Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 8 x^{17} - 4 x^{16} + 178 x^{15} - 265 x^{14} - 1405 x^{13} + 3503 x^{12} + 4295 x^{11} + \cdots - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(2.60297\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 2.60297 | 1.50282 | 0.751412 | − | 0.659833i | \(-0.229373\pi\) | ||||
0.751412 | + | 0.659833i | \(0.229373\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.183919 | 0.0822511 | 0.0411255 | − | 0.999154i | \(-0.486906\pi\) | ||||
0.0411255 | + | 0.999154i | \(0.486906\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.24534 | 1.22662 | 0.613312 | − | 0.789841i | \(-0.289837\pi\) | ||||
0.613312 | + | 0.789841i | \(0.289837\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.77545 | 1.25848 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.13693 | 0.644310 | 0.322155 | − | 0.946687i | \(-0.395593\pi\) | ||||
0.322155 | + | 0.946687i | \(0.395593\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.69478 | 0.470047 | 0.235024 | − | 0.971990i | \(-0.424483\pi\) | ||||
0.235024 | + | 0.971990i | \(0.424483\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.478736 | 0.123609 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.65056 | 0.837495 | 0.418747 | − | 0.908103i | \(-0.362469\pi\) | ||||
0.418747 | + | 0.908103i | \(0.362469\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.44753 | 1.84340 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.53848 | 1.36337 | 0.681684 | − | 0.731647i | \(-0.261248\pi\) | ||||
0.681684 | + | 0.731647i | \(0.261248\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96617 | −0.993235 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.01847 | 0.388455 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.31726 | 0.615999 | 0.308000 | − | 0.951386i | \(-0.400340\pi\) | ||||
0.308000 | + | 0.951386i | \(0.400340\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.57757 | −0.822156 | −0.411078 | − | 0.911600i | \(-0.634848\pi\) | ||||
−0.411078 | + | 0.911600i | \(0.634848\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.56237 | 0.968284 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.596880 | 0.100891 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.89290 | −0.639988 | −0.319994 | − | 0.947420i | \(-0.603681\pi\) | ||||
−0.319994 | + | 0.947420i | \(0.603681\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.41146 | 0.706399 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.20375 | 1.12504 | 0.562518 | − | 0.826785i | \(-0.309833\pi\) | ||||
0.562518 | + | 0.826785i | \(0.309833\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.66187 | −0.405932 | −0.202966 | − | 0.979186i | \(-0.565058\pi\) | ||||
−0.202966 | + | 0.979186i | \(0.565058\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.694377 | 0.103512 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.38769 | −1.22347 | −0.611735 | − | 0.791062i | \(-0.709528\pi\) | ||||
−0.611735 | + | 0.791062i | \(0.709528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.53225 | 0.504608 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.60297 | −0.364489 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.06541 | −1.10787 | −0.553934 | − | 0.832560i | \(-0.686874\pi\) | ||||
−0.553934 | + | 0.832560i | \(0.686874\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.393023 | 0.0529952 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.50228 | 1.25861 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.08619 | 0.395146 | 0.197573 | − | 0.980288i | \(-0.436694\pi\) | ||||
0.197573 | + | 0.980288i | \(0.436694\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.2526 | 1.54369 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.311702 | 0.0386619 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.66017 | 0.935839 | 0.467919 | − | 0.883771i | \(-0.345004\pi\) | ||||
0.467919 | + | 0.883771i | \(0.345004\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.0195 | 2.04890 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8657 | −1.28953 | −0.644763 | − | 0.764383i | \(-0.723044\pi\) | ||||
−0.644763 | + | 0.764383i | \(0.723044\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.91429 | −0.692216 | −0.346108 | − | 0.938195i | \(-0.612497\pi\) | ||||
−0.346108 | + | 0.938195i | \(0.612497\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.9268 | −1.49266 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.93508 | 0.790326 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00108 | 0.562665 | 0.281333 | − | 0.959610i | \(-0.409224\pi\) | ||||
0.281333 | + | 0.959610i | \(0.409224\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.07233 | −0.674704 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0316 | −1.32064 | −0.660321 | − | 0.750984i | \(-0.729580\pi\) | ||||
−0.660321 | + | 0.750984i | \(0.729580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.183919 | −0.0199488 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.63472 | 0.925739 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.08141 | 0.750628 | 0.375314 | − | 0.926898i | \(-0.377535\pi\) | ||||
0.375314 | + | 0.926898i | \(0.377535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.50014 | 0.576571 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.9153 | −1.23556 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.671407 | 0.0688849 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.4961 | 1.77646 | 0.888228 | − | 0.459404i | \(-0.151937\pi\) | ||||
0.888228 | + | 0.459404i | \(0.151937\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.06788 | 0.810853 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.118123 | −0.0117537 | −0.00587683 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587683 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.505459 | 0.0498043 | 0.0249022 | − | 0.999690i | \(-0.492073\pi\) | ||||
0.0249022 | + | 0.999690i | \(0.492073\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.55366 | 0.151622 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.11952 | 0.881617 | 0.440809 | − | 0.897601i | \(-0.354692\pi\) | ||||
0.440809 | + | 0.897601i | \(0.354692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.365529 | −0.0350113 | −0.0175057 | − | 0.999847i | \(-0.505573\pi\) | ||||
−0.0175057 | + | 0.999847i | \(0.505573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1331 | −0.961790 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.03957 | 0.662227 | 0.331114 | − | 0.943591i | \(-0.392576\pi\) | ||||
0.331114 | + | 0.943591i | \(0.392576\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.20255 | 0.112138 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.39855 | 0.591546 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.24534 | −0.297500 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.43352 | −0.584865 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.7511 | 1.69073 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.83297 | −0.163946 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.96968 | 0.440988 | 0.220494 | − | 0.975388i | \(-0.429233\pi\) | ||||
0.220494 | + | 0.975388i | \(0.429233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.92878 | −0.610045 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1572 | −0.974806 | −0.487403 | − | 0.873177i | \(-0.662056\pi\) | ||||
−0.487403 | + | 0.873177i | \(0.662056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.8473 | 1.02729 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.371235 | 0.0319508 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8885 | −1.69919 | −0.849594 | − | 0.527437i | \(-0.823153\pi\) | ||||
−0.849594 | + | 0.527437i | \(0.823153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.4697 | −1.56658 | −0.783290 | − | 0.621656i | \(-0.786460\pi\) | ||||
−0.783290 | + | 0.621656i | \(0.786460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.8329 | −1.83866 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.62163 | 0.302856 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.610107 | 0.0506666 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.19435 | 0.758337 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.17504 | 0.751649 | 0.375824 | − | 0.926691i | \(-0.377360\pi\) | ||||
0.375824 | + | 0.926691i | \(0.377360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0817592 | 0.00665347 | 0.00332673 | − | 0.999994i | \(-0.498941\pi\) | ||||
0.00332673 | + | 0.999994i | \(0.498941\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.77545 | −0.305227 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.841902 | −0.0676232 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.825742 | −0.0659014 | −0.0329507 | − | 0.999457i | \(-0.510490\pi\) | ||||
−0.0329507 | + | 0.999457i | \(0.510490\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.9940 | −1.66493 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.2196 | 1.67234 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.04508 | 0.473487 | 0.236744 | − | 0.971572i | \(-0.423920\pi\) | ||||
0.236744 | + | 0.971572i | \(0.423920\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.02303 | 0.0796425 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.2713 | 0.949583 | 0.474792 | − | 0.880098i | \(-0.342523\pi\) | ||||
0.474792 | + | 0.880098i | \(0.342523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1277 | −0.779056 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.7825 | 1.05397 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.7725 | 1.19916 | 0.599582 | − | 0.800313i | \(-0.295333\pi\) | ||||
0.599582 | + | 0.800313i | \(0.295333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.1169 | −1.21833 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.60297 | −0.195651 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00318 | 0.448699 | 0.224349 | − | 0.974509i | \(-0.427974\pi\) | ||||
0.224349 | + | 0.974509i | \(0.427974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.861323 | −0.0640216 | −0.0320108 | − | 0.999488i | \(-0.510191\pi\) | ||||
−0.0320108 | + | 0.999488i | \(0.510191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.03325 | 0.593835 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.715978 | −0.0526397 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.13693 | −0.156268 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.55063 | 0.476488 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.42486 | 0.103099 | 0.0515497 | − | 0.998670i | \(-0.483584\pi\) | ||||
0.0515497 | + | 0.998670i | \(0.483584\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.91882 | −0.498028 | −0.249014 | − | 0.968500i | \(-0.580106\pi\) | ||||
−0.249014 | + | 0.968500i | \(0.580106\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.811351 | 0.0581021 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.1858 | 1.36693 | 0.683465 | − | 0.729984i | \(-0.260472\pi\) | ||||
0.683465 | + | 0.729984i | \(0.260472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8550 | −1.05305 | −0.526523 | − | 0.850161i | \(-0.676505\pi\) | ||||
−0.526523 | + | 0.850161i | \(0.676505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.9392 | 1.40640 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7656 | 0.755600 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.32491 | 0.0925355 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 24.6857 | 1.71577 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.80099 | 0.539606 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.32963 | −0.0915358 | −0.0457679 | − | 0.998952i | \(-0.514573\pi\) | ||||
−0.0457679 | + | 0.998952i | \(0.514573\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.2832 | −1.93793 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.489569 | −0.0333883 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.8558 | −1.00848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.3947 | −1.04028 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.69478 | −0.114003 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.96669 | −0.667419 | −0.333709 | − | 0.942676i | \(-0.608300\pi\) | ||||
−0.333709 | + | 0.942676i | \(0.608300\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.7495 | −1.24997 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.96811 | −0.396117 | −0.198059 | − | 0.980190i | \(-0.563464\pi\) | ||||
−0.198059 | + | 0.980190i | \(0.563464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.72880 | 0.180324 | 0.0901622 | − | 0.995927i | \(-0.471261\pi\) | ||||
0.0901622 | + | 0.995927i | \(0.471261\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0518 | 1.18772 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.8885 | 0.975380 | 0.487690 | − | 0.873017i | \(-0.337840\pi\) | ||||
0.487690 | + | 0.873017i | \(0.337840\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.54266 | −0.100632 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.0176 | 0.845587 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.72236 | −0.305464 | −0.152732 | − | 0.988268i | \(-0.548807\pi\) | ||||
−0.152732 | + | 0.988268i | \(0.548807\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.3523 | 1.37542 | 0.687712 | − | 0.725983i | \(-0.258615\pi\) | ||||
0.687712 | + | 0.725983i | \(0.258615\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.8615 | −1.40242 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.649649 | 0.0415045 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.18689 | 0.393662 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.3179 | −1.98469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.6463 | 1.80814 | 0.904069 | − | 0.427387i | \(-0.140566\pi\) | ||||
0.904069 | + | 0.427387i | \(0.140566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.9723 | 0.878431 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.478736 | −0.0299796 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.3391 | −0.769692 | −0.384846 | − | 0.922981i | \(-0.625745\pi\) | ||||
−0.384846 | + | 0.922981i | \(0.625745\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.6338 | −0.785025 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.5241 | 0.775225 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.7665 | −1.03387 | −0.516934 | − | 0.856025i | \(-0.672927\pi\) | ||||
−0.516934 | + | 0.856025i | \(0.672927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.48338 | −0.0911234 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.4327 | 1.12806 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.54075 | 0.337825 | 0.168913 | − | 0.985631i | \(-0.445974\pi\) | ||||
0.168913 | + | 0.985631i | \(0.445974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0167 | −0.608472 | −0.304236 | − | 0.952597i | \(-0.598401\pi\) | ||||
−0.304236 | + | 0.952597i | \(0.598401\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.3167 | 0.866486 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.6124 | −0.639951 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.9671 | −1.86063 | −0.930317 | − | 0.366756i | \(-0.880469\pi\) | ||||
−0.930317 | + | 0.366756i | \(0.880469\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.2824 | −1.03467 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.3375 | 1.27289 | 0.636443 | − | 0.771324i | \(-0.280405\pi\) | ||||
0.636443 | + | 0.771324i | \(0.280405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.10174 | 0.541042 | 0.270521 | − | 0.962714i | \(-0.412804\pi\) | ||||
0.270521 | + | 0.962714i | \(0.412804\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.74765 | 0.103522 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.3786 | 1.38000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 45.5417 | 2.66970 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.4989 | 0.963874 | 0.481937 | − | 0.876206i | \(-0.339933\pi\) | ||||
0.481937 | + | 0.876206i | \(0.339933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.183919 | −0.0107082 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.31333 | 0.250285 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.0813 | 0.640847 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.63869 | −0.497926 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.307470 | −0.0176637 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.567608 | 0.0325012 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.92898 | −0.224239 | −0.112120 | − | 0.993695i | \(-0.535764\pi\) | ||||
−0.112120 | + | 0.993695i | \(0.535764\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.31569 | 0.0748472 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3868 | −0.702393 | −0.351197 | − | 0.936302i | \(-0.614225\pi\) | ||||
−0.351197 | + | 0.936302i | \(0.614225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.35016 | 0.302409 | 0.151204 | − | 0.988503i | \(-0.451685\pi\) | ||||
0.151204 | + | 0.988503i | \(0.451685\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.25349 | 0.126970 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.96467 | 0.391175 | 0.195587 | − | 0.980686i | \(-0.437339\pi\) | ||||
0.195587 | + | 0.980686i | \(0.437339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.08876 | 0.396894 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.7378 | 1.32492 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.65056 | −0.203122 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.41657 | −0.466867 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.951461 | −0.0526159 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.2209 | −1.50074 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.9195 | −1.25977 | −0.629885 | − | 0.776688i | \(-0.716898\pi\) | ||||
−0.629885 | + | 0.776688i | \(0.716898\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.6974 | −0.805414 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.40885 | 0.0769738 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.2584 | 1.48486 | 0.742429 | − | 0.669925i | \(-0.233674\pi\) | ||||
0.742429 | + | 0.669925i | \(0.233674\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.3238 | 0.995211 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.78196 | −0.529723 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.2540 | −0.607660 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.13020 | 0.168524 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.1749 | 1.72724 | 0.863621 | − | 0.504142i | \(-0.168191\pi\) | ||||
0.863621 | + | 0.504142i | \(0.168191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0679 | 0.592451 | 0.296226 | − | 0.955118i | \(-0.404272\pi\) | ||||
0.296226 | + | 0.955118i | \(0.404272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.42086 | 0.182592 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.7585 | −1.10486 | −0.552431 | − | 0.833559i | \(-0.686300\pi\) | ||||
−0.552431 | + | 0.833559i | \(0.686300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.99842 | −0.106065 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.44753 | −0.447091 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.945197 | 0.0498856 | 0.0249428 | − | 0.999689i | \(-0.492060\pi\) | ||||
0.0249428 | + | 0.999689i | \(0.492060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.67344 | −0.298602 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.7462 | −0.878950 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.08775 | −0.0569355 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.4931 | −1.64393 | −0.821964 | − | 0.569540i | \(-0.807121\pi\) | ||||
−0.821964 | + | 0.569540i | \(0.807121\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 27.1974 | 1.41584 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.1750 | −1.35894 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.8434 | −1.18279 | −0.591394 | − | 0.806383i | \(-0.701422\pi\) | ||||
−0.591394 | + | 0.806383i | \(0.701422\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.77116 | −0.246382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.62202 | 0.289549 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.5561 | −1.31273 | −0.656365 | − | 0.754444i | \(-0.727907\pi\) | ||||
−0.656365 | + | 0.754444i | \(0.727907\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.9359 | 0.662727 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.0633 | −0.871896 | −0.435948 | − | 0.899972i | \(-0.643587\pi\) | ||||
−0.435948 | + | 0.899972i | \(0.643587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.27549 | 0.0650052 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.0498 | −0.510858 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.62659 | −0.437385 | −0.218693 | − | 0.975794i | \(-0.570179\pi\) | ||||
−0.218693 | + | 0.975794i | \(0.570179\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.53848 | −0.330665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.0417 | −1.46496 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.919793 | 0.0462798 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.1729 | −1.36377 | −0.681885 | − | 0.731459i | \(-0.738840\pi\) | ||||
−0.681885 | + | 0.731459i | \(0.738840\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.8382 | 1.54384 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.84509 | 0.142077 | 0.0710386 | − | 0.997474i | \(-0.477369\pi\) | ||||
0.0710386 | + | 0.997474i | \(0.477369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.75797 | −0.386452 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.11682 | −0.0554951 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.31886 | −0.412350 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.3190 | −1.44973 | −0.724866 | − | 0.688890i | \(-0.758098\pi\) | ||||
−0.724866 | + | 0.688890i | \(0.758098\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −51.7691 | −2.55358 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.24534 | −0.159693 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.21284 | −0.108624 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −48.0761 | −2.35430 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.366603 | −0.0179097 | −0.00895487 | − | 0.999960i | \(-0.502850\pi\) | ||||
−0.00895487 | + | 0.999960i | \(0.502850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.2117 | −0.643898 | −0.321949 | − | 0.946757i | \(-0.604338\pi\) | ||||
−0.321949 | + | 0.946757i | \(0.604338\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.6673 | −1.53972 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.96617 | 0.240895 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0157 | 0.484695 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.42699 | 0.455139 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.7117 | 1.57567 | 0.787834 | − | 0.615888i | \(-0.211203\pi\) | ||||
0.787834 | + | 0.615888i | \(0.211203\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.2253 | 1.11614 | 0.558069 | − | 0.829795i | \(-0.311543\pi\) | ||||
0.558069 | + | 0.829795i | \(0.311543\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.58809 | 0.0761431 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.8691 | 1.14181 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8785 | 1.28284 | 0.641421 | − | 0.767189i | \(-0.278345\pi\) | ||||
0.641421 | + | 0.767189i | \(0.278345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.3358 | 0.635040 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.4738 | −0.735181 | −0.367591 | − | 0.929988i | \(-0.619817\pi\) | ||||
−0.367591 | + | 0.929988i | \(0.619817\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.30241 | 0.0617400 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.8824 | 1.12960 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4782 | 0.494498 | 0.247249 | − | 0.968952i | \(-0.420473\pi\) | ||||
0.247249 | + | 0.968952i | \(0.420473\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.3939 | 0.724871 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.212817 | 0.00999900 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.01158 | 0.0474236 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.36630 | −0.204247 | −0.102123 | − | 0.994772i | \(-0.532564\pi\) | ||||
−0.102123 | + | 0.994772i | \(0.532564\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.01847 | −0.0942141 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.5087 | −0.815461 | −0.407731 | − | 0.913102i | \(-0.633680\pi\) | ||||
−0.407731 | + | 0.913102i | \(0.633680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.9590 | 0.555780 | 0.277890 | − | 0.960613i | \(-0.410365\pi\) | ||||
0.277890 | + | 0.960613i | \(0.410365\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.19145 | −0.101626 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3561 | 0.618047 | 0.309024 | − | 0.951054i | \(-0.399998\pi\) | ||||
0.309024 | + | 0.951054i | \(0.399998\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.8599 | 1.14792 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.14938 | −0.0990383 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.68825 | −0.261546 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.1293 | −0.831829 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.4505 | −1.39423 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.59012 | 0.209728 | 0.104864 | − | 0.994487i | \(-0.466559\pi\) | ||||
0.104864 | + | 0.994487i | \(0.466559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.59760 | −0.300825 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 55.2340 | 2.51323 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.21786 | 0.146115 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5186 | −0.567270 | −0.283635 | − | 0.958932i | \(-0.591540\pi\) | ||||
−0.283635 | + | 0.958932i | \(0.591540\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.7352 | 0.711569 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.78378 | −0.306148 | −0.153074 | − | 0.988215i | \(-0.548917\pi\) | ||||
−0.153074 | + | 0.988215i | \(0.548917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.31726 | −0.149402 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.48384 | 0.0666935 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −35.2630 | −1.58176 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.3316 | −0.999699 | −0.499850 | − | 0.866112i | \(-0.666611\pi\) | ||||
−0.499850 | + | 0.866112i | \(0.666611\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.9419 | 1.42706 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.5501 | −0.514995 | −0.257497 | − | 0.966279i | \(-0.582898\pi\) | ||||
−0.257497 | + | 0.966279i | \(0.582898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0217251 | −0.000966752 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.3622 | −1.17078 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.5738 | −1.62111 | −0.810553 | − | 0.585665i | \(-0.800833\pi\) | ||||
−0.810553 | + | 0.585665i | \(0.800833\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.1939 | −0.849089 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.36854 | 0.325329 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.0929635 | 0.00409646 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.9239 | −0.788294 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 41.0555 | 1.80213 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.2569 | 1.15034 | 0.575168 | − | 0.818035i | \(-0.304937\pi\) | ||||
0.575168 | + | 0.818035i | \(0.304937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8328 | 1.04213 | 0.521067 | − | 0.853516i | \(-0.325534\pi\) | ||||
0.521067 | + | 0.853516i | \(0.325534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −41.9519 | −1.83093 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.57757 | 0.199402 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.7517 | 0.858771 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.77545 | −0.163841 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.2088 | 0.528820 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.67725 | 0.0725140 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.6261 | 0.674316 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.54819 | 0.325124 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7617 | 0.462682 | 0.231341 | − | 0.972873i | \(-0.425689\pi\) | ||||
0.231341 | + | 0.972873i | \(0.425689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.24200 | −0.0962133 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.0672277 | −0.00287972 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.6808 | 0.841492 | 0.420746 | − | 0.907178i | \(-0.361768\pi\) | ||||
0.420746 | + | 0.907178i | \(0.361768\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.6517 | 0.497284 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1098 | 0.515896 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.2302 | 0.690179 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.86367 | −0.0791083 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.4435 | −0.696733 | −0.348366 | − | 0.937358i | \(-0.613264\pi\) | ||||
−0.348366 | + | 0.937358i | \(0.613264\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.51129 | −0.190807 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.56237 | −0.234843 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0033 | 0.548024 | 0.274012 | − | 0.961726i | \(-0.411649\pi\) | ||||
0.274012 | + | 0.961726i | \(0.411649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.29471 | 0.0544689 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.7068 | −0.827608 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.88723 | −0.162961 | −0.0814805 | − | 0.996675i | \(-0.525965\pi\) | ||||
−0.0814805 | + | 0.996675i | \(0.525965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.7365 | 1.32813 | 0.664065 | − | 0.747675i | \(-0.268830\pi\) | ||||
0.664065 | + | 0.747675i | \(0.268830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.70887 | 0.154940 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.4712 | −1.35414 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.8866 | 1.74376 | 0.871880 | − | 0.489719i | \(-0.162901\pi\) | ||||
0.871880 | + | 0.489719i | \(0.162901\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.0095 | −0.748448 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.0467 | −1.61993 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.2352 | −0.713810 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.17682 | 0.0486553 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.2349 | 0.711362 | 0.355681 | − | 0.934607i | \(-0.384249\pi\) | ||||
0.355681 | + | 0.934607i | \(0.384249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7107 | −0.688551 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 49.9400 | 2.05426 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.7853 | −1.26420 | −0.632100 | − | 0.774887i | \(-0.717807\pi\) | ||||
−0.632100 | + | 0.774887i | \(0.717807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.596880 | −0.0244697 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.6672 | −1.58254 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.12331 | 0.168474 | 0.0842370 | − | 0.996446i | \(-0.473155\pi\) | ||||
0.0842370 | + | 0.996446i | \(0.473155\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.4662 | −1.48749 | −0.743743 | − | 0.668466i | \(-0.766951\pi\) | ||||
−0.743743 | + | 0.668466i | \(0.766951\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.9206 | 1.17774 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.18325 | −0.0481058 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.2809 | 1.43201 | 0.716003 | − | 0.698097i | \(-0.245969\pi\) | ||||
0.716003 | + | 0.698097i | \(0.245969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.0226 | 1.13553 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.2153 | −0.575089 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.13748 | 0.0863321 | 0.0431661 | − | 0.999068i | \(-0.486256\pi\) | ||||
0.0431661 | + | 0.999068i | \(0.486256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.44869 | 0.139065 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.20487 | 0.290057 | 0.145029 | − | 0.989427i | \(-0.453673\pi\) | ||||
0.145029 | + | 0.989427i | \(0.453673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.7759 | 0.593895 | 0.296947 | − | 0.954894i | \(-0.404031\pi\) | ||||
0.296947 | + | 0.954894i | \(0.404031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.1977 | 0.529606 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.9816 | 0.920739 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4938 | 0.979750 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.3057 | 0.810933 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.89290 | 0.155220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.6050 | −0.621224 | −0.310612 | − | 0.950537i | \(-0.600534\pi\) | ||||
−0.310612 | + | 0.950537i | \(0.600534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.46100 | −0.137562 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.914019 | 0.0362717 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.98639 | 0.237190 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −41.0230 | −1.62285 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.5795 | 1.52380 | 0.761899 | − | 0.647696i | \(-0.224267\pi\) | ||||
0.761899 | + | 0.647696i | \(0.224267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.6467 | 1.60295 | 0.801475 | − | 0.598028i | \(-0.204049\pi\) | ||||
0.801475 | + | 0.598028i | \(0.204049\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.27433 | −0.0501768 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.8337 | −1.33014 | −0.665070 | − | 0.746781i | \(-0.731598\pi\) | ||||
−0.665070 | + | 0.746781i | \(0.731598\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.13693 | −0.0838820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.6692 | −1.51556 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.9691 | −1.72064 | −0.860321 | − | 0.509752i | \(-0.829737\pi\) | ||||
−0.860321 | + | 0.509752i | \(0.829737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.05201 | −0.0801788 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.3291 | −0.871142 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.8087 | 0.927453 | 0.463727 | − | 0.885978i | \(-0.346512\pi\) | ||||
0.463727 | + | 0.885978i | \(0.346512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.60095 | −0.373434 | −0.186717 | − | 0.982414i | \(-0.559785\pi\) | ||||
−0.186717 | + | 0.982414i | \(0.559785\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.41146 | −0.171327 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.17895 | 0.0844959 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.6898 | 0.839833 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.9430 | −1.00301 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.59497 | 0.254596 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3624 | 0.437988 | 0.218994 | − | 0.975726i | \(-0.429722\pi\) | ||||
0.218994 | + | 0.975726i | \(0.429722\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.0241 | −0.385827 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.7465 | 0.643622 | 0.321811 | − | 0.946804i | \(-0.395709\pi\) | ||||
0.321811 | + | 0.946804i | \(0.395709\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 56.7807 | 2.17904 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.5348 | −0.595295 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.9375 | 1.48990 | 0.744952 | − | 0.667119i | \(-0.232473\pi\) | ||||
0.744952 | + | 0.667119i | \(0.232473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.65787 | −0.139760 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.10299 | 0.270996 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.6691 | −0.520751 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1823 | −0.957979 | −0.478990 | − | 0.877821i | \(-0.658997\pi\) | ||||
−0.478990 | + | 0.877821i | \(0.658997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26.1830 | 0.994612 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.39693 | −0.128853 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.20375 | −0.272861 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.7544 | 1.46583 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.3224 | −1.59849 | −0.799247 | − | 0.601003i | \(-0.794768\pi\) | ||||
−0.799247 | + | 0.601003i | \(0.794768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.2112 | −0.535987 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.01549 | −0.151232 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.383349 | −0.0144173 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.2136 | −0.796692 | −0.398346 | − | 0.917235i | \(-0.630416\pi\) | ||||
−0.398346 | + | 0.917235i | \(0.630416\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.8813 | 0.708104 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.9304 | −1.12090 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.666087 | 0.0249102 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.2922 | −0.459059 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.4405 | 0.538539 | 0.269270 | − | 0.963065i | \(-0.413218\pi\) | ||||
0.269270 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.64039 | 0.0610912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 55.5795 | 2.06702 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.4741 | −0.611832 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4292 | −0.609327 | −0.304663 | − | 0.952460i | \(-0.598544\pi\) | ||||
−0.304663 | + | 0.952460i | \(0.598544\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.6878 | −1.43288 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.66187 | 0.0984530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.953899 | 0.0352331 | 0.0176165 | − | 0.999845i | \(-0.494392\pi\) | ||||
0.0176165 | + | 0.999845i | \(0.494392\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.69102 | 0.0623741 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.3693 | 0.602970 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.9730 | −1.17615 | −0.588073 | − | 0.808808i | \(-0.700113\pi\) | ||||
−0.588073 | + | 0.808808i | \(0.700113\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.1043 | 0.591605 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.6652 | −1.16168 | −0.580842 | − | 0.814016i | \(-0.697277\pi\) | ||||
−0.580842 | + | 0.814016i | \(0.697277\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.68746 | 0.0618239 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.4247 | −1.66200 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.5960 | 1.08141 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.9261 | −1.63938 | −0.819688 | − | 0.572811i | \(-0.805853\pi\) | ||||
−0.819688 | + | 0.572811i | \(0.805853\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 74.5654 | 2.71731 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0150371 | 0.000547255 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.6888 | −0.897331 | −0.448665 | − | 0.893700i | \(-0.648100\pi\) | ||||
−0.448665 | + | 0.893700i | \(0.648100\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.3695 | 1.32013 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.9158 | 0.830696 | 0.415348 | − | 0.909663i | \(-0.363660\pi\) | ||||
0.415348 | + | 0.909663i | \(0.363660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.18627 | −0.0429458 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.694377 | −0.0251053 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.69478 | −0.0611949 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.3755 | −0.446270 | −0.223135 | − | 0.974788i | \(-0.571629\pi\) | ||||
−0.223135 | + | 0.974788i | \(0.571629\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.1183 | −1.15671 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.8799 | 0.679062 | 0.339531 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339531 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.7330 | 0.816594 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.8854 | −1.17976 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.2977 | 0.942212 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.2193 | −0.830854 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.69578 | 0.239288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.151870 | −0.00542046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.2831 | −0.580428 | −0.290214 | − | 0.956962i | \(-0.593727\pi\) | ||||
−0.290214 | + | 0.956962i | \(0.593727\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −43.6427 | −1.55372 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.8458 | 0.812304 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.23040 | 0.185737 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.86120 | −0.136943 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.2982 | −0.648155 | −0.324077 | − | 0.946031i | \(-0.605054\pi\) | ||||
−0.324077 | + | 0.946031i | \(0.605054\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.38769 | 0.296735 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.7355 | 0.944652 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.6385 | −0.446001 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.90269 | 0.137552 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.4224 | 0.507692 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.56100 | 0.265831 | 0.132915 | − | 0.991127i | \(-0.457566\pi\) | ||||
0.132915 | + | 0.991127i | \(0.457566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.4716 | 0.613511 | 0.306755 | − | 0.951788i | \(-0.400757\pi\) | ||||
0.306755 | + | 0.951788i | \(0.400757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.0732 | −0.914428 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.11181 | 0.0389449 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.71732 | −0.339966 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.7655 | 0.725605 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.8426 | −1.42542 | −0.712709 | − | 0.701460i | \(-0.752532\pi\) | ||||
−0.712709 | + | 0.701460i | \(0.752532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.3304 | −0.604100 | −0.302050 | − | 0.953292i | \(-0.597671\pi\) | ||||
−0.302050 | + | 0.953292i | \(0.597671\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.6237 | −0.961734 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.0880 | 0.524662 | 0.262331 | − | 0.964978i | \(-0.415509\pi\) | ||||
0.262331 | + | 0.964978i | \(0.415509\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.7604 | −1.62406 | −0.812029 | − | 0.583617i | \(-0.801637\pi\) | ||||
−0.812029 | + | 0.583617i | \(0.801637\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −80.6065 | −2.79621 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.53225 | −0.122385 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.25693 | 0.0781043 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.23969 | −0.319370 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.4456 | 0.360621 | 0.180311 | − | 0.983610i | \(-0.442290\pi\) | ||||
0.180311 | + | 0.983610i | \(0.442290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9958 | −0.620545 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55.5408 | 1.91293 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.86268 | −0.0640782 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.8790 | −0.717410 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.6916 | 0.813092 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.4536 | −0.872539 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.8169 | −0.918195 | −0.459097 | − | 0.888386i | \(-0.651827\pi\) | ||||
−0.459097 | + | 0.888386i | \(0.651827\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.53486 | 0.0866904 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.6027 | 0.942891 | 0.471445 | − | 0.881895i | \(-0.343732\pi\) | ||||
0.471445 | + | 0.881895i | \(0.343732\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.9599 | 0.749262 | 0.374631 | − | 0.927174i | \(-0.377769\pi\) | ||||
0.374631 | + | 0.927174i | \(0.377769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60.8539 | 2.07389 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.10215 | −0.275801 | −0.137900 | − | 0.990446i | \(-0.544035\pi\) | ||||
−0.137900 | + | 0.990446i | \(0.544035\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.90087 | 0.0986326 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.60297 | 0.0884015 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.6870 | 0.362530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.9823 | 0.439888 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 66.0555 | 2.23564 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.94861 | −0.201100 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.18009 | 0.276222 | 0.138111 | − | 0.990417i | \(-0.455897\pi\) | ||||
0.138111 | + | 0.990417i | \(0.455897\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.9461 | 1.44853 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.3846 | 1.36059 | 0.680296 | − | 0.732937i | \(-0.261851\pi\) | ||||
0.680296 | + | 0.732937i | \(0.261851\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.8592 | −1.34137 | −0.670685 | − | 0.741743i | \(-0.734000\pi\) | ||||
−0.670685 | + | 0.741743i | \(0.734000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.478736 | −0.0160925 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.3243 | 0.413811 | 0.206905 | − | 0.978361i | \(-0.433661\pi\) | ||||
0.206905 | + | 0.978361i | \(0.433661\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.1283 | 0.540926 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.9762 | −0.434718 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.6197 | −1.02465 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.10410 | 0.0369060 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.8442 | 0.963081 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.1850 | −0.506447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.06541 | 0.268698 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.4863 | −0.748296 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.158414 | −0.00526585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.0243 | 0.963735 | 0.481868 | − | 0.876244i | \(-0.339959\pi\) | ||||
0.481868 | + | 0.876244i | \(0.339959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.445967 | −0.0147918 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.5806 | 0.913785 | 0.456892 | − | 0.889522i | \(-0.348962\pi\) | ||||
0.456892 | + | 0.889522i | \(0.348962\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.7108 | −0.850902 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.47747 | 0.0488435 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.2088 | −1.19572 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.6436 | −1.40668 | −0.703341 | − | 0.710853i | \(-0.748309\pi\) | ||||
−0.703341 | + | 0.710853i | \(0.748309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.2270 | −0.336992 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.4150 | −0.606138 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.3328 | 0.635658 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.90833 | 0.0626779 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.44369 | 0.309837 | 0.154919 | − | 0.987927i | \(-0.450488\pi\) | ||||
0.154919 | + | 0.987927i | \(0.450488\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.8947 | 0.422606 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.2426 | −1.05557 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.393023 | −0.0128532 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.0831 | −1.14612 | −0.573058 | − | 0.819515i | \(-0.694243\pi\) | ||||
−0.573058 | + | 0.819515i | \(0.694243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.9263 | 0.454468 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.0471 | −1.01211 | −0.506053 | − | 0.862502i | \(-0.668896\pi\) | ||||
−0.506053 | + | 0.862502i | \(0.668896\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.1016 | 1.53384 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.20479 | 0.0391917 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.2669 | 1.53597 | 0.767983 | − | 0.640470i | \(-0.221260\pi\) | ||||
0.767983 | + | 0.640470i | \(0.221260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0234 | −0.325374 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.1288 | 0.587867 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.2110 | −1.07581 | −0.537904 | − | 0.843006i | \(-0.680784\pi\) | ||||
−0.537904 | + | 0.843006i | \(0.680784\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.262059 | 0.00848004 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.4518 | 0.596463 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −64.5450 | −2.08427 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0459 | −0.324060 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.4303 | 1.10950 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.27250 | −0.0409633 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4762 | 0.754945 | 0.377473 | − | 0.926021i | \(-0.376793\pi\) | ||||
0.377473 | + | 0.926021i | \(0.376793\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.50228 | −0.305257 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.2975 | 0.747651 | 0.373826 | − | 0.927499i | \(-0.378046\pi\) | ||||
0.373826 | + | 0.927499i | \(0.378046\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.9406 | −1.92161 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.9081 | −0.701620 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.1370 | 0.900183 | 0.450092 | − | 0.892982i | \(-0.351391\pi\) | ||||
0.450092 | + | 0.892982i | \(0.351391\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.1325 | 0.483637 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.38004 | −0.0440612 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.62570 | −0.147537 | −0.0737684 | − | 0.997275i | \(-0.523503\pi\) | ||||
−0.0737684 | + | 0.997275i | \(0.523503\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.52863 | 0.112431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −70.8553 | −2.25535 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.4046 | −0.553434 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.26892 | −0.0403084 | −0.0201542 | − | 0.999797i | \(-0.506416\pi\) | ||||
−0.0201542 | + | 0.999797i | \(0.506416\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −59.6588 | −1.89322 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.73213 | −0.0866142 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.4826 | −0.395329 | −0.197665 | − | 0.980270i | \(-0.563336\pi\) | ||||
−0.197665 | + | 0.980270i | \(0.563336\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.85769 | −0.248606 |
(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 | 4012.2.a.i.1.15 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.i.1.15 | ✓ | 18 | 1.1 | even | 1 | trivial |