5279 | −0.454311 | ||||||||
\(538\) | 1.38197 | 0.0595808 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.61803 | −0.0695647 | −0.0347824 | − | 0.999395i | \(-0.511074\pi\) | ||||
−0.0347824 | + | 0.999395i | \(0.511074\pi\) | |||||||
\(542\) | 29.7426 | 1.27756 | ||||||||
\(543\) | −0.763932 | −0.0327835 | ||||||||
\(544\) | 6.76393 | 0.290001 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −27.4164 | −1.17331 | ||||||||
\(547\) | −19.3607 | −0.827803 | −0.413901 | − | 0.910322i | \(-0.635834\pi\) | ||||
−0.413901 | + | 0.910322i | \(0.635834\pi\) | |||||||
\(548\) | −3.27051 | −0.139709 | ||||||||
\(549\) | 7.00000 | 0.298753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.27051 | 0.181930 | ||||||||
\(552\) | 10.3262 | 0.439514 | ||||||||
\(553\) | 16.1803 | 0.688058 | ||||||||
\(554\) | −36.6525 | −1.55721 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.729490 | −0.0309373 | ||||||||
\(557\) | 42.3951 | 1.79634 | 0.898169 | − | 0.439649i | \(-0.144897\pi\) | ||||
0.898169 | + | 0.439649i | \(0.144897\pi\) | |||||||
\(558\) | 11.3262 | 0.479478 | ||||||||
\(559\) | 29.4164 | 1.24418 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.76393 | −0.0744070 | ||||||||
\(563\) | −20.6738 | −0.871295 | −0.435648 | − | 0.900117i | \(-0.643481\pi\) | ||||
−0.435648 | + | 0.900117i | \(0.643481\pi\) | |||||||
\(564\) | 3.76393 | 0.158490 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.9443 | 1.09052 | ||||||||
\(567\) | 5.23607 | 0.219894 | ||||||||
\(568\) | 17.8885 | 0.750587 | ||||||||
\(569\) | −22.5623 | −0.945861 | −0.472931 | − | 0.881100i | \(-0.656804\pi\) | ||||
−0.472931 | + | 0.881100i | \(0.656804\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0902 | −0.464109 | −0.232055 | − | 0.972703i | \(-0.574545\pi\) | ||||
−0.232055 | + | 0.972703i | \(0.574545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.4164 | −0.685805 | ||||||||
\(574\) | 97.1935 | 4.05678 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | −30.0132 | −1.24946 | −0.624732 | − | 0.780839i | \(-0.714792\pi\) | ||||
−0.624732 | + | 0.780839i | \(0.714792\pi\) | |||||||
\(578\) | −21.0344 | −0.874917 | ||||||||
\(579\) | −8.03444 | −0.333900 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.3607 | −1.67444 | ||||||||
\(582\) | −4.09017 | −0.169543 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.1246 | −0.418959 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41.2148 | −1.70257 | ||||||||
\(587\) | 21.6180 | 0.892272 | 0.446136 | − | 0.894965i | \(-0.352800\pi\) | ||||
0.446136 | + | 0.894965i | \(0.352800\pi\) | |||||||
\(588\) | 12.6180 | 0.520359 | ||||||||
\(589\) | 35.0000 | 1.44215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.76393 | −0.401634 | ||||||||
\(592\) | 7.14590 | 0.293695 | ||||||||
\(593\) | −3.11146 | −0.127772 | −0.0638861 | − | 0.997957i | \(-0.520349\pi\) | ||||
−0.0638861 | + | 0.997957i | \(0.520349\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.4377 | −0.509468 | ||||||||
\(597\) | −4.79837 | −0.196384 | ||||||||
\(598\) | 24.1803 | 0.988808 | ||||||||
\(599\) | −17.7639 | −0.725815 | −0.362907 | − | 0.931825i | \(-0.618216\pi\) | ||||
−0.362907 | + | 0.931825i | \(0.618216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.3607 | −0.422621 | −0.211310 | − | 0.977419i | \(-0.567773\pi\) | ||||
−0.211310 | + | 0.977419i | \(0.567773\pi\) | |||||||
\(602\) | −77.0132 | −3.13882 | ||||||||
\(603\) | 11.6180 | 0.473123 | ||||||||
\(604\) | −9.41641 | −0.383148 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 31.6525 | 1.28579 | ||||||||
\(607\) | 33.0000 | 1.33943 | 0.669714 | − | 0.742619i | \(-0.266417\pi\) | ||||
0.669714 | + | 0.742619i | \(0.266417\pi\) | |||||||
\(608\) | −16.9098 | −0.685784 | ||||||||
\(609\) | 4.47214 | 0.181220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7082 | −0.797309 | ||||||||
\(612\) | −1.23607 | −0.0499651 | ||||||||
\(613\) | −3.76393 | −0.152024 | −0.0760119 | − | 0.997107i | \(-0.524219\pi\) | ||||
−0.0760119 | + | 0.997107i | \(0.524219\pi\) | |||||||
\(614\) | 45.5066 | 1.83650 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.2492 | −1.70089 | −0.850445 | − | 0.526064i | \(-0.823667\pi\) | ||||
−0.850445 | + | 0.526064i | \(0.823667\pi\) | |||||||
\(618\) | −7.47214 | −0.300573 | ||||||||
\(619\) | 42.8885 | 1.72384 | 0.861918 | − | 0.507048i | \(-0.169263\pi\) | ||||
0.861918 | + | 0.507048i | \(0.169263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.61803 | −0.185315 | ||||||||
\(622\) | 20.2705 | 0.812773 | ||||||||
\(623\) | 21.7082 | 0.869721 | ||||||||
\(624\) | 15.7082 | 0.628831 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.7082 | 0.547890 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.61803 | −0.303993 | ||||||||
\(629\) | 2.94427 | 0.117396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.6312 | −1.57769 | −0.788846 | − | 0.614590i | \(-0.789321\pi\) | ||||
−0.788846 | + | 0.614590i | \(0.789321\pi\) | |||||||
\(632\) | −6.90983 | −0.274858 | ||||||||
\(633\) | 2.85410 | 0.113440 | ||||||||
\(634\) | −5.79837 | −0.230283 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.32624 | 0.131894 | ||||||||
\(637\) | −66.0689 | −2.61774 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | −0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.23607 | 0.167315 | 0.0836573 | − | 0.996495i | \(-0.473340\pi\) | ||||
0.0836573 | + | 0.996495i | \(0.473340\pi\) | |||||||
\(642\) | 6.23607 | 0.246118 | ||||||||
\(643\) | 13.6738 | 0.539241 | 0.269620 | − | 0.962967i | \(-0.413102\pi\) | ||||
0.269620 | + | 0.962967i | \(0.413102\pi\) | |||||||
\(644\) | −14.9443 | −0.588887 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.1803 | −0.636607 | ||||||||
\(647\) | −31.5967 | −1.24220 | −0.621098 | − | 0.783733i | \(-0.713313\pi\) | ||||
−0.621098 | + | 0.783733i | \(0.713313\pi\) | |||||||
\(648\) | −2.23607 | −0.0878410 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.6525 | 1.43652 | ||||||||
\(652\) | 4.05573 | 0.158835 | ||||||||
\(653\) | −43.5623 | −1.70472 | −0.852362 | − | 0.522952i | \(-0.824831\pi\) | ||||
−0.852362 | + | 0.522952i | \(0.824831\pi\) | |||||||
\(654\) | 17.5623 | 0.686741 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −55.6869 | −2.17421 | ||||||||
\(657\) | 4.52786 | 0.176649 | ||||||||
\(658\) | 51.5967 | 2.01145 | ||||||||
\(659\) | 42.0344 | 1.63743 | 0.818715 | − | 0.574201i | \(-0.194687\pi\) | ||||
0.818715 | + | 0.574201i | \(0.194687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.0902 | 0.586940 | 0.293470 | − | 0.955968i | \(-0.405190\pi\) | ||||
0.293470 | + | 0.955968i | \(0.405190\pi\) | |||||||
\(662\) | −44.6525 | −1.73547 | ||||||||
\(663\) | 6.47214 | 0.251357 | ||||||||
\(664\) | 17.2361 | 0.668889 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.38197 | −0.0922993 | ||||||||
\(667\) | −3.94427 | −0.152723 | ||||||||
\(668\) | −5.58359 | −0.216036 | ||||||||
\(669\) | 21.0344 | 0.813239 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −17.7082 | −0.683109 | ||||||||
\(673\) | 35.3050 | 1.36091 | 0.680453 | − | 0.732792i | \(-0.261783\pi\) | ||||
0.680453 | + | 0.732792i | \(0.261783\pi\) | |||||||
\(674\) | 46.6869 | 1.79831 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.56231 | −0.0600887 | ||||||||
\(677\) | −5.94427 | −0.228457 | −0.114228 | − | 0.993455i | \(-0.536440\pi\) | ||||
−0.114228 | + | 0.993455i | \(0.536440\pi\) | |||||||
\(678\) | 5.61803 | 0.215759 | ||||||||
\(679\) | −13.2361 | −0.507954 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.05573 | −0.308696 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.7082 | 0.601058 | 0.300529 | − | 0.953773i | \(-0.402837\pi\) | ||||
0.300529 | + | 0.953773i | \(0.402837\pi\) | |||||||
\(684\) | 3.09017 | 0.118156 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 113.666 | 4.33977 | ||||||||
\(687\) | 6.90983 | 0.263626 | ||||||||
\(688\) | 44.1246 | 1.68224 | ||||||||
\(689\) | −17.4164 | −0.663512 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3050 | −1.11481 | −0.557406 | − | 0.830240i | \(-0.688203\pi\) | ||||
−0.557406 | + | 0.830240i | \(0.688203\pi\) | |||||||
\(692\) | 10.2361 | 0.389117 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −45.5967 | −1.73083 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.90983 | −0.0723919 | ||||||||
\(697\) | −22.9443 | −0.869076 | ||||||||
\(698\) | 52.1591 | 1.97425 | ||||||||
\(699\) | −10.2705 | −0.388466 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.4164 | 1.52651 | 0.763253 | − | 0.646099i | \(-0.223601\pi\) | ||||
0.763253 | + | 0.646099i | \(0.223601\pi\) | |||||||
\(702\) | −5.23607 | −0.197623 | ||||||||
\(703\) | −7.36068 | −0.277613 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −28.8541 | −1.08594 | ||||||||
\(707\) | 102.430 | 3.85226 | ||||||||
\(708\) | 4.14590 | 0.155812 | ||||||||
\(709\) | 18.8197 | 0.706787 | 0.353394 | − | 0.935475i | \(-0.385028\pi\) | ||||
0.353394 | + | 0.935475i | \(0.385028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.09017 | 0.115890 | ||||||||
\(712\) | −9.27051 | −0.347427 | ||||||||
\(713\) | −32.3262 | −1.21063 | ||||||||
\(714\) | −16.9443 | −0.634123 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.50658 | −0.243162 | ||||||||
\(717\) | 22.0344 | 0.822891 | ||||||||
\(718\) | 5.32624 | 0.198773 | ||||||||
\(719\) | 26.9098 | 1.00357 | 0.501784 | − | 0.864993i | \(-0.332677\pi\) | ||||
0.501784 | + | 0.864993i | \(0.332677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.1803 | −0.900523 | ||||||||
\(722\) | 9.70820 | 0.361302 | ||||||||
\(723\) | 0.618034 | 0.0229849 | ||||||||
\(724\) | −0.472136 | −0.0175468 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.6738 | −0.803835 | −0.401918 | − | 0.915676i | \(-0.631656\pi\) | ||||
−0.401918 | + | 0.915676i | \(0.631656\pi\) | |||||||
\(728\) | 37.8885 | 1.40424 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.1803 | 0.672424 | ||||||||
\(732\) | 4.32624 | 0.159902 | ||||||||
\(733\) | 4.85410 | 0.179290 | 0.0896452 | − | 0.995974i | \(-0.471427\pi\) | ||||
0.0896452 | + | 0.995974i | \(0.471427\pi\) | |||||||
\(734\) | −35.7984 | −1.32134 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.6180 | 0.575688 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 18.5623 | 0.683288 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.1803 | −0.594400 | ||||||||
\(742\) | 45.5967 | 1.67391 | ||||||||
\(743\) | −31.6525 | −1.16122 | −0.580608 | − | 0.814183i | \(-0.697185\pi\) | ||||
−0.580608 | + | 0.814183i | \(0.697185\pi\) | |||||||
\(744\) | −15.6525 | −0.573848 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 52.9787 | 1.93969 | ||||||||
\(747\) | −7.70820 | −0.282028 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.1803 | 0.737374 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.1115 | −0.368972 | −0.184486 | − | 0.982835i | \(-0.559062\pi\) | ||||
−0.184486 | + | 0.982835i | \(0.559062\pi\) | |||||||
\(752\) | −29.5623 | −1.07803 | ||||||||
\(753\) | 16.4721 | 0.600278 | ||||||||
\(754\) | −4.47214 | −0.162866 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.23607 | 0.117695 | ||||||||
\(757\) | 1.81966 | 0.0661367 | 0.0330683 | − | 0.999453i | \(-0.489472\pi\) | ||||
0.0330683 | + | 0.999453i | \(0.489472\pi\) | |||||||
\(758\) | −8.09017 | −0.293848 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.96556 | 0.361251 | 0.180626 | − | 0.983552i | \(-0.442188\pi\) | ||||
0.180626 | + | 0.983552i | \(0.442188\pi\) | |||||||
\(762\) | 3.14590 | 0.113964 | ||||||||
\(763\) | 56.8328 | 2.05749 | ||||||||
\(764\) | −10.1459 | −0.367066 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.6180 | −0.781091 | ||||||||
\(767\) | −21.7082 | −0.783838 | ||||||||
\(768\) | 13.5623 | 0.489388 | ||||||||
\(769\) | 17.2361 | 0.621549 | 0.310774 | − | 0.950484i | \(-0.399412\pi\) | ||||
0.310774 | + | 0.950484i | \(0.399412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.56231 | −0.344378 | ||||||||
\(772\) | −4.96556 | −0.178714 | ||||||||
\(773\) | −27.5066 | −0.989343 | −0.494671 | − | 0.869080i | \(-0.664712\pi\) | ||||
−0.494671 | + | 0.869080i | \(0.664712\pi\) | |||||||
\(774\) | −14.7082 | −0.528675 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.65248 | 0.202912 | ||||||||
\(777\) | −7.70820 | −0.276530 | ||||||||
\(778\) | −34.0689 | −1.22143 | ||||||||
\(779\) | 57.3607 | 2.05516 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 14.9443 | 0.534406 | ||||||||
\(783\) | 0.854102 | 0.0305231 | ||||||||
\(784\) | −99.1033 | −3.53940 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.8541 | −0.529828 | ||||||||
\(787\) | 32.7984 | 1.16914 | 0.584568 | − | 0.811345i | \(-0.301264\pi\) | ||||
0.584568 | + | 0.811345i | \(0.301264\pi\) | |||||||
\(788\) | −6.03444 | −0.214968 | ||||||||
\(789\) | −24.2148 | −0.862069 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.1803 | 0.646418 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.6525 | −0.804413 | ||||||||
\(794\) | −4.41641 | −0.156732 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.96556 | −0.105111 | ||||||||
\(797\) | −15.2918 | −0.541663 | −0.270832 | − | 0.962627i | \(-0.587299\pi\) | ||||
−0.270832 | + | 0.962627i | \(0.587299\pi\) | |||||||
\(798\) | 42.3607 | 1.49955 | ||||||||
\(799\) | −12.1803 | −0.430909 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.14590 | 0.146488 | ||||||||
\(802\) | −49.9787 | −1.76481 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.18034 | 0.253231 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.6525 | −1.29103 | ||||||||
\(807\) | 0.854102 | 0.0300658 | ||||||||
\(808\) | −43.7426 | −1.53886 | ||||||||
\(809\) | 29.6738 | 1.04327 | 0.521637 | − | 0.853168i | \(-0.325322\pi\) | ||||
0.521637 | + | 0.853168i | \(0.325322\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.6312 | 1.53210 | 0.766049 | − | 0.642782i | \(-0.222220\pi\) | ||||
0.766049 | + | 0.642782i | \(0.222220\pi\) | |||||||
\(812\) | 2.76393 | 0.0969950 | ||||||||
\(813\) | 18.3820 | 0.644684 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.70820 | 0.339855 | ||||||||
\(817\) | −45.4508 | −1.59012 | ||||||||
\(818\) | −42.5623 | −1.48816 | ||||||||
\(819\) | −16.9443 | −0.592081 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.8197 | 0.726611 | 0.363306 | − | 0.931670i | \(-0.381648\pi\) | ||||
0.363306 | + | 0.931670i | \(0.381648\pi\) | |||||||
\(822\) | −8.56231 | −0.298645 | ||||||||
\(823\) | −16.5279 | −0.576125 | −0.288063 | − | 0.957612i | \(-0.593011\pi\) | ||||
−0.288063 | + | 0.957612i | \(0.593011\pi\) | |||||||
\(824\) | 10.3262 | 0.359732 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 56.8328 | 1.97747 | ||||||||
\(827\) | 51.4164 | 1.78792 | 0.893962 | − | 0.448143i | \(-0.147914\pi\) | ||||
0.893962 | + | 0.448143i | \(0.147914\pi\) | |||||||
\(828\) | −2.85410 | −0.0991869 | ||||||||
\(829\) | −32.8885 | −1.14227 | −0.571133 | − | 0.820857i | \(-0.693496\pi\) | ||||
−0.571133 | + | 0.820857i | \(0.693496\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.6525 | −0.785806 | ||||||||
\(832\) | −13.7082 | −0.475246 | ||||||||
\(833\) | −40.8328 | −1.41477 | ||||||||
\(834\) | −1.90983 | −0.0661320 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.00000 | 0.241955 | ||||||||
\(838\) | −39.7984 | −1.37481 | ||||||||
\(839\) | 36.3050 | 1.25339 | 0.626693 | − | 0.779266i | \(-0.284408\pi\) | ||||
0.626693 | + | 0.779266i | \(0.284408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2705 | −0.974845 | ||||||||
\(842\) | −6.23607 | −0.214909 | ||||||||
\(843\) | −1.09017 | −0.0375474 | ||||||||
\(844\) | 1.76393 | 0.0607170 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.85410 | 0.338791 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −26.1246 | −0.897123 | ||||||||
\(849\) | 16.0344 | 0.550301 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.79837 | 0.233045 | ||||||||
\(852\) | −4.94427 | −0.169388 | ||||||||
\(853\) | −23.3607 | −0.799854 | −0.399927 | − | 0.916547i | \(-0.630965\pi\) | ||||
−0.399927 | + | 0.916547i | \(0.630965\pi\) | |||||||
\(854\) | 59.3050 | 2.02937 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.61803 | −0.294558 | ||||||||
\(857\) | 41.0132 | 1.40098 | 0.700491 | − | 0.713661i | \(-0.252964\pi\) | ||||
0.700491 | + | 0.713661i | \(0.252964\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.2705 | −1.33989 | −0.669946 | − | 0.742410i | \(-0.733683\pi\) | ||||
−0.669946 | + | 0.742410i | \(0.733683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60.0689 | 2.04714 | ||||||||
\(862\) | −25.7082 | −0.875625 | ||||||||
\(863\) | −23.0344 | −0.784102 | −0.392051 | − | 0.919944i | \(-0.628234\pi\) | ||||
−0.392051 | + | 0.919944i | \(0.628234\pi\) | |||||||
\(864\) | −3.38197 | −0.115057 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.67376 | 0.0568768 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 22.6525 | 0.768875 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.5967 | −1.27392 | ||||||||
\(872\) | −24.2705 | −0.821903 | ||||||||
\(873\) | −2.52786 | −0.0855552 | ||||||||
\(874\) | −37.3607 | −1.26374 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.79837 | 0.0945483 | ||||||||
\(877\) | −7.52786 | −0.254198 | −0.127099 | − | 0.991890i | \(-0.540567\pi\) | ||||
−0.127099 | + | 0.991890i | \(0.540567\pi\) | |||||||
\(878\) | 40.9787 | 1.38296 | ||||||||
\(879\) | −25.4721 | −0.859154 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.1459 | −0.577660 | −0.288830 | − | 0.957380i | \(-0.593266\pi\) | ||||
−0.288830 | + | 0.957380i | \(0.593266\pi\) | |||||||
\(882\) | 33.0344 | 1.11233 | ||||||||
\(883\) | −23.2361 | −0.781956 | −0.390978 | − | 0.920400i | \(-0.627863\pi\) | ||||
−0.390978 | + | 0.920400i | \(0.627863\pi\) | |||||||
\(884\) | 4.00000 | 0.134535 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.3820 | 0.449576 | ||||||||
\(887\) | −0.167184 | −0.00561350 | −0.00280675 | − | 0.999996i | \(-0.500893\pi\) | ||||
−0.00280675 | + | 0.999996i | \(0.500893\pi\) | |||||||
\(888\) | 3.29180 | 0.110465 | ||||||||
\(889\) | 10.1803 | 0.341438 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.0000 | 0.435272 | ||||||||
\(893\) | 30.4508 | 1.01900 | ||||||||
\(894\) | −32.5623 | −1.08905 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 71.3050 | 2.38213 | ||||||||
\(897\) | 14.9443 | 0.498975 | ||||||||
\(898\) | −55.4508 | −1.85042 | ||||||||
\(899\) | 5.97871 | 0.199401 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.7639 | −0.358599 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −47.5967 | −1.58392 | ||||||||
\(904\) | −7.76393 | −0.258225 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −24.6525 | −0.819024 | ||||||||
\(907\) | −44.8885 | −1.49050 | −0.745250 | − | 0.666785i | \(-0.767670\pi\) | ||||
−0.745250 | + | 0.666785i | \(0.767670\pi\) | |||||||
\(908\) | −4.97871 | −0.165224 | ||||||||
\(909\) | 19.5623 | 0.648841 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.9017 | 1.75271 | 0.876356 | − | 0.481664i | \(-0.159968\pi\) | ||||
0.876356 | + | 0.481664i | \(0.159968\pi\) | |||||||
\(912\) | −24.2705 | −0.803677 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 12.0902 | 0.399907 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.27051 | 0.141102 | ||||||||
\(917\) | −48.0689 | −1.58737 | ||||||||
\(918\) | −3.23607 | −0.106806 | ||||||||
\(919\) | −22.2361 | −0.733500 | −0.366750 | − | 0.930319i | \(-0.619530\pi\) | ||||
−0.366750 | + | 0.930319i | \(0.619530\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.1246 | 0.926737 | ||||||||
\(922\) | 13.0344 | 0.429266 | ||||||||
\(923\) | 25.8885 | 0.852132 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.437694 | −0.0143835 | ||||||||
\(927\) | −4.61803 | −0.151676 | ||||||||
\(928\) | −2.88854 | −0.0948211 | ||||||||
\(929\) | −10.8541 | −0.356112 | −0.178056 | − | 0.984020i | \(-0.556981\pi\) | ||||
−0.178056 | + | 0.984020i | \(0.556981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 102.082 | 3.34560 | ||||||||
\(932\) | −6.34752 | −0.207920 | ||||||||
\(933\) | 12.5279 | 0.410144 | ||||||||
\(934\) | 49.9787 | 1.63535 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.23607 | 0.236518 | ||||||||
\(937\) | −17.2016 | −0.561953 | −0.280976 | − | 0.959715i | \(-0.590658\pi\) | ||||
−0.280976 | + | 0.959715i | \(0.590658\pi\) | |||||||
\(938\) | 98.4296 | 3.21384 | ||||||||
\(939\) | 8.47214 | 0.276478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.70820 | −0.316478 | −0.158239 | − | 0.987401i | \(-0.550582\pi\) | ||||
−0.158239 | + | 0.987401i | \(0.550582\pi\) | |||||||
\(942\) | −19.9443 | −0.649819 | ||||||||
\(943\) | −52.9787 | −1.72522 | ||||||||
\(944\) | −32.5623 | −1.05981 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.56231 | −0.148255 | −0.0741275 | − | 0.997249i | \(-0.523617\pi\) | ||||
−0.0741275 | + | 0.997249i | \(0.523617\pi\) | |||||||
\(948\) | 1.90983 | 0.0620284 | ||||||||
\(949\) | −14.6525 | −0.475639 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.58359 | −0.116206 | ||||||||
\(952\) | 23.4164 | 0.758930 | ||||||||
\(953\) | −49.0902 | −1.59019 | −0.795093 | − | 0.606487i | \(-0.792578\pi\) | ||||
−0.795093 | + | 0.606487i | \(0.792578\pi\) | |||||||
\(954\) | 8.70820 | 0.281939 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.6180 | 0.440439 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.6525 | 0.344166 | ||||||||
\(959\) | −27.7082 | −0.894745 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 7.70820 | 0.248522 | ||||||||
\(963\) | 3.85410 | 0.124197 | ||||||||
\(964\) | 0.381966 | 0.0123023 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −39.1246 | −1.25881 | ||||||||
\(967\) | 32.6738 | 1.05072 | 0.525359 | − | 0.850881i | \(-0.323931\pi\) | ||||
0.525359 | + | 0.850881i | \(0.323931\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.0000 | −0.321246 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.5410 | −1.01220 | −0.506100 | − | 0.862475i | \(-0.668913\pi\) | ||||
−0.506100 | + | 0.862475i | \(0.668913\pi\) | |||||||
\(972\) | 0.618034 | 0.0198234 | ||||||||
\(973\) | −6.18034 | −0.198133 | ||||||||
\(974\) | −13.2361 | −0.424111 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33.9787 | −1.08763 | ||||||||
\(977\) | 46.0902 | 1.47456 | 0.737278 | − | 0.675590i | \(-0.236111\pi\) | ||||
0.737278 | + | 0.675590i | \(0.236111\pi\) | |||||||
\(978\) | 10.6180 | 0.339527 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.8541 | 0.346545 | ||||||||
\(982\) | 11.6525 | 0.371845 | ||||||||
\(983\) | 19.0000 | 0.606006 | 0.303003 | − | 0.952990i | \(-0.402011\pi\) | ||||
0.303003 | + | 0.952990i | \(0.402011\pi\) | |||||||
\(984\) | −25.6525 | −0.817771 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.76393 | −0.0880215 | ||||||||
\(987\) | 31.8885 | 1.01502 | ||||||||
\(988\) | −10.0000 | −0.318142 | ||||||||
\(989\) | 41.9787 | 1.33485 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −23.6738 | −0.751643 | ||||||||
\(993\) | −27.5967 | −0.875756 | ||||||||
\(994\) | −67.7771 | −2.14976 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.76393 | −0.150951 | ||||||||
\(997\) | 11.2918 | 0.357615 | 0.178807 | − | 0.983884i | \(-0.442776\pi\) | ||||
0.178807 | + | 0.983884i | \(0.442776\pi\) | |||||||
\(998\) | 18.0902 | 0.572634 | ||||||||
\(999\) | −1.47214 | −0.0465763 |
(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 | 9075.2.a.by.1.2 | 2 | ||
5.4 | even | 2 | 9075.2.a.z.1.1 | 2 | |||
11.3 | even | 5 | 825.2.n.d.526.1 | yes | 4 | ||
11.4 | even | 5 | 825.2.n.d.676.1 | yes | 4 | ||
11.10 | odd | 2 | 9075.2.a.bc.1.1 | 2 | |||
55.3 | odd | 20 | 825.2.bx.c.724.1 | 8 | |||
55.4 | even | 10 | 825.2.n.b.676.1 | yes | 4 | ||
55.14 | even | 10 | 825.2.n.b.526.1 | ✓ | 4 | ||
55.37 | odd | 20 | 825.2.bx.c.49.1 | 8 | |||
55.47 | odd | 20 | 825.2.bx.c.724.2 | 8 | |||
55.48 | odd | 20 | 825.2.bx.c.49.2 | 8 | |||
55.54 | odd | 2 | 9075.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.n.b.526.1 | ✓ | 4 | 55.14 | even | 10 | ||
825.2.n.b.676.1 | yes | 4 | 55.4 | even | 10 | ||
825.2.n.d.526.1 | yes | 4 | 11.3 | even | 5 | ||
825.2.n.d.676.1 | yes | 4 | 11.4 | even | 5 | ||
825.2.bx.c.49.1 | 8 | 55.37 | odd | 20 | |||
825.2.bx.c.49.2 | 8 | 55.48 | odd | 20 | |||
825.2.bx.c.724.1 | 8 | 55.3 | odd | 20 | |||
825.2.bx.c.724.2 | 8 | 55.47 | odd | 20 | |||
9075.2.a.z.1.1 | 2 | 5.4 | even | 2 | |||
9075.2.a.bc.1.1 | 2 | 11.10 | odd | 2 | |||
9075.2.a.bt.1.2 | 2 | 55.54 | odd | 2 | |||
9075.2.a.by.1.2 | 2 | 1.1 | even | 1 | trivial |