Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.47047 | −1.42633 | −0.713163 | − | 0.700998i | \(-0.752738\pi\) | ||||
−0.713163 | + | 0.700998i | \(0.752738\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.726513 | −0.274596 | −0.137298 | − | 0.990530i | \(-0.543842\pi\) | ||||
−0.137298 | + | 0.990530i | \(0.543842\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.10322 | 1.03441 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.45955 | 0.440070 | 0.220035 | − | 0.975492i | \(-0.429383\pi\) | ||||
0.220035 | + | 0.975492i | \(0.429383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.71653 | 1.03078 | 0.515390 | − | 0.856956i | \(-0.327647\pi\) | ||||
0.515390 | + | 0.856956i | \(0.327647\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.47047 | −0.637872 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.16672 | −1.49565 | −0.747825 | − | 0.663896i | \(-0.768902\pi\) | ||||
−0.747825 | + | 0.663896i | \(0.768902\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.31425 | 0.530925 | 0.265462 | − | 0.964121i | \(-0.414475\pi\) | ||||
0.265462 | + | 0.964121i | \(0.414475\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.79483 | 0.391663 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.33500 | 1.32094 | 0.660470 | − | 0.750853i | \(-0.270357\pi\) | ||||
0.660470 | + | 0.750853i | \(0.270357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.254992 | −0.0490733 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.60854 | 0.670089 | 0.335044 | − | 0.942202i | \(-0.391249\pi\) | ||||
0.335044 | + | 0.942202i | \(0.391249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.30751 | −0.414441 | −0.207221 | − | 0.978294i | \(-0.566442\pi\) | ||||
−0.207221 | + | 0.978294i | \(0.566442\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.60576 | −0.627683 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.726513 | −0.122803 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.575787 | 0.0946588 | 0.0473294 | − | 0.998879i | \(-0.484929\pi\) | ||||
0.0473294 | + | 0.998879i | \(0.484929\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.18158 | −1.47023 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.674336 | 0.105314 | 0.0526568 | − | 0.998613i | \(-0.483231\pi\) | ||||
0.0526568 | + | 0.998613i | \(0.483231\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.97471 | 0.911134 | 0.455567 | − | 0.890201i | \(-0.349437\pi\) | ||||
0.455567 | + | 0.890201i | \(0.349437\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.10322 | 0.462600 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.22008 | −0.615562 | −0.307781 | − | 0.951457i | \(-0.599586\pi\) | ||||
−0.307781 | + | 0.951457i | \(0.599586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47218 | −0.924597 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.2347 | 2.13328 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.4139 | 1.97990 | 0.989951 | − | 0.141412i | \(-0.0451643\pi\) | ||||
0.989951 | + | 0.141412i | \(0.0451643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.45955 | 0.196805 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.71728 | −0.757272 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.6629 | −1.90895 | −0.954473 | − | 0.298297i | \(-0.903581\pi\) | ||||
−0.954473 | + | 0.298297i | \(0.903581\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.26703 | −0.162227 | −0.0811136 | − | 0.996705i | \(-0.525848\pi\) | ||||
−0.0811136 | + | 0.996705i | \(0.525848\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.25453 | −0.284044 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.71653 | 0.460979 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.62513 | 0.931557 | 0.465779 | − | 0.884901i | \(-0.345774\pi\) | ||||
0.465779 | + | 0.884901i | \(0.345774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.6504 | −1.88409 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.13882 | 0.135153 | 0.0675766 | − | 0.997714i | \(-0.478473\pi\) | ||||
0.0675766 | + | 0.997714i | \(0.478473\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.45595 | 0.872653 | 0.436326 | − | 0.899789i | \(-0.356279\pi\) | ||||
0.436326 | + | 0.899789i | \(0.356279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.47047 | −0.285265 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.06038 | −0.120841 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.32427 | −0.148992 | −0.0744961 | − | 0.997221i | \(-0.523735\pi\) | ||||
−0.0744961 | + | 0.997221i | \(0.523735\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.67970 | −0.964411 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.58904 | −0.284184 | −0.142092 | − | 0.989853i | \(-0.545383\pi\) | ||||
−0.142092 | + | 0.989853i | \(0.545383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.16672 | −0.668875 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.91478 | −0.955765 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.09211 | 0.645762 | 0.322881 | − | 0.946440i | \(-0.395349\pi\) | ||||
0.322881 | + | 0.946440i | \(0.395349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70011 | −0.283048 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.70063 | 0.591128 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.31425 | 0.237437 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.36737 | 0.748043 | 0.374022 | − | 0.927420i | \(-0.377979\pi\) | ||||
0.374022 | + | 0.927420i | \(0.377979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.52929 | 0.455210 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.87752 | 0.485331 | 0.242666 | − | 0.970110i | \(-0.421978\pi\) | ||||
0.242666 | + | 0.970110i | \(0.421978\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.7618 | −1.55305 | −0.776527 | − | 0.630084i | \(-0.783021\pi\) | ||||
−0.776527 | + | 0.630084i | \(0.783021\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.79483 | 0.175157 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.22827 | 0.215415 | 0.107708 | − | 0.994183i | \(-0.465649\pi\) | ||||
0.107708 | + | 0.994183i | \(0.465649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0544 | 1.53773 | 0.768864 | − | 0.639412i | \(-0.220822\pi\) | ||||
0.768864 | + | 0.639412i | \(0.220822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.42246 | −0.135014 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.06250 | 0.288096 | 0.144048 | − | 0.989571i | \(-0.453988\pi\) | ||||
0.144048 | + | 0.989571i | \(0.453988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.33500 | 0.590742 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.5332 | 1.06624 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.48020 | 0.410700 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.86973 | −0.806339 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.66593 | −0.150211 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.63777 | −0.234065 | −0.117032 | − | 0.993128i | \(-0.537338\pi\) | ||||
−0.117032 | + | 0.993128i | \(0.537338\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.7603 | −1.29957 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.5589 | −1.09727 | −0.548636 | − | 0.836061i | \(-0.684853\pi\) | ||||
−0.548636 | + | 0.836061i | \(0.684853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.68133 | −0.145790 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.254992 | −0.0219463 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.98876 | 0.597090 | 0.298545 | − | 0.954396i | \(-0.403499\pi\) | ||||
0.298545 | + | 0.954396i | \(0.403499\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3797 | −1.13485 | −0.567427 | − | 0.823424i | \(-0.692061\pi\) | ||||
−0.567427 | + | 0.823424i | \(0.692061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4256 | 0.877992 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.42445 | 0.453615 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.60854 | 0.299673 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.9893 | 1.31878 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.00899 | 0.410353 | 0.205176 | − | 0.978725i | \(-0.434223\pi\) | ||||
0.205176 | + | 0.978725i | \(0.434223\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24.4395 | −1.98886 | −0.994431 | − | 0.105390i | \(-0.966391\pi\) | ||||
−0.994431 | + | 0.105390i | \(0.966391\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.1367 | −1.54711 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.30751 | −0.185344 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.32288 | −0.664238 | −0.332119 | − | 0.943237i | \(-0.607764\pi\) | ||||
−0.332119 | + | 0.943237i | \(0.607764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −35.6091 | −2.82398 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.60246 | −0.362725 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0051 | −0.783656 | −0.391828 | − | 0.920038i | \(-0.628157\pi\) | ||||
−0.391828 | + | 0.920038i | \(0.628157\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.60576 | −0.280708 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.70550 | 0.286740 | 0.143370 | − | 0.989669i | \(-0.454206\pi\) | ||||
0.143370 | + | 0.989669i | \(0.454206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.812607 | 0.0625082 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.18161 | 0.549191 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.19393 | −0.470915 | −0.235458 | − | 0.971885i | \(-0.575659\pi\) | ||||
−0.235458 | + | 0.971885i | \(0.575659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.726513 | −0.0549192 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 36.2242 | 2.72278 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0201 | 1.27214 | 0.636070 | − | 0.771631i | \(-0.280559\pi\) | ||||
0.636070 | + | 0.771631i | \(0.280559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6866 | 0.794329 | 0.397165 | − | 0.917747i | \(-0.369994\pi\) | ||||
0.397165 | + | 0.917747i | \(0.369994\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.13017 | 0.231389 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.575787 | 0.0423327 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00061 | −0.658190 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.185255 | 0.0134753 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.17850 | −0.447060 | −0.223530 | − | 0.974697i | \(-0.571758\pi\) | ||||
−0.223530 | + | 0.974697i | \(0.571758\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.2624 | 1.02663 | 0.513315 | − | 0.858200i | \(-0.328417\pi\) | ||||
0.513315 | + | 0.858200i | \(0.328417\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.18158 | −0.657506 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.8069 | 1.83867 | 0.919334 | − | 0.393478i | \(-0.128728\pi\) | ||||
0.919334 | + | 0.393478i | \(0.128728\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.5786 | −1.45878 | −0.729390 | − | 0.684098i | \(-0.760196\pi\) | ||||
−0.729390 | + | 0.684098i | \(0.760196\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.8376 | −1.32870 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.62165 | −0.184004 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.674336 | 0.0470977 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.6589 | 1.36639 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.37775 | 0.233644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9388 | 1.30380 | 0.651899 | − | 0.758306i | \(-0.273973\pi\) | ||||
0.651899 | + | 0.758306i | \(0.273973\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.81342 | −0.192772 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.97471 | 0.407472 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.67644 | 0.113804 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.4197 | −1.24469 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.9188 | −1.54169 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.3883 | 1.63316 | 0.816580 | − | 0.577233i | \(-0.195867\pi\) | ||||
0.816580 | + | 0.577233i | \(0.195867\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.10322 | 0.206881 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.9988 | 1.19462 | 0.597312 | − | 0.802009i | \(-0.296235\pi\) | ||||
0.597312 | + | 0.802009i | \(0.296235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.95818 | 0.261564 | 0.130782 | − | 0.991411i | \(-0.458251\pi\) | ||||
0.130782 | + | 0.991411i | \(0.458251\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.61963 | 0.172359 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.17047 | 0.273217 | 0.136608 | − | 0.990625i | \(-0.456380\pi\) | ||||
0.136608 | + | 0.990625i | \(0.456380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.22008 | −0.275288 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.27157 | 0.212511 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.54470 | −0.358657 | −0.179328 | − | 0.983789i | \(-0.557392\pi\) | ||||
−0.179328 | + | 0.983789i | \(0.557392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.1780 | 0.977700 | 0.488850 | − | 0.872368i | \(-0.337417\pi\) | ||||
0.488850 | + | 0.872368i | \(0.337417\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2079 | 1.42464 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.47218 | −0.413492 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.60097 | 0.547267 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.39613 | 0.405338 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.7844 | −1.75373 | −0.876867 | − | 0.480732i | \(-0.840371\pi\) | ||||
−0.876867 | + | 0.480732i | \(0.840371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.24623 | 0.581305 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.2347 | 0.954034 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.2813 | −0.953223 | −0.476611 | − | 0.879114i | \(-0.658135\pi\) | ||||
−0.476611 | + | 0.879114i | \(0.658135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.418317 | −0.0259929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.1981 | 0.693143 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.9217 | −1.84505 | −0.922524 | − | 0.385939i | \(-0.873878\pi\) | ||||
−0.922524 | + | 0.385939i | \(0.873878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.4139 | 0.885439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.0504 | −0.921067 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.28426 | −0.200245 | −0.100123 | − | 0.994975i | \(-0.531923\pi\) | ||||
−0.100123 | + | 0.994975i | \(0.531923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8398 | 0.779964 | 0.389982 | − | 0.920823i | \(-0.372481\pi\) | ||||
0.389982 | + | 0.920823i | \(0.372481\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.67053 | 0.403719 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.45955 | 0.0880139 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.1556 | −1.27112 | −0.635558 | − | 0.772053i | \(-0.719230\pi\) | ||||
−0.635558 | + | 0.772053i | \(0.719230\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.16071 | −0.428700 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.6501 | −0.814294 | −0.407147 | − | 0.913363i | \(-0.633476\pi\) | ||||
−0.407147 | + | 0.913363i | \(0.633476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.3614 | −0.972586 | −0.486293 | − | 0.873796i | \(-0.661651\pi\) | ||||
−0.486293 | + | 0.873796i | \(0.661651\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.71728 | −0.338662 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.489914 | −0.0289187 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.0285 | 1.23697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.2009 | −1.06695 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.31367 | 0.135166 | 0.0675830 | − | 0.997714i | \(-0.478471\pi\) | ||||
0.0675830 | + | 0.997714i | \(0.478471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.6629 | −0.853707 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.372173 | −0.0215957 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.5442 | 1.36160 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.34070 | −0.250194 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.0498 | −0.692240 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.26703 | −0.0725502 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.7601 | −1.47021 | −0.735105 | − | 0.677954i | \(-0.762867\pi\) | ||||
−0.735105 | + | 0.677954i | \(0.762867\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 38.9390 | 2.21516 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.35859 | −0.303858 | −0.151929 | − | 0.988391i | \(-0.548548\pi\) | ||||
−0.151929 | + | 0.988391i | \(0.548548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.6618 | 1.84615 | 0.923077 | − | 0.384616i | \(-0.125666\pi\) | ||||
0.923077 | + | 0.384616i | \(0.125666\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.25453 | −0.127028 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.4637 | 1.48635 | 0.743175 | − | 0.669097i | \(-0.233319\pi\) | ||||
0.743175 | + | 0.669097i | \(0.233319\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.26683 | 0.294886 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.50487 | −0.307252 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.2713 | −0.794077 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.71653 | 0.206156 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −39.6618 | −2.19330 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.06594 | 0.169031 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.1069 | 1.48993 | 0.744966 | − | 0.667102i | \(-0.232466\pi\) | ||||
0.744966 | + | 0.667102i | \(0.232466\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.78679 | 0.0979156 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.62513 | 0.416605 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.87037 | −0.210833 | −0.105416 | − | 0.994428i | \(-0.533618\pi\) | ||||
−0.105416 | + | 0.994428i | \(0.533618\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.56581 | −0.410918 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.36792 | −0.182383 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.78771 | 0.528487 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.6504 | −0.842591 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.3819 | 1.09416 | 0.547079 | − | 0.837081i | \(-0.315740\pi\) | ||||
0.547079 | + | 0.837081i | \(0.315740\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8958 | −0.636766 | −0.318383 | − | 0.947962i | \(-0.603140\pi\) | ||||
−0.318383 | + | 0.947962i | \(0.603140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.947687 | −0.0505838 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.0907 | 1.38867 | 0.694333 | − | 0.719654i | \(-0.255700\pi\) | ||||
0.694333 | + | 0.719654i | \(0.255700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.13882 | 0.0604423 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.0682 | −0.585791 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.5500 | 0.715141 | 0.357571 | − | 0.933886i | \(-0.383605\pi\) | ||||
0.357571 | + | 0.933886i | \(0.383605\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.6443 | −0.718119 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.9124 | 1.15010 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.45595 | 0.390262 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5521 | −1.12501 | −0.562505 | − | 0.826794i | \(-0.690162\pi\) | ||||
−0.562505 | + | 0.826794i | \(0.690162\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.09261 | 0.108937 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4719 | −0.543673 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0797 | 0.625461 | 0.312730 | − | 0.949842i | \(-0.398756\pi\) | ||||
0.312730 | + | 0.949842i | \(0.398756\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.47047 | −0.127574 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.4112 | 0.690714 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.8380 | 1.42994 | 0.714972 | − | 0.699153i | \(-0.246439\pi\) | ||||
0.714972 | + | 0.699153i | \(0.246439\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.51654 | 0.333852 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.0629 | 0.514188 | 0.257094 | − | 0.966386i | \(-0.417235\pi\) | ||||
0.257094 | + | 0.966386i | \(0.417235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.06038 | −0.0540419 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.5408 | 0.942482 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.07206 | 0.358568 | 0.179284 | − | 0.983797i | \(-0.442622\pi\) | ||||
0.179284 | + | 0.983797i | \(0.442622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.0662 | −1.97566 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.0263 | 1.56507 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.32427 | −0.0666313 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.764152 | −0.0383517 | −0.0191758 | − | 0.999816i | \(-0.506104\pi\) | ||||
−0.0191758 | + | 0.999816i | \(0.506104\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.15367 | 0.207944 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.57594 | −0.427198 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.67970 | −0.431298 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.840388 | 0.0416565 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.82301 | 0.287929 | 0.143965 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143965 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.2655 | −0.851645 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.6528 | 0.524189 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.58904 | −0.127091 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.0542 | 1.61867 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.7846 | 0.575718 | 0.287859 | − | 0.957673i | \(-0.407057\pi\) | ||||
0.287859 | + | 0.957673i | \(0.407057\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5483 | −0.660301 | −0.330151 | − | 0.943928i | \(-0.607100\pi\) | ||||
−0.330151 | + | 0.943928i | \(0.607100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.0958 | −0.636741 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.16672 | −0.299130 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.920517 | 0.0445469 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.4009 | −0.647003 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.2624 | 1.89120 | 0.945601 | − | 0.325328i | \(-0.105475\pi\) | ||||
0.945601 | + | 0.325328i | \(0.105475\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.7474 | 0.804828 | 0.402414 | − | 0.915458i | \(-0.368171\pi\) | ||||
0.402414 | + | 0.915458i | \(0.368171\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.91478 | −0.427431 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.6608 | 0.701319 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.3978 | 1.88035 | 0.940177 | − | 0.340688i | \(-0.110660\pi\) | ||||
0.940177 | + | 0.340688i | \(0.110660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.0846 | −0.956408 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.8812 | 0.897075 | 0.448538 | − | 0.893764i | \(-0.351945\pi\) | ||||
0.448538 | + | 0.893764i | \(0.351945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.09211 | 0.288794 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.3746 | −0.585296 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5278 | 1.01596 | 0.507979 | − | 0.861369i | \(-0.330393\pi\) | ||||
0.507979 | + | 0.861369i | \(0.330393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.984224 | 0.0463453 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 60.3771 | 2.83677 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.70011 | −0.126583 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6308 | 1.05862 | 0.529311 | − | 0.848428i | \(-0.322450\pi\) | ||||
0.529311 | + | 0.848428i | \(0.322450\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.57247 | 0.0733965 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.1289 | 1.03065 | 0.515323 | − | 0.856996i | \(-0.327672\pi\) | ||||
0.515323 | + | 0.856996i | \(0.327672\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.78716 | −0.268952 | −0.134476 | − | 0.990917i | \(-0.542935\pi\) | ||||
−0.134476 | + | 0.990917i | \(0.542935\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.70063 | 0.264361 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.556011 | 0.0257291 | 0.0128646 | − | 0.999917i | \(-0.495905\pi\) | ||||
0.0128646 | + | 0.999917i | \(0.495905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.53975 | −0.255802 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.5614 | 0.947420 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.72036 | 0.400963 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.31425 | 0.106185 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 44.7295 | 2.04802 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.6638 | 0.989845 | 0.494923 | − | 0.868937i | \(-0.335196\pi\) | ||||
0.494923 | + | 0.868937i | \(0.335196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.13993 | 0.0975724 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3702 | 0.517364 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.36737 | 0.334535 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.4708 | −0.927621 | −0.463811 | − | 0.885934i | \(-0.653518\pi\) | ||||
−0.463811 | + | 0.885934i | \(0.653518\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.7172 | 1.11775 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.1429 | 0.548002 | 0.274001 | − | 0.961729i | \(-0.411653\pi\) | ||||
0.274001 | + | 0.961729i | \(0.411653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.2528 | −1.00222 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.52929 | 0.203576 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.827368 | −0.0371125 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.50320 | 0.380655 | 0.190328 | − | 0.981721i | \(-0.439045\pi\) | ||||
0.190328 | + | 0.981721i | \(0.439045\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.15433 | −0.408985 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6010 | −0.695615 | −0.347807 | − | 0.937566i | \(-0.613074\pi\) | ||||
−0.347807 | + | 0.937566i | \(0.613074\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.87752 | 0.217047 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.00752 | −0.0891571 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.9556 | 0.884515 | 0.442257 | − | 0.896888i | \(-0.354178\pi\) | ||||
0.442257 | + | 0.896888i | \(0.354178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.41684 | −0.239627 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.590115 | −0.0260542 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.7618 | −0.694547 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.15940 | −0.270890 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.3019 | 0.671679 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.4373 | −0.632510 | −0.316255 | − | 0.948674i | \(-0.602425\pi\) | ||||
−0.316255 | + | 0.948674i | \(0.602425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7908 | 0.821664 | 0.410832 | − | 0.911711i | \(-0.365238\pi\) | ||||
0.410832 | + | 0.911711i | \(0.365238\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.79483 | 0.0783327 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.2298 | 0.619859 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.1322 | 0.744880 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −45.5021 | −1.97462 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.50619 | 0.108555 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.22827 | 0.0963366 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −42.0476 | −1.81449 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.44644 | −0.406887 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.8477 | 1.62720 | 0.813601 | − | 0.581424i | \(-0.197504\pi\) | ||||
0.813601 | + | 0.581424i | \(0.197504\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.4009 | −1.13297 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.0544 | 0.687693 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.3659 | 1.29835 | 0.649176 | − | 0.760638i | \(-0.275114\pi\) | ||||
0.649176 | + | 0.760638i | \(0.275114\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.93188 | −0.167809 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.35105 | 0.355767 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.962100 | 0.0409127 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.42246 | −0.0603802 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8269 | 0.628238 | 0.314119 | − | 0.949384i | \(-0.398291\pi\) | ||||
0.314119 | + | 0.949384i | \(0.398291\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2052 | 0.939179 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.2357 | 0.938794 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.26621 | −0.179799 | −0.0898997 | − | 0.995951i | \(-0.528655\pi\) | ||||
−0.0898997 | + | 0.995951i | \(0.528655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.06250 | 0.128840 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.30591 | 0.264823 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.8430 | 0.999549 | 0.499775 | − | 0.866155i | \(-0.333416\pi\) | ||||
0.499775 | + | 0.866155i | \(0.333416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.9759 | −1.21260 | −0.606302 | − | 0.795234i | \(-0.707348\pi\) | ||||
−0.606302 | + | 0.795234i | \(0.707348\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2638 | 0.637654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.33500 | 0.264188 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.4129 | 1.68241 | 0.841206 | − | 0.540715i | \(-0.181846\pi\) | ||||
0.841206 | + | 0.540715i | \(0.181846\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −35.2348 | −1.46431 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.88097 | 0.0780357 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.0378 | 0.871295 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.5332 | 0.476839 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.1088 | 1.16018 | 0.580088 | − | 0.814554i | \(-0.303018\pi\) | ||||
0.580088 | + | 0.814554i | \(0.303018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.34015 | −0.220037 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −63.7552 | −2.62254 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.56359 | −0.105274 | −0.0526369 | − | 0.998614i | \(-0.516763\pi\) | ||||
−0.0526369 | + | 0.998614i | \(0.516763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.48020 | 0.183670 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 50.8388 | 2.08069 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.8711 | −1.42480 | −0.712398 | − | 0.701776i | \(-0.752391\pi\) | ||||
−0.712398 | + | 0.701776i | \(0.752391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.38421 | −0.0972538 | −0.0486269 | − | 0.998817i | \(-0.515485\pi\) | ||||
−0.0486269 | + | 0.998817i | \(0.515485\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.6624 | 0.963608 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.86973 | −0.360606 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.0153986 | −0.000625011 0 | −0.000312506 | − | 1.00000i | \(-0.500099\pi\) | ||||
−0.000312506 | 1.00000i | \(0.500099\pi\) | ||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.47670 | 0.262449 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.6841 | −0.634509 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.36715 | −0.0552186 | −0.0276093 | − | 0.999619i | \(-0.508789\pi\) | ||||
−0.0276093 | + | 0.999619i | \(0.508789\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.66593 | −0.0671766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8726 | 0.759781 | 0.379890 | − | 0.925032i | \(-0.375962\pi\) | ||||
0.379890 | + | 0.925032i | \(0.375962\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1507 | 0.970698 | 0.485349 | − | 0.874320i | \(-0.338693\pi\) | ||||
0.485349 | + | 0.874320i | \(0.338693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.61538 | −0.0648229 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.42600 | −0.177324 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.34463 | −0.333252 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.55072 | −0.141576 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.5122 | 1.21467 | 0.607336 | − | 0.794445i | \(-0.292238\pi\) | ||||
0.607336 | + | 0.794445i | \(0.292238\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.7876 | −1.85964 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.63777 | −0.104677 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.0541 | −0.953056 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.53401 | 0.139803 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.4463 | −1.28155 | −0.640776 | − | 0.767728i | \(-0.721387\pi\) | ||||
−0.640776 | + | 0.767728i | \(0.721387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.110690 | −0.00436518 | −0.00218259 | − | 0.999998i | \(-0.500695\pi\) | ||||
−0.00218259 | + | 0.999998i | \(0.500695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.7603 | −0.581187 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.45331 | 0.332334 | 0.166167 | − | 0.986098i | \(-0.446861\pi\) | ||||
0.166167 | + | 0.986098i | \(0.446861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.4012 | −0.840069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.14158 | −0.162322 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.5478 | −1.46936 | −0.734680 | − | 0.678414i | \(-0.762668\pi\) | ||||
−0.734680 | + | 0.678414i | \(0.762668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5589 | −0.490715 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.1374 | 0.902677 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.8692 | 0.618175 | 0.309087 | − | 0.951034i | \(-0.399976\pi\) | ||||
0.309087 | + | 0.951034i | \(0.399976\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.9566 | −1.59303 | −0.796514 | − | 0.604621i | \(-0.793325\pi\) | ||||
−0.796514 | + | 0.604621i | \(0.793325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.6202 | 2.19895 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.68133 | −0.0651992 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.8601 | 0.885146 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −60.2505 | −2.32942 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.84929 | −0.0713912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.3073 | −1.66938 | −0.834688 | − | 0.550724i | \(-0.814352\pi\) | ||||
−0.834688 | + | 0.550724i | \(0.814352\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.254992 | −0.00981466 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.5692 | −0.752107 | −0.376053 | − | 0.926598i | \(-0.622719\pi\) | ||||
−0.376053 | + | 0.926598i | \(0.622719\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.35249 | −0.205410 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −44.4655 | −1.70392 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.7377 | 0.487395 | 0.243697 | − | 0.969851i | \(-0.421640\pi\) | ||||
0.243697 | + | 0.969851i | \(0.421640\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.98876 | 0.267027 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.77855 | −0.373075 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 53.5697 | 2.04084 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.22621 | −0.350982 | −0.175491 | − | 0.984481i | \(-0.556151\pi\) | ||||
−0.175491 | + | 0.984481i | \(0.556151\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.29059 | −0.124999 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.3797 | −0.507522 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.15844 | −0.157512 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.3030 | −0.389696 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.1740 | −1.70620 | −0.853098 | − | 0.521750i | \(-0.825279\pi\) | ||||
−0.853098 | + | 0.521750i | \(0.825279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.33251 | 0.0502567 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.4256 | 0.392650 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.54358 | −0.133270 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.10059 | 0.266668 | 0.133334 | − | 0.991071i | \(-0.457432\pi\) | ||||
0.133334 | + | 0.991071i | \(0.457432\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.10950 | −0.154118 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.6181 | −0.547452 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.42445 | 0.202863 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.6980 | 0.511561 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.2807 | 0.830928 | 0.415464 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415464 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.4511 | 0.426463 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −37.4967 | −1.39452 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.60854 | 0.134018 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.3064 | 1.56906 | 0.784529 | − | 0.620092i | \(-0.212905\pi\) | ||||
0.784529 | + | 0.620092i | \(0.212905\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.8248 | −1.06759 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.8444 | −1.36274 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.1373 | −1.74106 | −0.870528 | − | 0.492118i | \(-0.836223\pi\) | ||||
−0.870528 | + | 0.492118i | \(0.836223\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.9893 | 0.589775 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.1292 | 0.409950 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3658 | −0.381312 | −0.190656 | − | 0.981657i | \(-0.561062\pi\) | ||||
−0.190656 | + | 0.981657i | \(0.561062\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.2484 | −0.780581 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.11245 | 0.224244 | 0.112122 | − | 0.993694i | \(-0.464235\pi\) | ||||
0.112122 | + | 0.993694i | \(0.464235\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00899 | 0.183515 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.03434 | −0.293961 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.61887 | −0.0591521 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.98955 | −0.145581 | −0.0727903 | − | 0.997347i | \(-0.523190\pi\) | ||||
−0.0727903 | + | 0.997347i | \(0.523190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 68.6404 | 2.50140 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.4395 | −0.889446 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.89107 | 0.105078 | 0.0525389 | − | 0.998619i | \(-0.483269\pi\) | ||||
0.0525389 | + | 0.998619i | \(0.483269\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.8425 | −0.829131 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.2107 | 1.38514 | 0.692569 | − | 0.721352i | \(-0.256479\pi\) | ||||
0.692569 | + | 0.721352i | \(0.256479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.6637 | −0.422254 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.1367 | −0.691888 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −54.4951 | −1.96770 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.4090 | 1.56537 | 0.782684 | − | 0.622420i | \(-0.213850\pi\) | ||||
0.782684 | + | 0.622420i | \(0.213850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.7520 | 1.35961 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.6466 | 1.71373 | 0.856864 | − | 0.515543i | \(-0.172410\pi\) | ||||
0.856864 | + | 0.515543i | \(0.172410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.30751 | −0.0828883 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.03344 | 0.0370744 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.56058 | 0.0559136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.66216 | 0.0594768 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.920150 | −0.0328835 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.32288 | −0.297056 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.4071 | 1.58294 | 0.791470 | − | 0.611208i | \(-0.209316\pi\) | ||||
0.791470 | + | 0.611208i | \(0.209316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 73.9205 | 2.63164 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.22494 | −0.0791099 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.70897 | −0.167221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −35.6091 | −1.26292 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.9489 | 0.387829 | 0.193914 | − | 0.981018i | \(-0.437882\pi\) | ||||
0.193914 | + | 0.981018i | \(0.437882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.0241 | 0.920665 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.9051 | 0.667980 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.8823 | 0.384028 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.60246 | −0.162215 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.11367 | 0.285615 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.7150 | −0.798617 | −0.399309 | − | 0.916817i | \(-0.630750\pi\) | ||||
−0.399309 | + | 0.916817i | \(0.630750\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.03580 | −0.211946 | −0.105973 | − | 0.994369i | \(-0.533796\pi\) | ||||
−0.105973 | + | 0.994369i | \(0.533796\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.7204 | −1.11248 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0051 | −0.350462 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8269 | 0.483744 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.37902 | −0.292787 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.57926 | −0.0900167 | −0.0450083 | − | 0.998987i | \(-0.514331\pi\) | ||||
−0.0450083 | + | 0.998987i | \(0.514331\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.82892 | 0.342615 | 0.171307 | − | 0.985218i | \(-0.445201\pi\) | ||||
0.171307 | + | 0.985218i | \(0.445201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.60576 | −0.125537 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.4158 | −0.953342 | −0.476671 | − | 0.879082i | \(-0.658157\pi\) | ||||
−0.476671 | + | 0.879082i | \(0.658157\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.2280 | −1.64030 | −0.820148 | − | 0.572151i | \(-0.806109\pi\) | ||||
−0.820148 | + | 0.572151i | \(0.806109\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.2642 | 1.81302 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.9121 | 1.38287 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.70550 | 0.128234 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.588398 | 0.0203380 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.1716 | 1.55950 | 0.779749 | − | 0.626092i | \(-0.215347\pi\) | ||||
0.779749 | + | 0.626092i | \(0.215347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9785 | −0.550981 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.7221 | 1.16145 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.812607 | 0.0279545 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.44397 | 0.221417 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.4204 | 1.38722 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.64761 | 0.125038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.6370 | −1.56258 | −0.781290 | − | 0.624168i | \(-0.785438\pi\) | ||||
−0.781290 | + | 0.624168i | \(0.785438\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.18161 | 0.245606 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.5351 | −0.769783 | −0.384891 | − | 0.922962i | \(-0.625761\pi\) | ||||
−0.384891 | + | 0.922962i | \(0.625761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.2935 | −0.828882 | −0.414441 | − | 0.910076i | \(-0.636023\pi\) | ||||
−0.414441 | + | 0.910076i | \(0.636023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.21032 | 0.0412475 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.8615 | 1.39094 | 0.695471 | − | 0.718554i | \(-0.255196\pi\) | ||||
0.695471 | + | 0.718554i | \(0.255196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.19393 | −0.210600 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −51.9501 | −1.76432 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.93284 | −0.0655670 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.3390 | 0.960231 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.8625 | 0.773780 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.726513 | −0.0245606 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.61456 | 0.0545198 | 0.0272599 | − | 0.999628i | \(-0.491322\pi\) | ||||
0.0272599 | + | 0.999628i | \(0.491322\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.71585 | −0.192791 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.7743 | −1.34003 | −0.670015 | − | 0.742348i | \(-0.733712\pi\) | ||||
−0.670015 | + | 0.742348i | \(0.733712\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.0006 | −1.11056 | −0.555279 | − | 0.831664i | \(-0.687389\pi\) | ||||
−0.555279 | + | 0.831664i | \(0.687389\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.2242 | 1.21766 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.2071 | −1.35002 | −0.675012 | − | 0.737807i | \(-0.735861\pi\) | ||||
−0.675012 | + | 0.737807i | \(0.735861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.91638 | 0.0642732 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.6684 | −0.424408 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.76631 | −0.326817 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.0201 | 0.568918 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −58.1653 | −1.94208 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.32674 | −0.277712 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −88.8865 | −2.96124 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.7236 | 0.356858 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.6866 | 0.355235 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.02603 | −0.0340686 | −0.0170343 | − | 0.999855i | \(-0.505422\pi\) | ||||
−0.0170343 | + | 0.999855i | \(0.505422\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.1360 | 0.502029 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.41039 | −0.179254 | −0.0896271 | − | 0.995975i | \(-0.528568\pi\) | ||||
−0.0896271 | + | 0.995975i | \(0.528568\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.77882 | −0.125061 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.13017 | 0.103480 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.12417 | 0.301307 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.3384 | 1.16571 | 0.582853 | − | 0.812578i | \(-0.301936\pi\) | ||||
0.582853 | + | 0.812578i | \(0.301936\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 63.6396 | 2.09700 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.23246 | 0.139313 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.575787 | 0.0189318 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −48.9122 | −1.60649 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.1573 | 0.398867 | 0.199433 | − | 0.979911i | \(-0.436090\pi\) | ||||
0.199433 | + | 0.979911i | \(0.436090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.9782 | −0.490891 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.2382 | 0.433400 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.00061 | −0.294352 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6996 | 0.545554 | 0.272777 | − | 0.962077i | \(-0.412058\pi\) | ||||
0.272777 | + | 0.962077i | \(0.412058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −80.6899 | −2.63322 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.3099 | 1.37926 | 0.689632 | − | 0.724160i | \(-0.257772\pi\) | ||||
0.689632 | + | 0.724160i | \(0.257772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.27192 | 0.139113 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.185255 | 0.00602635 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.40261 | 0.110570 | 0.0552849 | − | 0.998471i | \(-0.482393\pi\) | ||||
0.0552849 | + | 0.998471i | \(0.482393\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.7103 | 0.899513 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −65.3778 | −2.12002 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.8392 | −0.998979 | −0.499489 | − | 0.866320i | \(-0.666479\pi\) | ||||
−0.499489 | + | 0.866320i | \(0.666479\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.17850 | −0.199931 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.0115 | −0.420603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.07742 | −0.163959 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.6754 | −0.828238 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.91481 | 0.222827 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.2624 | 0.459123 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.8323 | 1.50602 | 0.753012 | − | 0.658006i | \(-0.228600\pi\) | ||||
0.753012 | + | 0.658006i | \(0.228600\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 35.2568 | 1.13261 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.7271 | 0.536797 | 0.268398 | − | 0.963308i | \(-0.413506\pi\) | ||||
0.268398 | + | 0.963308i | \(0.413506\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.72055 | 0.311626 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.18158 | −0.294046 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.36237 | 0.0755789 | 0.0377895 | − | 0.999286i | \(-0.487968\pi\) | ||||
0.0377895 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.89171 | 0.284180 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 49.8201 | 1.59063 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.5751 | 0.401082 | 0.200541 | − | 0.979685i | \(-0.435730\pi\) | ||||
0.200541 | + | 0.979685i | \(0.435730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.8069 | 0.822277 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.57432 | −0.241093 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.8498 | 1.20355 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7263 | 1.48431 | 0.742155 | − | 0.670228i | \(-0.233804\pi\) | ||||
0.742155 | + | 0.670228i | \(0.233804\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −66.9669 | −2.12513 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.5786 | −0.652386 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.3761 | −1.37373 | −0.686867 | − | 0.726783i | \(-0.741015\pi\) | ||||
−0.686867 | + | 0.726783i | \(0.741015\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.146821 | −0.00464522 |
(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 | 8020.2.a.f.1.5 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.f.1.5 | ✓ | 37 | 1.1 | even | 1 | trivial |