Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 3.39399 | 1.95952 | 0.979761 | − | 0.200170i | \(-0.0641495\pi\) | ||||
0.979761 | + | 0.200170i | \(0.0641495\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.84335 | −0.824373 | −0.412187 | − | 0.911099i | \(-0.635235\pi\) | ||||
−0.412187 | + | 0.911099i | \(0.635235\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.40053 | 0.529352 | 0.264676 | − | 0.964337i | \(-0.414735\pi\) | ||||
0.264676 | + | 0.964337i | \(0.414735\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.51918 | 2.83973 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77705 | 1.44034 | 0.720168 | − | 0.693800i | \(-0.244065\pi\) | ||||
0.720168 | + | 0.693800i | \(0.244065\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.38340 | −1.21574 | −0.607868 | − | 0.794038i | \(-0.707975\pi\) | ||||
−0.607868 | + | 0.794038i | \(0.707975\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.25633 | −1.61538 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.98913 | 0.967506 | 0.483753 | − | 0.875205i | \(-0.339273\pi\) | ||||
0.483753 | + | 0.875205i | \(0.339273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.05133 | 0.700024 | 0.350012 | − | 0.936745i | \(-0.386178\pi\) | ||||
0.350012 | + | 0.936745i | \(0.386178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.75340 | 1.03728 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.20078 | 1.08444 | 0.542218 | − | 0.840238i | \(-0.317585\pi\) | ||||
0.542218 | + | 0.840238i | \(0.317585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.60204 | −0.320409 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.7321 | 3.60499 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.58232 | −1.03661 | −0.518306 | − | 0.855195i | \(-0.673437\pi\) | ||||
−0.518306 | + | 0.855195i | \(0.673437\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.38580 | 1.50613 | 0.753067 | − | 0.657944i | \(-0.228574\pi\) | ||||
0.753067 | + | 0.657944i | \(0.228574\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.2133 | 2.82237 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.58168 | −0.436383 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.29402 | −1.19913 | −0.599565 | − | 0.800326i | \(-0.704660\pi\) | ||||
−0.599565 | + | 0.800326i | \(0.704660\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.8772 | −2.38226 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.29108 | −0.826327 | −0.413164 | − | 0.910657i | \(-0.635576\pi\) | ||||
−0.413164 | + | 0.910657i | \(0.635576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.60690 | −1.31254 | −0.656270 | − | 0.754526i | \(-0.727867\pi\) | ||||
−0.656270 | + | 0.754526i | \(0.727867\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −15.7039 | −2.34100 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.56256 | −0.519653 | −0.259826 | − | 0.965655i | \(-0.583665\pi\) | ||||
−0.259826 | + | 0.965655i | \(0.583665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.03851 | −0.719787 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.5391 | 1.89585 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.07015 | −0.146996 | −0.0734981 | − | 0.997295i | \(-0.523416\pi\) | ||||
−0.0734981 | + | 0.997295i | \(0.523416\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.80580 | −1.18737 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.3562 | 1.37171 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7289 | 1.52697 | 0.763485 | − | 0.645826i | \(-0.223487\pi\) | ||||
0.763485 | + | 0.645826i | \(0.223487\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.87603 | 0.240200 | 0.120100 | − | 0.992762i | \(-0.461678\pi\) | ||||
0.120100 | + | 0.992762i | \(0.461678\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.9314 | 1.50322 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.08015 | 1.00222 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5600 | −1.53445 | −0.767227 | − | 0.641376i | \(-0.778364\pi\) | ||||
−0.767227 | + | 0.641376i | \(0.778364\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.6514 | 2.12498 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.78679 | −0.805444 | −0.402722 | − | 0.915322i | \(-0.631936\pi\) | ||||
−0.402722 | + | 0.915322i | \(0.631936\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3111 | 1.55794 | 0.778972 | − | 0.627059i | \(-0.215741\pi\) | ||||
0.778972 | + | 0.627059i | \(0.215741\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.43732 | −0.627848 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.69042 | 0.762444 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.8420 | 1.89487 | 0.947436 | − | 0.319946i | \(-0.103665\pi\) | ||||
0.947436 | + | 0.319946i | \(0.103665\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 38.0189 | 4.22433 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.43147 | 0.266889 | 0.133444 | − | 0.991056i | \(-0.457396\pi\) | ||||
0.133444 | + | 0.991056i | \(0.457396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.35338 | −0.797586 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.9464 | −2.03126 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3588 | −1.52203 | −0.761017 | − | 0.648732i | \(-0.775300\pi\) | ||||
−0.761017 | + | 0.648732i | \(0.775300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.13909 | −0.643552 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 28.4613 | 2.95130 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.62469 | −0.577081 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.75137 | −0.482429 | −0.241214 | − | 0.970472i | \(-0.577546\pi\) | ||||
−0.241214 | + | 0.970472i | \(0.577546\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 40.6966 | 4.09016 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.08097 | 0.704583 | 0.352291 | − | 0.935890i | \(-0.385403\pi\) | ||||
0.352291 | + | 0.935890i | \(0.385403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4588 | 1.22760 | 0.613801 | − | 0.789461i | \(-0.289640\pi\) | ||||
0.613801 | + | 0.789461i | \(0.289640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.76220 | −0.855103 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.90438 | −0.957493 | −0.478746 | − | 0.877953i | \(-0.658909\pi\) | ||||
−0.478746 | + | 0.877953i | \(0.658909\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0878728 | −0.00841669 | −0.00420834 | − | 0.999991i | \(-0.501340\pi\) | ||||
−0.00420834 | + | 0.999991i | \(0.501340\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −24.7558 | −2.34972 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.46984 | 0.514559 | 0.257280 | − | 0.966337i | \(-0.417174\pi\) | ||||
0.257280 | + | 0.966337i | \(0.417174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.58687 | −0.893980 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −37.3430 | −3.45236 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.58691 | 0.512151 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8202 | 1.07457 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.9579 | −1.61921 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1699 | 1.08851 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.6060 | 1.65102 | 0.825509 | − | 0.564389i | \(-0.190888\pi\) | ||||
0.825509 | + | 0.564389i | \(0.190888\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −29.2117 | −2.57195 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.41585 | 0.211074 | 0.105537 | − | 0.994415i | \(-0.466344\pi\) | ||||
0.105537 | + | 0.994415i | \(0.466344\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.27349 | 0.370559 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −34.5298 | −2.97186 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.3205 | 1.73610 | 0.868050 | − | 0.496477i | \(-0.165373\pi\) | ||||
0.868050 | + | 0.496477i | \(0.165373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.5923 | −1.15289 | −0.576444 | − | 0.817137i | \(-0.695560\pi\) | ||||
−0.576444 | + | 0.817137i | \(0.695560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.0913 | −1.01827 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.9397 | −1.75107 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.2902 | 0.854555 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.1007 | −1.41044 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.86674 | −0.152929 | −0.0764645 | − | 0.997072i | \(-0.524363\pi\) | ||||
−0.0764645 | + | 0.997072i | \(0.524363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.63198 | −0.539703 | −0.269852 | − | 0.962902i | \(-0.586975\pi\) | ||||
−0.269852 | + | 0.962902i | \(0.586975\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33.9841 | 2.74745 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.4580 | −1.24162 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.99472 | −0.398622 | −0.199311 | − | 0.979936i | \(-0.563870\pi\) | ||||
−0.199311 | + | 0.979936i | \(0.563870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.63207 | −0.288042 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.28386 | 0.574048 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3940 | −0.892448 | −0.446224 | − | 0.894921i | \(-0.647232\pi\) | ||||
−0.446224 | + | 0.894921i | \(0.647232\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −29.8868 | −2.32669 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.26981 | 0.253025 | 0.126513 | − | 0.991965i | \(-0.459622\pi\) | ||||
0.126513 | + | 0.991965i | \(0.459622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.21416 | 0.478013 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 25.9949 | 1.98788 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.17358 | 0.317311 | 0.158656 | − | 0.987334i | \(-0.449284\pi\) | ||||
0.158656 | + | 0.987334i | \(0.449284\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.24372 | −0.169609 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 39.8077 | 2.99213 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.86920 | −0.513428 | −0.256714 | − | 0.966487i | \(-0.582640\pi\) | ||||
−0.256714 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.12093 | 0.603624 | 0.301812 | − | 0.953367i | \(-0.402408\pi\) | ||||
0.301812 | + | 0.953367i | \(0.402408\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.36722 | 0.470678 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.4455 | 0.988530 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.0563 | 1.39353 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 26.2349 | 1.90831 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.9393 | −1.15333 | −0.576665 | − | 0.816981i | \(-0.695646\pi\) | ||||
−0.576665 | + | 0.816981i | \(0.695646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.5715 | −0.976895 | −0.488448 | − | 0.872593i | \(-0.662437\pi\) | ||||
−0.488448 | + | 0.872593i | \(0.662437\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 27.4240 | 1.96387 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.2258 | 1.36978 | 0.684889 | − | 0.728647i | \(-0.259851\pi\) | ||||
0.684889 | + | 0.728647i | \(0.259851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.5614 | 1.67022 | 0.835111 | − | 0.550081i | \(-0.185403\pi\) | ||||
0.835111 | + | 0.550081i | \(0.185403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −42.6287 | −3.00680 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.81823 | −0.548732 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.75333 | 0.681202 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 44.3064 | 3.07950 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.5764 | 1.00827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2329 | 0.773305 | 0.386652 | − | 0.922225i | \(-0.373631\pi\) | ||||
0.386652 | + | 0.922225i | \(0.373631\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.0343 | −1.57828 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.8656 | 1.08202 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.7446 | 0.797275 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 45.1777 | 3.05283 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.4859 | −1.17623 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7261 | −0.785236 | −0.392618 | − | 0.919702i | \(-0.628431\pi\) | ||||
−0.392618 | + | 0.919702i | \(0.628431\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.6481 | −0.909874 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.27754 | −0.350283 | −0.175141 | − | 0.984543i | \(-0.556038\pi\) | ||||
−0.175141 | + | 0.984543i | \(0.556038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.4766 | −1.02272 | −0.511360 | − | 0.859366i | \(-0.670858\pi\) | ||||
−0.511360 | + | 0.859366i | \(0.670858\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.7072 | 1.49403 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.95226 | −0.127897 | −0.0639484 | − | 0.997953i | \(-0.520369\pi\) | ||||
−0.0639484 | + | 0.997953i | \(0.520369\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.56706 | 0.428388 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 57.1616 | 3.71304 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.10139 | 0.200612 | 0.100306 | − | 0.994957i | \(-0.468018\pi\) | ||||
0.100306 | + | 0.994957i | \(0.468018\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.9756 | −1.22233 | −0.611163 | − | 0.791505i | \(-0.709298\pi\) | ||||
−0.611163 | + | 0.791505i | \(0.709298\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 72.8398 | 4.67267 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.28775 | 0.593373 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3752 | −0.851044 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.25240 | 0.522975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.8444 | 1.56195 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −24.9573 | −1.56289 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.4307 | −1.83584 | −0.917918 | − | 0.396771i | \(-0.870131\pi\) | ||||
−0.917918 | + | 0.396771i | \(0.870131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.2155 | −0.634761 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −47.5568 | −2.94369 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5204 | −0.833702 | −0.416851 | − | 0.908975i | \(-0.636866\pi\) | ||||
−0.416851 | + | 0.908975i | \(0.636866\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.97266 | 0.121180 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −48.7338 | −2.98246 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.9875 | −1.82837 | −0.914184 | − | 0.405299i | \(-0.867168\pi\) | ||||
−0.914184 | + | 0.405299i | \(0.867168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2684 | −0.623762 | −0.311881 | − | 0.950121i | \(-0.600959\pi\) | ||||
−0.311881 | + | 0.950121i | \(0.600959\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −20.8360 | −1.26105 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.65305 | −0.461496 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.91642 | −0.595820 | −0.297910 | − | 0.954594i | \(-0.596290\pi\) | ||||
−0.297910 | + | 0.954594i | \(0.596290\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 71.4402 | 4.27701 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.3153 | 0.675017 | 0.337508 | − | 0.941323i | \(-0.390416\pi\) | ||||
0.337508 | + | 0.941323i | \(0.390416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.8104 | 0.761499 | 0.380749 | − | 0.924678i | \(-0.375666\pi\) | ||||
0.380749 | + | 0.924678i | \(0.375666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.0901 | −1.13080 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.41033 | −0.437418 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.08684 | −0.0639317 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.1261 | −0.945330 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.67644 | 0.156359 | 0.0781796 | − | 0.996939i | \(-0.475089\pi\) | ||||
0.0781796 | + | 0.996939i | \(0.475089\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.6205 | −1.25879 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 89.4841 | 5.19239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.7971 | −1.31839 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0542 | −0.694795 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.0328 | 1.38065 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.45818 | −0.198015 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.698323 | 0.0398554 | 0.0199277 | − | 0.999801i | \(-0.493656\pi\) | ||||
0.0199277 | + | 0.999801i | \(0.493656\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 42.2851 | 2.40551 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.52864 | −0.200091 | −0.100046 | − | 0.994983i | \(-0.531899\pi\) | ||||
−0.100046 | + | 0.994983i | \(0.531899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.1365 | −1.53385 | −0.766924 | − | 0.641738i | \(-0.778213\pi\) | ||||
−0.766924 | + | 0.641738i | \(0.778213\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.9938 | −1.23921 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.3806 | −1.20085 | −0.600427 | − | 0.799680i | \(-0.705003\pi\) | ||||
−0.600427 | + | 0.799680i | \(0.705003\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.6671 | −1.49307 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.6154 | −1.87623 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.1722 | 0.677277 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.02239 | 0.389532 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.298240 | −0.0164927 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.98948 | −0.275079 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9447 | 1.04129 | 0.520646 | − | 0.853773i | \(-0.325691\pi\) | ||||
0.520646 | + | 0.853773i | \(0.325691\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −62.1391 | −3.40520 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.1526 | 1.26496 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.5232 | −0.954548 | −0.477274 | − | 0.878755i | \(-0.658375\pi\) | ||||
−0.477274 | + | 0.878755i | \(0.658375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.5646 | 1.00829 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.0594 | 2.16934 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.8603 | −0.910372 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −32.5378 | −1.75177 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.4297 | −1.31146 | −0.655728 | − | 0.754997i | \(-0.727638\pi\) | ||||
−0.655728 | + | 0.754997i | \(0.727638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.46353 | 0.506571 | 0.253286 | − | 0.967392i | \(-0.418489\pi\) | ||||
0.253286 | + | 0.967392i | \(0.418489\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −82.1101 | −4.38271 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.34269 | −0.444037 | −0.222018 | − | 0.975043i | \(-0.571264\pi\) | ||||
−0.222018 | + | 0.975043i | \(0.571264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.5105 | 0.663986 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.9619 | 1.00357 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.1164 | 0.745033 | 0.372516 | − | 0.928026i | \(-0.378495\pi\) | ||||
0.372516 | + | 0.928026i | \(0.378495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.68937 | −0.509967 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 40.1178 | 2.10564 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.5370 | −1.28433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.9280 | 1.61443 | 0.807215 | − | 0.590258i | \(-0.200974\pi\) | ||||
0.807215 | + | 0.590258i | \(0.200974\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −45.0756 | −2.34654 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.49878 | −0.0778127 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.438620 | 0.0227109 | 0.0113554 | − | 0.999936i | \(-0.496385\pi\) | ||||
0.0113554 | + | 0.999936i | \(0.496385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 41.3046 | 2.13296 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.4695 | 1.26025 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.13296 | −0.315029 | −0.157514 | − | 0.987517i | \(-0.550348\pi\) | ||||
−0.157514 | + | 0.987517i | \(0.550348\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 63.1487 | 3.23521 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0614 | −0.922895 | −0.461448 | − | 0.887167i | \(-0.652670\pi\) | ||||
−0.461448 | + | 0.887167i | \(0.652670\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.3328 | −0.628539 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −73.3237 | −3.72726 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.7955 | −0.598056 | −0.299028 | − | 0.954244i | \(-0.596662\pi\) | ||||
−0.299028 | + | 0.954244i | \(0.596662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7466 | 1.04920 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.19938 | 0.413604 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.0458 | −1.56208 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.72182 | 0.236982 | 0.118491 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118491 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.5042 | 0.726118 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1995 | 0.709087 | 0.354544 | − | 0.935039i | \(-0.384636\pi\) | ||||
0.354544 | + | 0.935039i | \(0.384636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.7583 | −1.83106 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −70.0824 | −3.48242 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.8439 | −1.72715 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4793 | 0.913741 | 0.456871 | − | 0.889533i | \(-0.348970\pi\) | ||||
0.456871 | + | 0.889533i | \(0.348970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 68.9677 | 3.40193 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.4267 | 0.808304 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.48207 | −0.220016 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −46.1323 | −2.25911 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.75585 | 0.183485 | 0.0917427 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917427 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4301 | 1.43433 | 0.717167 | − | 0.696901i | \(-0.245438\pi\) | ||||
0.717167 | + | 0.696901i | \(0.245438\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.3501 | −1.47567 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.39076 | −0.309998 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.62744 | 0.127151 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −71.0692 | −3.43125 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.5126 | −1.22890 | −0.614449 | − | 0.788957i | \(-0.710621\pi\) | ||||
−0.614449 | + | 0.788957i | \(0.710621\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.21250 | −0.346611 | −0.173305 | − | 0.984868i | \(-0.555445\pi\) | ||||
−0.173305 | + | 0.984868i | \(0.555445\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 34.9249 | 1.67452 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.8693 | 0.759131 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.6607 | 0.795173 | 0.397587 | − | 0.917565i | \(-0.369848\pi\) | ||||
0.397587 | + | 0.917565i | \(0.369848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.9240 | −2.04400 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.8396 | −0.705053 | −0.352526 | − | 0.935802i | \(-0.614677\pi\) | ||||
−0.352526 | + | 0.935802i | \(0.614677\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.4684 | 1.25472 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.33569 | −0.299668 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.9646 | −1.31973 | −0.659866 | − | 0.751384i | \(-0.729387\pi\) | ||||
−0.659866 | + | 0.751384i | \(0.729387\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.2757 | −1.19019 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.5089 | −1.05756 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.3165 | 0.530527 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.13668 | −0.427396 | −0.213698 | − | 0.976900i | \(-0.568551\pi\) | ||||
−0.213698 | + | 0.976900i | \(0.568551\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 74.7247 | 3.48785 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.83738 | 0.132150 | 0.0660750 | − | 0.997815i | \(-0.478952\pi\) | ||||
0.0660750 | + | 0.997815i | \(0.478952\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.80612 | −0.316307 | −0.158154 | − | 0.987415i | \(-0.550554\pi\) | ||||
−0.158154 | + | 0.987415i | \(0.550554\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −52.4643 | −2.43298 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.10149 | −0.374892 | −0.187446 | − | 0.982275i | \(-0.560021\pi\) | ||||
−0.187446 | + | 0.982275i | \(0.560021\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5908 | −0.812266 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9520 | −0.781109 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.1156 | −1.89050 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.88837 | −0.224294 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.11679 | −0.417429 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.3545 | −1.56970 | −0.784849 | − | 0.619687i | \(-0.787260\pi\) | ||||
−0.784849 | + | 0.619687i | \(0.787260\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.9726 | 1.45782 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.7214 | 1.12486 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.75846 | 0.397701 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.2753 | −1.59848 | −0.799239 | − | 0.601014i | \(-0.794764\pi\) | ||||
−0.799239 | + | 0.601014i | \(0.794764\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −38.6712 | −1.74877 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7936 | −0.487107 | −0.243554 | − | 0.969887i | \(-0.578313\pi\) | ||||
−0.243554 | + | 0.969887i | \(0.578313\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.2686 | −1.00293 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −75.0182 | −3.37182 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.50512 | −0.426363 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.8451 | 1.11222 | 0.556109 | − | 0.831109i | \(-0.312294\pi\) | ||||
0.556109 | + | 0.831109i | \(0.312294\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.0977 | 0.495809 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5262 | −0.469339 | −0.234669 | − | 0.972075i | \(-0.575401\pi\) | ||||
−0.234669 | + | 0.972075i | \(0.575401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.0527 | −0.580839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.0908 | 0.936676 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.8969 | −1.05921 | −0.529606 | − | 0.848244i | \(-0.677660\pi\) | ||||
−0.529606 | + | 0.848244i | \(0.677660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.6426 | 0.824700 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 57.1578 | 2.52358 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.9660 | −1.01200 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.0185 | −0.748474 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.1651 | 0.621779 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.35855 | −0.278573 | −0.139287 | − | 0.990252i | \(-0.544481\pi\) | ||||
−0.139287 | + | 0.990252i | \(0.544481\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.6614 | 0.816008 | 0.408004 | − | 0.912980i | \(-0.366225\pi\) | ||||
0.408004 | + | 0.912980i | \(0.366225\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.61515 | −0.332353 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.4521 | 1.45719 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.04806 | 0.176003 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 99.9204 | 4.33618 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.1929 | 1.00460 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.2573 | 0.789331 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.3140 | −1.00607 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.0692 | −1.03673 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.0074 | 0.903180 | 0.451590 | − | 0.892226i | \(-0.350857\pi\) | ||||
0.451590 | + | 0.892226i | \(0.350857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.5624 | 1.18281 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.161981 | 0.00693849 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.7191 | 1.74102 | 0.870512 | − | 0.492147i | \(-0.163788\pi\) | ||||
0.870512 | + | 0.492147i | \(0.163788\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.9822 | 0.682104 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.0335 | −0.725652 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.5878 | 1.00305 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 45.6338 | 1.93705 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.4706 | −1.79954 | −0.899769 | − | 0.436367i | \(-0.856265\pi\) | ||||
−0.899769 | + | 0.436367i | \(0.856265\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.7274 | 1.59570 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 64.6769 | 2.73066 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.7100 | 0.830676 | 0.415338 | − | 0.909667i | \(-0.363663\pi\) | ||||
0.415338 | + | 0.909667i | \(0.363663\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0829 | −0.424189 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 53.2468 | 2.23615 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.0950 | 1.55510 | 0.777551 | − | 0.628820i | \(-0.216462\pi\) | ||||
0.777551 | + | 0.628820i | \(0.216462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.6347 | −1.15648 | −0.578238 | − | 0.815868i | \(-0.696260\pi\) | ||||
−0.578238 | + | 0.815868i | \(0.696260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.0980 | −2.25998 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.33187 | −0.347463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.64302 | 0.0683999 | 0.0341999 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341999 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −46.0614 | −1.91425 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.40536 | 0.141278 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.11215 | −0.211724 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 68.8363 | 2.84603 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.2520 | −0.629516 | −0.314758 | − | 0.949172i | \(-0.601923\pi\) | ||||
−0.314758 | + | 0.949172i | \(0.601923\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.5879 | 1.05433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 65.2521 | 2.68411 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.20855 | −0.0906943 | −0.0453472 | − | 0.998971i | \(-0.514439\pi\) | ||||
−0.0453472 | + | 0.998971i | \(0.514439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.2987 | −0.422204 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 79.9672 | 3.27284 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.3973 | −1.32372 | −0.661859 | − | 0.749628i | \(-0.730232\pi\) | ||||
−0.661859 | + | 0.749628i | \(0.730232\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2203 | 1.47746 | 0.738729 | − | 0.674003i | \(-0.235426\pi\) | ||||
0.738729 | + | 0.674003i | \(0.235426\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −107.001 | −4.35743 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.7889 | −0.885844 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.2944 | 1.02667 | 0.513335 | − | 0.858188i | \(-0.328410\pi\) | ||||
0.513335 | + | 0.858188i | \(0.328410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −26.5350 | −1.07525 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.6161 | 0.631760 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.4143 | −0.743748 | −0.371874 | − | 0.928283i | \(-0.621285\pi\) | ||||
−0.371874 | + | 0.928283i | \(0.621285\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 33.1027 | 1.33483 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.35977 | 0.0547422 | 0.0273711 | − | 0.999625i | \(-0.491286\pi\) | ||||
0.0273711 | + | 0.999625i | \(0.491286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5085 | −1.02527 | −0.512636 | − | 0.858606i | \(-0.671331\pi\) | ||||
−0.512636 | + | 0.858606i | \(0.671331\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 97.4213 | 3.90938 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.1100 | −0.805692 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.4232 | −0.576929 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 49.4721 | 1.97573 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.0968 | −1.16017 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.7112 | 0.585642 | 0.292821 | − | 0.956167i | \(-0.405406\pi\) | ||||
0.292821 | + | 0.956167i | \(0.405406\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 38.1244 | 1.51531 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.2975 | −1.36105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.0858 | 0.875070 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −57.8179 | −2.28724 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7342 | 0.937444 | 0.468722 | − | 0.883346i | \(-0.344715\pi\) | ||||
0.468722 | + | 0.883346i | \(0.344715\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.6792 | −0.657764 | −0.328882 | − | 0.944371i | \(-0.606672\pi\) | ||||
−0.328882 | + | 0.944371i | \(0.606672\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 53.8476 | 2.12025 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.1697 | −0.950208 | −0.475104 | − | 0.879930i | \(-0.657590\pi\) | ||||
−0.475104 | + | 0.879930i | \(0.657590\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.0295 | 2.19935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 39.8611 | 1.56228 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.4713 | −1.42723 | −0.713615 | − | 0.700538i | \(-0.752944\pi\) | ||||
−0.713615 | + | 0.700538i | \(0.752944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.45327 | −0.174004 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 113.400 | 4.42414 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.31362 | −0.129080 | −0.0645401 | − | 0.997915i | \(-0.520558\pi\) | ||||
−0.0645401 | + | 0.997915i | \(0.520558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.9178 | 1.31925 | 0.659626 | − | 0.751594i | \(-0.270715\pi\) | ||||
0.659626 | + | 0.751594i | \(0.270715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −59.3471 | −2.30485 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.87756 | −0.305479 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.0324 | −1.12414 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.7982 | −1.53869 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.96187 | 0.345969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.5453 | 1.90983 | 0.954915 | − | 0.296879i | \(-0.0959459\pi\) | ||||
0.954915 | + | 0.296879i | \(0.0959459\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −30.0096 | −1.15507 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.1096 | −0.734442 | −0.367221 | − | 0.930134i | \(-0.619691\pi\) | ||||
−0.367221 | + | 0.930134i | \(0.619691\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.65445 | −0.255375 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.9119 | −0.686387 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.83998 | 0.261724 | 0.130862 | − | 0.991401i | \(-0.458225\pi\) | ||||
0.130862 | + | 0.991401i | \(0.458225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.4579 | −1.43119 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −52.5274 | −2.00404 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.69088 | 0.178708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.2778 | 1.64637 | 0.823183 | − | 0.567776i | \(-0.192196\pi\) | ||||
0.823183 | + | 0.567776i | \(0.192196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 56.9969 | 2.16513 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.0555 | 0.950410 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.1068 | −0.799477 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.62595 | −0.250617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.7344 | −0.669817 | −0.334909 | − | 0.942251i | \(-0.608705\pi\) | ||||
−0.334909 | + | 0.942251i | \(0.608705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.2565 | −0.839419 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.2885 | 0.839435 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.91713 | 0.372972 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.9542 | 1.04984 | 0.524921 | − | 0.851151i | \(-0.324095\pi\) | ||||
0.524921 | + | 0.851151i | \(0.324095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 143.480 | 5.38092 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43.6127 | 1.63331 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.5993 | 1.44353 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.5261 | 0.393104 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.64866 | −0.285247 | −0.142623 | − | 0.989777i | \(-0.545554\pi\) | ||||
−0.142623 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.4490 | 0.649833 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −64.4030 | −2.39517 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.94313 | 0.332139 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.82864 | 0.290348 | 0.145174 | − | 0.989406i | \(-0.453626\pi\) | ||||
0.145174 | + | 0.989406i | \(0.453626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 133.161 | 4.93188 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.3340 | −1.26989 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.9936 | −1.03397 | −0.516983 | − | 0.855996i | \(-0.672945\pi\) | ||||
−0.516983 | + | 0.855996i | \(0.672945\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.5226 | 1.16273 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −60.0000 | −2.21013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.1441 | 1.69744 | 0.848719 | − | 0.528844i | \(-0.177374\pi\) | ||||
0.848719 | + | 0.528844i | \(0.177374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.3953 | −1.66764 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7107 | 0.869860 | 0.434930 | − | 0.900464i | \(-0.356773\pi\) | ||||
0.434930 | + | 0.900464i | \(0.356773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.44106 | 0.126071 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.7142 | 0.757892 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.8714 | −0.506850 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.9780 | 1.34935 | 0.674673 | − | 0.738116i | \(-0.264285\pi\) | ||||
0.674673 | + | 0.738116i | \(0.264285\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.39399 | 0.123684 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2251 | 0.444917 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.4471 | −1.76084 | −0.880420 | − | 0.474196i | \(-0.842739\pi\) | ||||
−0.880420 | + | 0.474196i | \(0.842739\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 84.3216 | 3.06068 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.34501 | −0.338756 | −0.169378 | − | 0.985551i | \(-0.554176\pi\) | ||||
−0.169378 | + | 0.985551i | \(0.554176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.123069 | −0.00445539 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −62.6448 | −2.26493 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −51.4123 | −1.85639 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.0335 | 0.938794 | 0.469397 | − | 0.882987i | \(-0.344471\pi\) | ||||
0.469397 | + | 0.882987i | \(0.344471\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −99.8875 | −3.59736 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.7858 | −0.495842 | −0.247921 | − | 0.968780i | \(-0.579747\pi\) | ||||
−0.247921 | + | 0.968780i | \(0.579747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.4344 | −0.482579 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −34.6714 | −1.24383 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.1448 | −0.578449 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.4208 | −1.16011 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −104.568 | −3.73697 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.20704 | 0.328613 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.7457 | −0.561274 | −0.280637 | − | 0.959814i | \(-0.590546\pi\) | ||||
−0.280637 | + | 0.959814i | \(0.590546\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −45.8881 | −1.63366 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.66069 | 0.272383 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.22336 | −0.292020 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.69520 | 0.237454 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.7717 | 1.05457 | 0.527284 | − | 0.849689i | \(-0.323210\pi\) | ||||
0.527284 | + | 0.849689i | \(0.323210\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.2115 | −0.502767 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −122.326 | −4.32216 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 63.5877 | 2.24396 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.4267 | −0.473230 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −101.777 | −3.58273 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.1292 | 0.567073 | 0.283536 | − | 0.958961i | \(-0.408492\pi\) | ||||
0.283536 | + | 0.958961i | \(0.408492\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.8744 | −1.29484 | −0.647418 | − | 0.762135i | \(-0.724151\pi\) | ||||
−0.647418 | + | 0.762135i | \(0.724151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.8510 | −1.22228 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.0032 | 0.735710 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.2625 | −0.918809 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −52.3001 | −1.82751 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.2812 | −0.533319 | −0.266659 | − | 0.963791i | \(-0.585920\pi\) | ||||
−0.266659 | + | 0.963791i | \(0.585920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0565 | 0.768842 | 0.384421 | − | 0.923158i | \(-0.374401\pi\) | ||||
0.384421 | + | 0.923158i | \(0.374401\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.9744 | −0.904312 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.3239 | 1.78471 | 0.892353 | − | 0.451337i | \(-0.149053\pi\) | ||||
0.892353 | + | 0.451337i | \(0.149053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −55.0672 | −1.91256 | −0.956282 | − | 0.292447i | \(-0.905531\pi\) | ||||
−0.956282 | + | 0.292447i | \(0.905531\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.6563 | −1.16752 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.0993 | −0.696398 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.02741 | −0.208587 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 157.083 | 5.42960 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.1112 | 0.590744 | 0.295372 | − | 0.955382i | \(-0.404556\pi\) | ||||
0.295372 | + | 0.955382i | \(0.404556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.16233 | 0.0745632 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.4042 | 1.32271 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.4549 | −0.394061 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.5546 | 0.568824 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.4784 | 1.49217 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.9346 | −1.30038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.7633 | 0.676684 | 0.338342 | − | 0.941023i | \(-0.390134\pi\) | ||||
0.338342 | + | 0.941023i | \(0.390134\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −47.9177 | −1.63875 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4967 | 0.836791 | 0.418396 | − | 0.908265i | \(-0.362593\pi\) | ||||
0.418396 | + | 0.908265i | \(0.362593\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.7099 | 0.706612 | 0.353306 | − | 0.935508i | \(-0.385058\pi\) | ||||
0.353306 | + | 0.935508i | \(0.385058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.1506 | −0.857130 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.1636 | −0.822538 | −0.411269 | − | 0.911514i | \(-0.634914\pi\) | ||||
−0.411269 | + | 0.911514i | \(0.634914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.69339 | −0.261583 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.68872 | −0.125276 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 80.4551 | 2.72925 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.0557 | 1.86549 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −40.4778 | −1.36997 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.0444 | 0.576205 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.99030 | −0.202278 | −0.101139 | − | 0.994872i | \(-0.532249\pi\) | ||||
−0.101139 | + | 0.994872i | \(0.532249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.08382 | 0.306390 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.901329 | −0.0303666 | −0.0151833 | − | 0.999885i | \(-0.504833\pi\) | ||||
−0.0151833 | + | 0.999885i | \(0.504833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.5894 | 1.29864 | 0.649318 | − | 0.760517i | \(-0.275054\pi\) | ||||
0.649318 | + | 0.760517i | \(0.275054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −73.3797 | −2.46663 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.31707 | 0.111376 | 0.0556881 | − | 0.998448i | \(-0.482265\pi\) | ||||
0.0556881 | + | 0.998448i | \(0.482265\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.0584 | 0.873969 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 181.618 | 6.08445 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.8706 | −0.363769 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.6624 | 0.423256 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −77.3730 | −2.58341 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.8122 | −1.56128 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.26896 | −0.142220 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −40.9120 | −1.36147 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.9698 | −0.497612 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.9616 | −1.06127 | −0.530633 | − | 0.847602i | \(-0.678046\pi\) | ||||
−0.530633 | + | 0.847602i | \(0.678046\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 60.3241 | 2.00082 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.6487 | 0.419072 | 0.209536 | − | 0.977801i | \(-0.432805\pi\) | ||||
0.209536 | + | 0.977801i | \(0.432805\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.6153 | 0.384410 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.7370 | −0.388014 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.38348 | 0.111732 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.78557 | −0.124874 | −0.0624371 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624371 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.37010 | 0.0780976 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.7492 | 0.979206 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6853 | 0.384212 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 106.139 | 3.48606 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.6045 | −1.39781 | −0.698905 | − | 0.715215i | \(-0.746329\pi\) | ||||
−0.698905 | + | 0.715215i | \(0.746329\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.3742 | −0.503868 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.9762 | −0.392083 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.1275 | −1.14879 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.5011 | 0.963759 | 0.481880 | − | 0.876237i | \(-0.339954\pi\) | ||||
0.481880 | + | 0.876237i | \(0.339954\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −92.1012 | −3.00561 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.54909 | −0.311291 | −0.155646 | − | 0.987813i | \(-0.549746\pi\) | ||||
−0.155646 | + | 0.987813i | \(0.549746\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.5177 | −0.896099 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −48.3602 | −1.57316 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.4278 | −1.02127 | −0.510634 | − | 0.859798i | \(-0.670589\pi\) | ||||
−0.510634 | + | 0.859798i | \(0.670589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −58.3477 | −1.89405 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.5655 | −2.35310 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.1158 | 1.52623 | 0.763116 | − | 0.646262i | \(-0.223669\pi\) | ||||
0.763116 | + | 0.646262i | \(0.223669\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.3818 | 0.950774 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −90.5078 | −2.92570 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.4596 | 0.919007 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.3216 | 1.26844 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −84.3772 | −2.71902 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.0170 | 0.805326 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.3038 | −1.36040 | −0.680200 | − | 0.733027i | \(-0.738107\pi\) | ||||
−0.680200 | + | 0.733027i | \(0.738107\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.3122 | 1.32714 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.26896 | −0.0728143 | −0.0364072 | − | 0.999337i | \(-0.511591\pi\) | ||||
−0.0364072 | + | 0.999337i | \(0.511591\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.0365 | −0.610283 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.8340 | 0.763297 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.6079 | 1.26717 | 0.633584 | − | 0.773674i | \(-0.281583\pi\) | ||||
0.633584 | + | 0.773674i | \(0.281583\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −68.5929 | −2.19224 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.748604 | −0.0239011 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.2362 | 0.454063 | 0.227032 | − | 0.973887i | \(-0.427098\pi\) | ||||
0.227032 | + | 0.973887i | \(0.427098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.4399 | −1.12921 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.9343 | −0.539024 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.7625 | −1.42337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.6156 | 1.92552 | 0.962758 | − | 0.270363i | \(-0.0871438\pi\) | ||||
0.962758 | + | 0.270363i | \(0.0871438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.2980 | 2.04044 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −43.4320 | −1.37689 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.2190 | −0.703682 | −0.351841 | − | 0.936060i | \(-0.614444\pi\) | ||||
−0.351841 | + | 0.936060i | \(0.614444\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −136.632 | −4.32285 |
(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 | 4016.2.a.m.1.23 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.1 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.1 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.23 | 23 | 1.1 | even | 1 | trivial |