Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} - 4x^{5} + 60x^{4} + 31x^{3} - 75x^{2} - 60x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.33338\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | 1.33338 | 0.769830 | 0.384915 | − | 0.922952i | \(-0.374231\pi\) | ||||
0.384915 | + | 0.922952i | \(0.374231\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.76687 | 0.790168 | 0.395084 | − | 0.918645i | \(-0.370715\pi\) | ||||
0.395084 | + | 0.918645i | \(0.370715\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.22209 | −0.407362 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.48727 | −0.749939 | −0.374970 | − | 0.927037i | \(-0.622347\pi\) | ||||
−0.374970 | + | 0.927037i | \(0.622347\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.30214 | −0.638498 | −0.319249 | − | 0.947671i | \(-0.603431\pi\) | ||||
−0.319249 | + | 0.947671i | \(0.603431\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.35592 | 0.608295 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.40413 | −0.340552 | −0.170276 | − | 0.985396i | \(-0.554466\pi\) | ||||
−0.170276 | + | 0.985396i | \(0.554466\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.95607 | 0.907586 | 0.453793 | − | 0.891107i | \(-0.350071\pi\) | ||||
0.453793 | + | 0.891107i | \(0.350071\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0405520 | −0.00845568 | −0.00422784 | − | 0.999991i | \(-0.501346\pi\) | ||||
−0.00422784 | + | 0.999991i | \(0.501346\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.87817 | −0.375634 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.62966 | −1.08343 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.20359 | 1.15198 | 0.575989 | − | 0.817457i | \(-0.304617\pi\) | ||||
0.575989 | + | 0.817457i | \(0.304617\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.98573 | −0.536253 | −0.268127 | − | 0.963384i | \(-0.586405\pi\) | ||||
−0.268127 | + | 0.963384i | \(0.586405\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.31648 | −0.577326 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.195125 | 0.0320784 | 0.0160392 | − | 0.999871i | \(-0.494894\pi\) | ||||
0.0160392 | + | 0.999871i | \(0.494894\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.06963 | −0.491535 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.19665 | −0.182488 | −0.0912438 | − | 0.995829i | \(-0.529084\pi\) | ||||
−0.0912438 | + | 0.995829i | \(0.529084\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.15927 | −0.321884 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.43927 | −1.08513 | −0.542565 | − | 0.840014i | \(-0.682547\pi\) | ||||
−0.542565 | + | 0.840014i | \(0.682547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.87225 | −0.262167 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.7999 | −1.62085 | −0.810424 | − | 0.585844i | \(-0.800763\pi\) | ||||
−0.810424 | + | 0.585844i | \(0.800763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.39468 | −0.592578 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.27497 | 0.698686 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.50846 | −0.717140 | −0.358570 | − | 0.933503i | \(-0.616736\pi\) | ||||
−0.358570 | + | 0.933503i | \(0.616736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.91456 | 0.501208 | 0.250604 | − | 0.968090i | \(-0.419371\pi\) | ||||
0.250604 | + | 0.968090i | \(0.419371\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.06758 | −0.504521 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.79845 | 0.708394 | 0.354197 | − | 0.935171i | \(-0.384754\pi\) | ||||
0.354197 | + | 0.935171i | \(0.384754\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0540714 | −0.00650943 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2887 | 1.22105 | 0.610524 | − | 0.791997i | \(-0.290959\pi\) | ||||
0.610524 | + | 0.791997i | \(0.290959\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.2984 | −1.43942 | −0.719710 | − | 0.694275i | \(-0.755725\pi\) | ||||
−0.719710 | + | 0.694275i | \(0.755725\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.50432 | −0.289174 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.35940 | −0.152945 | −0.0764723 | − | 0.997072i | \(-0.524366\pi\) | ||||
−0.0764723 | + | 0.997072i | \(0.524366\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.84025 | −0.426694 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.02722 | 0.661573 | 0.330787 | − | 0.943706i | \(-0.392686\pi\) | ||||
0.330787 | + | 0.943706i | \(0.392686\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.48092 | −0.269093 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.27178 | 0.886828 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.226063 | −0.0239627 | −0.0119813 | − | 0.999928i | \(-0.503814\pi\) | ||||
−0.0119813 | + | 0.999928i | \(0.503814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.98113 | −0.412824 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.98987 | 0.717145 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.43170 | 0.145367 | 0.0726836 | − | 0.997355i | \(-0.476844\pi\) | ||||
0.0726836 | + | 0.997355i | \(0.476844\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.03965 | 0.305497 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.73578 | −0.670235 | −0.335117 | − | 0.942176i | \(-0.608776\pi\) | ||||
−0.335117 | + | 0.942176i | \(0.608776\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.93264 | −0.683093 | −0.341547 | − | 0.939865i | \(-0.610951\pi\) | ||||
−0.341547 | + | 0.939865i | \(0.610951\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.6739 | −1.12856 | −0.564278 | − | 0.825585i | \(-0.690845\pi\) | ||||
−0.564278 | + | 0.825585i | \(0.690845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.20063 | −0.210782 | −0.105391 | − | 0.994431i | \(-0.533609\pi\) | ||||
−0.105391 | + | 0.994431i | \(0.533609\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.260177 | 0.0246949 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.83479 | 0.925180 | 0.462590 | − | 0.886572i | \(-0.346920\pi\) | ||||
0.462590 | + | 0.886572i | \(0.346920\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0716501 | −0.00668141 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.81341 | 0.260100 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.81350 | −0.437591 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.33338 | 0.120227 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1528 | −1.08698 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.5602 | −1.82443 | −0.912213 | − | 0.409716i | \(-0.865628\pi\) | ||||
−0.912213 | + | 0.409716i | \(0.865628\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.59560 | −0.140484 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.26440 | −0.722064 | −0.361032 | − | 0.932553i | \(-0.617575\pi\) | ||||
−0.361032 | + | 0.932553i | \(0.617575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.94689 | −0.856092 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.681112 | −0.0581913 | −0.0290956 | − | 0.999577i | \(-0.509263\pi\) | ||||
−0.0290956 | + | 0.999577i | \(0.509263\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.1700 | −1.11706 | −0.558531 | − | 0.829484i | \(-0.688635\pi\) | ||||
−0.558531 | + | 0.829484i | \(0.688635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.91941 | −0.835365 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.72603 | 0.478835 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.9609 | 0.910257 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.2961 | −1.25310 | −0.626551 | − | 0.779380i | \(-0.715534\pi\) | ||||
−0.626551 | + | 0.779380i | \(0.715534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.98315 | −0.324144 | −0.162072 | − | 0.986779i | \(-0.551818\pi\) | ||||
−0.162072 | + | 0.986779i | \(0.551818\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.71597 | 0.138728 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.27540 | −0.423730 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.5140 | 1.15835 | 0.579173 | − | 0.815205i | \(-0.303376\pi\) | ||||
0.579173 | + | 0.815205i | \(0.303376\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.7339 | −1.24778 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.2886 | 1.19750 | 0.598749 | − | 0.800937i | \(-0.295665\pi\) | ||||
0.598749 | + | 0.800937i | \(0.295665\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.85980 | −0.456184 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.7533 | −1.06426 | −0.532130 | − | 0.846663i | \(-0.678608\pi\) | ||||
−0.532130 | + | 0.846663i | \(0.678608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.70017 | −0.592321 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.83466 | −0.369716 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.7093 | 1.19436 | 0.597179 | − | 0.802108i | \(-0.296288\pi\) | ||||
0.597179 | + | 0.802108i | \(0.296288\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.34489 | −0.552076 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.21506 | −0.464535 | −0.232268 | − | 0.972652i | \(-0.574615\pi\) | ||||
−0.232268 | + | 0.972652i | \(0.574615\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.6181 | −1.16088 | −0.580441 | − | 0.814302i | \(-0.697120\pi\) | ||||
−0.580441 | + | 0.814302i | \(0.697120\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.21961 | 0.385845 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.344761 | 0.0253473 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.49245 | 0.255393 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.36348 | −0.315730 | −0.157865 | − | 0.987461i | \(-0.550461\pi\) | ||||
−0.157865 | + | 0.987461i | \(0.550461\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.1674 | −1.09177 | −0.545887 | − | 0.837859i | \(-0.683807\pi\) | ||||
−0.545887 | + | 0.837859i | \(0.683807\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.42364 | −0.388395 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.34032 | −0.309235 | −0.154618 | − | 0.987974i | \(-0.549415\pi\) | ||||
−0.154618 | + | 0.987974i | \(0.549415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.07448 | 0.217944 | 0.108972 | − | 0.994045i | \(-0.465244\pi\) | ||||
0.108972 | + | 0.994045i | \(0.465244\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.73157 | 0.545343 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.76687 | 0.123404 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0495580 | 0.00344452 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.83981 | −0.680634 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.480367 | 0.0330698 | 0.0165349 | − | 0.999863i | \(-0.494737\pi\) | ||||
0.0165349 | + | 0.999863i | \(0.494737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.7188 | 0.940000 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.11433 | −0.144196 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.3985 | −1.10811 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.23250 | 0.217442 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.20336 | −0.482373 | −0.241186 | − | 0.970479i | \(-0.577537\pi\) | ||||
−0.241186 | + | 0.970479i | \(0.577537\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.29528 | 0.153019 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.92532 | 0.526022 | 0.263011 | − | 0.964793i | \(-0.415284\pi\) | ||||
0.263011 | + | 0.964793i | \(0.415284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3980 | 1.21577 | 0.607886 | − | 0.794024i | \(-0.292018\pi\) | ||||
0.607886 | + | 0.794024i | \(0.292018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7877 | 0.968773 | 0.484386 | − | 0.874854i | \(-0.339043\pi\) | ||||
0.484386 | + | 0.874854i | \(0.339043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.1442 | −0.857435 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.81260 | −0.117741 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.7876 | −1.66806 | −0.834031 | − | 0.551717i | \(-0.813973\pi\) | ||||
−0.834031 | + | 0.551717i | \(0.813973\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1914 | −1.04298 | −0.521491 | − | 0.853257i | \(-0.674624\pi\) | ||||
−0.521491 | + | 0.853257i | \(0.674624\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7685 | 0.754947 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.10742 | −0.579491 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.03660 | 0.509299 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.47665 | 0.0932054 | 0.0466027 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466027 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.100864 | 0.00634124 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.30802 | −0.207156 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.36748 | −0.397193 | −0.198596 | − | 0.980081i | \(-0.563638\pi\) | ||||
−0.198596 | + | 0.980081i | \(0.563638\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.58132 | −0.469272 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.1131 | 1.11690 | 0.558450 | − | 0.829538i | \(-0.311396\pi\) | ||||
0.558450 | + | 0.829538i | \(0.311396\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.8490 | −1.28074 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.301430 | −0.0184472 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.1746 | −1.04715 | −0.523577 | − | 0.851978i | \(-0.675403\pi\) | ||||
−0.523577 | + | 0.851978i | \(0.675403\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.7499 | −0.956739 | −0.478369 | − | 0.878159i | \(-0.658772\pi\) | ||||
−0.478369 | + | 0.878159i | \(0.658772\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.67151 | 0.281703 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.6270 | 1.17927 | 0.589635 | − | 0.807670i | \(-0.299272\pi\) | ||||
0.589635 | + | 0.807670i | \(0.299272\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.64882 | 0.218449 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.20950 | 0.489738 | 0.244869 | − | 0.969556i | \(-0.421255\pi\) | ||||
0.244869 | + | 0.969556i | \(0.421255\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.9706 | 1.06824 | 0.534120 | − | 0.845409i | \(-0.320643\pi\) | ||||
0.534120 | + | 0.845409i | \(0.320643\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.32018 | 0.552080 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0284 | −0.884024 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.90901 | 0.111908 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.45654 | 0.435616 | 0.217808 | − | 0.975992i | \(-0.430109\pi\) | ||||
0.217808 | + | 0.975992i | \(0.430109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.73273 | −0.566662 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.0025 | 0.812506 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0933562 | 0.00539893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.98138 | −0.515967 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.91652 | 0.396039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0440 | 0.687387 | 0.343693 | − | 0.939082i | \(-0.388322\pi\) | ||||
0.343693 | + | 0.939082i | \(0.388322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.24388 | −0.525866 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.7692 | 1.51794 | 0.758970 | − | 0.651126i | \(-0.225703\pi\) | ||||
0.758970 | + | 0.651126i | \(0.225703\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.24338 | −0.126804 | −0.0634018 | − | 0.997988i | \(-0.520195\pi\) | ||||
−0.0634018 | + | 0.997988i | \(0.520195\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.4626 | −1.59862 | −0.799309 | − | 0.600921i | \(-0.794801\pi\) | ||||
−0.799309 | + | 0.600921i | \(0.794801\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.4300 | −0.863914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.5658 | −0.868796 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.55485 | −0.309080 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.32380 | 0.239841 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.93428 | −0.162266 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.23741 | 0.232909 | 0.116455 | − | 0.993196i | \(-0.462847\pi\) | ||||
0.116455 | + | 0.993196i | \(0.462847\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.238460 | −0.0130675 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.2451 | 0.559751 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.10406 | −0.495930 | −0.247965 | − | 0.968769i | \(-0.579762\pi\) | ||||
−0.247965 | + | 0.968769i | \(0.579762\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.1136 | 0.712231 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.42631 | 0.402157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0955372 | −0.00514355 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.1193 | 0.543233 | 0.271617 | − | 0.962406i | \(-0.412442\pi\) | ||||
0.271617 | + | 0.962406i | \(0.412442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.60171 | 0.406910 | 0.203455 | − | 0.979084i | \(-0.434783\pi\) | ||||
0.203455 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.9603 | 0.691767 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.34227 | 0.497239 | 0.248619 | − | 0.968601i | \(-0.420023\pi\) | ||||
0.248619 | + | 0.968601i | \(0.420023\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.1789 | 0.964834 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.57052 | −0.241223 | −0.120611 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120611 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.34948 | −0.176289 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.41825 | −0.336871 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.7297 | −1.13738 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.6165 | 1.70257 | 0.851283 | − | 0.524707i | \(-0.175825\pi\) | ||||
0.851283 | + | 0.524707i | \(0.175825\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.22209 | −0.0636192 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.5720 | −1.32407 | −0.662034 | − | 0.749474i | \(-0.730306\pi\) | ||||
−0.662034 | + | 0.749474i | \(0.730306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.2044 | −0.836792 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.2815 | −0.735536 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.0887 | 1.64828 | 0.824142 | − | 0.566383i | \(-0.191658\pi\) | ||||
0.824142 | + | 0.566383i | \(0.191658\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.4147 | −1.40450 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.470160 | 0.0240240 | 0.0120120 | − | 0.999928i | \(-0.496176\pi\) | ||||
0.0120120 | + | 0.999928i | \(0.496176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.46241 | 0.0743385 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.4769 | −0.784710 | −0.392355 | − | 0.919814i | \(-0.628340\pi\) | ||||
−0.392355 | + | 0.919814i | \(0.628340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0569403 | 0.00287960 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.0196 | −0.555866 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.40189 | −0.120852 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3764 | 1.42417 | 0.712086 | − | 0.702092i | \(-0.247750\pi\) | ||||
0.712086 | + | 0.702092i | \(0.247750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.0305 | −1.24996 | −0.624982 | − | 0.780639i | \(-0.714894\pi\) | ||||
−0.624982 | + | 0.780639i | \(0.714894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.87356 | 0.342396 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.78522 | −0.337160 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.485328 | −0.0240568 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1559 | 1.24388 | 0.621940 | − | 0.783065i | \(-0.286345\pi\) | ||||
0.621940 | + | 0.783065i | \(0.286345\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.908184 | −0.0447974 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6493 | 0.522754 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.5606 | −0.859947 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.32306 | −0.162342 | −0.0811710 | − | 0.996700i | \(-0.525866\pi\) | ||||
−0.0811710 | + | 0.996700i | \(0.525866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.67892 | −0.179300 | −0.0896498 | − | 0.995973i | \(-0.528575\pi\) | ||||
−0.0896498 | + | 0.995973i | \(0.528575\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.09143 | 0.442040 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.63720 | 0.127923 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.63500 | 0.368621 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.8602 | 1.19747 | 0.598737 | − | 0.800946i | \(-0.295670\pi\) | ||||
0.598737 | + | 0.800946i | \(0.295670\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.5625 | 1.85320 | 0.926599 | − | 0.376052i | \(-0.122719\pi\) | ||||
0.926599 | + | 0.376052i | \(0.122719\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.6152 | 0.700743 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.160427 | −0.00767425 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4440 | 1.21437 | 0.607187 | − | 0.794559i | \(-0.292298\pi\) | ||||
0.607187 | + | 0.794559i | \(0.292298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.76272 | 0.178772 | 0.0893860 | − | 0.995997i | \(-0.471510\pi\) | ||||
0.0893860 | + | 0.995997i | \(0.471510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.399425 | −0.0189346 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.3955 | −0.964676 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.9012 | 1.41113 | 0.705563 | − | 0.708647i | \(-0.250694\pi\) | ||||
0.705563 | + | 0.708647i | \(0.250694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.48727 | −0.117121 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.31107 | −0.249536 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.1086 | −0.566415 | −0.283208 | − | 0.959059i | \(-0.591399\pi\) | ||||
−0.283208 | + | 0.959059i | \(0.591399\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.90479 | 0.368964 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.92540 | −0.182824 | −0.0914120 | − | 0.995813i | \(-0.529138\pi\) | ||||
−0.0914120 | + | 0.995813i | \(0.529138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.6329 | −0.633575 | −0.316788 | − | 0.948496i | \(-0.602604\pi\) | ||||
−0.316788 | + | 0.948496i | \(0.602604\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.03414 | −0.326200 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.9213 | 0.551651 | 0.275826 | − | 0.961208i | \(-0.411049\pi\) | ||||
0.275826 | + | 0.961208i | \(0.411049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.3528 | 0.891729 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.97639 | 0.136855 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.43018 | −0.340920 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.4205 | 0.660272 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.55874 | 0.116912 | 0.0584558 | − | 0.998290i | \(-0.481382\pi\) | ||||
0.0584558 | + | 0.998290i | \(0.481382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.449205 | −0.0204820 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.52963 | 0.114865 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.99748 | 0.0905143 | 0.0452572 | − | 0.998975i | \(-0.485589\pi\) | ||||
0.0452572 | + | 0.998975i | \(0.485589\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.3856 | 0.921869 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.72991 | 0.393975 | 0.196988 | − | 0.980406i | \(-0.436884\pi\) | ||||
0.196988 | + | 0.980406i | \(0.436884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.71066 | −0.392308 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.37067 | 0.241394 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.82275 | −0.439727 | −0.219863 | − | 0.975531i | \(-0.570561\pi\) | ||||
−0.219863 | + | 0.975531i | \(0.570561\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.3384 | −0.819299 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.7626 | 0.747407 | 0.373703 | − | 0.927548i | \(-0.378088\pi\) | ||||
0.373703 | + | 0.927548i | \(0.378088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.9012 | −0.529598 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.2673 | −0.455986 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.21673 | 0.364200 | 0.182100 | − | 0.983280i | \(-0.441711\pi\) | ||||
0.182100 | + | 0.983280i | \(0.441711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.2714 | −0.983305 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.2491 | −0.539759 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.5035 | 0.813781 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.9466 | 0.919452 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.4558 | −0.983805 | −0.491903 | − | 0.870650i | \(-0.663698\pi\) | ||||
−0.491903 | + | 0.870650i | \(0.663698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.4841 | −1.33298 | −0.666488 | − | 0.745516i | \(-0.732203\pi\) | ||||
−0.666488 | + | 0.745516i | \(0.732203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.19236 | 0.182622 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9984 | −0.999929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.73181 | 0.292136 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.30214 | −0.0997166 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.6262 | −0.891749 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.28706 | −0.357613 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.4708 | 0.794120 | 0.397060 | − | 0.917793i | \(-0.370031\pi\) | ||||
0.397060 | + | 0.917793i | \(0.370031\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.8249 | −0.893682 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.88823 | −0.166553 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1709 | −1.11899 | −0.559494 | − | 0.828834i | \(-0.689005\pi\) | ||||
−0.559494 | + | 0.828834i | \(0.689005\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.78392 | −0.204173 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.5419 | 1.04552 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.459699 | 0.0195131 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.2203 | 0.517791 | 0.258896 | − | 0.965905i | \(-0.416641\pi\) | ||||
0.258896 | + | 0.965905i | \(0.416641\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.75485 | 0.116518 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.65678 | 0.196609 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.2098 | 1.23105 | 0.615524 | − | 0.788118i | \(-0.288945\pi\) | ||||
0.615524 | + | 0.788118i | \(0.288945\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.3768 | 0.731048 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.3875 | 1.31583 | 0.657916 | − | 0.753092i | \(-0.271438\pi\) | ||||
0.657916 | + | 0.753092i | \(0.271438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.7026 | −1.61965 | −0.809826 | − | 0.586670i | \(-0.800439\pi\) | ||||
−0.809826 | + | 0.586670i | \(0.800439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.81820 | −0.243059 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0761635 | 0.00317624 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.3521 | 1.30521 | 0.652603 | − | 0.757700i | \(-0.273677\pi\) | ||||
0.652603 | + | 0.757700i | \(0.273677\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.2240 | −0.840480 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.3496 | 1.21554 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.97093 | 0.205523 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.78318 | −0.321246 | −0.160623 | − | 0.987016i | \(-0.551350\pi\) | ||||
−0.160623 | + | 0.987016i | \(0.551350\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8118 | −0.486696 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.78732 | −0.238059 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.5107 | −1.54038 | −0.770190 | − | 0.637815i | \(-0.779838\pi\) | ||||
−0.770190 | + | 0.637815i | \(0.779838\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.09946 | 0.167780 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.9236 | 0.895775 | 0.447887 | − | 0.894090i | \(-0.352177\pi\) | ||||
0.447887 | + | 0.894090i | \(0.352177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.9765 | −1.05960 | −0.529802 | − | 0.848122i | \(-0.677734\pi\) | ||||
−0.529802 | + | 0.848122i | \(0.677734\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.08621 | −0.288573 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.50484 | −0.345771 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.6351 | −0.756375 | −0.378188 | − | 0.925729i | \(-0.623453\pi\) | ||||
−0.378188 | + | 0.925729i | \(0.623453\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.1262 | 0.692853 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.7402 | −1.08003 | −0.540013 | − | 0.841657i | \(-0.681581\pi\) | ||||
−0.540013 | + | 0.841657i | \(0.681581\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.35592 | 0.0949998 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.57592 | 0.143961 | 0.0719805 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719805 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.31677 | 0.133312 | 0.0666561 | − | 0.997776i | \(-0.478767\pi\) | ||||
0.0666561 | + | 0.997776i | \(0.478767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.228294 | 0.00916113 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0816 | −0.483265 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.1203 | −0.523972 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.273981 | −0.0109244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.9093 | −1.66838 | −0.834191 | − | 0.551475i | \(-0.814065\pi\) | ||||
−0.834191 | + | 0.551475i | \(0.814065\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.640514 | 0.0254581 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −36.3273 | −1.44160 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.5737 | −0.497409 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.3984 | −0.963681 | −0.481840 | − | 0.876259i | \(-0.660031\pi\) | ||||
−0.481840 | + | 0.876259i | \(0.660031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.91248 | −0.233166 | −0.116583 | − | 0.993181i | \(-0.537194\pi\) | ||||
−0.116583 | + | 0.993181i | \(0.537194\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.81921 | −0.111006 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.0189 | −0.747709 | −0.373855 | − | 0.927487i | \(-0.621964\pi\) | ||||
−0.373855 | + | 0.927487i | \(0.621964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.7010 | 0.537812 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.9021 | 0.544032 | 0.272016 | − | 0.962293i | \(-0.412310\pi\) | ||||
0.272016 | + | 0.962293i | \(0.412310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.6021 | −0.570552 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.0297 | 0.586365 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.2641 | 0.789379 | 0.394689 | − | 0.918815i | \(-0.370852\pi\) | ||||
0.394689 | + | 0.918815i | \(0.370852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.13328 | −0.0829749 | −0.0414875 | − | 0.999139i | \(-0.513210\pi\) | ||||
−0.0414875 | + | 0.999139i | \(0.513210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.31017 | 0.167393 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.251568 | −0.00974076 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.60485 | −0.371345 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.73655 | −0.375875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.81059 | −0.108340 | −0.0541702 | − | 0.998532i | \(-0.517251\pi\) | ||||
−0.0541702 | + | 0.998532i | \(0.517251\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.5735 | 0.406973 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.0339 | −0.424066 | −0.212033 | − | 0.977262i | \(-0.568008\pi\) | ||||
−0.212033 | + | 0.977262i | \(0.568008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5675 | 0.404948 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.7222 | 1.02250 | 0.511248 | − | 0.859433i | \(-0.329183\pi\) | ||||
0.511248 | + | 0.859433i | \(0.329183\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.20344 | −0.0459809 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.5316 | 0.935938 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.1651 | 1.03491 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.7729 | 0.866320 | 0.433160 | − | 0.901317i | \(-0.357398\pi\) | ||||
0.433160 | + | 0.901317i | \(0.357398\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.2696 | −0.882667 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.40413 | −0.0531853 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.7177 | 0.745790 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.9521 | −1.96220 | −0.981102 | − | 0.193494i | \(-0.938018\pi\) | ||||
−0.981102 | + | 0.193494i | \(0.938018\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.771929 | 0.0291139 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.5263 | −0.660079 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.70478 | −0.251803 | −0.125902 | − | 0.992043i | \(-0.540182\pi\) | ||||
−0.125902 | + | 0.992043i | \(0.540182\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.66131 | 0.0623038 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.121077 | 0.00453438 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.1171 | 0.378360 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.3848 | −1.28412 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.1180 | −1.08592 | −0.542959 | − | 0.839759i | \(-0.682696\pi\) | ||||
−0.542959 | + | 0.839759i | \(0.682696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.5894 | −0.802919 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.6514 | −0.432722 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.2981 | −1.12369 | −0.561846 | − | 0.827242i | \(-0.689909\pi\) | ||||
−0.561846 | + | 0.827242i | \(0.689909\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.2126 | 1.00788 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.68026 | 0.0621465 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.3061 | 0.750021 | 0.375011 | − | 0.927020i | \(-0.377639\pi\) | ||||
0.375011 | + | 0.927020i | \(0.377639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.4223 | −0.531252 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.74185 | −0.284788 | −0.142394 | − | 0.989810i | \(-0.545480\pi\) | ||||
−0.142394 | + | 0.989810i | \(0.545480\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.1437 | −0.446110 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.5135 | 1.15612 | 0.578058 | − | 0.815995i | \(-0.303811\pi\) | ||||
0.578058 | + | 0.815995i | \(0.303811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.0262 | −0.990162 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.36578 | −0.269500 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.1877 | 0.919112 | 0.459556 | − | 0.888149i | \(-0.348008\pi\) | ||||
0.459556 | + | 0.888149i | \(0.348008\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.96894 | 0.0717523 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.03771 | −0.256128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.2989 | −1.02854 | −0.514270 | − | 0.857628i | \(-0.671937\pi\) | ||||
−0.514270 | + | 0.857628i | \(0.671937\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.134490 | 0.00488168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.10751 | −0.330147 | −0.165074 | − | 0.986281i | \(-0.552786\pi\) | ||||
−0.165074 | + | 0.986281i | \(0.552786\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.03189 | 0.109618 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.6812 | 0.457893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0188 | 0.577653 | 0.288826 | − | 0.957381i | \(-0.406735\pi\) | ||||
0.288826 | + | 0.957381i | \(0.406735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.49031 | −0.305771 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.3488 | 1.09157 | 0.545786 | − | 0.837925i | \(-0.316231\pi\) | ||||
0.545786 | + | 0.837925i | \(0.316231\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.60771 | 0.201435 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.95607 | 0.141741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.5908 | −0.915712 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −34.9241 | −1.24809 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.6444 | 0.915288 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9886 | 1.21156 | 0.605781 | − | 0.795631i | \(-0.292861\pi\) | ||||
0.605781 | + | 0.795631i | \(0.292861\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.1517 | 0.859823 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.01185 | −0.320020 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.7997 | −0.985954 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.5444 | 1.57784 | 0.788922 | − | 0.614494i | \(-0.210640\pi\) | ||||
0.788922 | + | 0.614494i | \(0.210640\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.4457 | 0.369543 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.276269 | 0.00976148 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.5894 | 1.07948 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.9004 | −0.806131 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.8608 | −0.944376 | −0.472188 | − | 0.881498i | \(-0.656536\pi\) | ||||
−0.472188 | + | 0.881498i | \(0.656536\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.5647 | 1.35419 | 0.677095 | − | 0.735896i | \(-0.263239\pi\) | ||||
0.677095 | + | 0.735896i | \(0.263239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.0007 | −0.736526 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.0130 | 0.946224 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.73404 | −0.165623 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.8147 | −0.970741 | −0.485370 | − | 0.874309i | \(-0.661315\pi\) | ||||
−0.485370 | + | 0.874309i | \(0.661315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.7746 | −0.793872 | −0.396936 | − | 0.917846i | \(-0.629927\pi\) | ||||
−0.396936 | + | 0.917846i | \(0.629927\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.22892 | 0.216863 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.6139 | 1.27319 | 0.636595 | − | 0.771198i | \(-0.280342\pi\) | ||||
0.636595 | + | 0.771198i | \(0.280342\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.6456 | 0.925440 | 0.462720 | − | 0.886504i | \(-0.346873\pi\) | ||||
0.462720 | + | 0.886504i | \(0.346873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.1703 | 0.907837 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.3003 | −0.840945 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.8087 | 0.580992 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.1618 | 0.488920 | 0.244460 | − | 0.969659i | \(-0.421389\pi\) | ||||
0.244460 | + | 0.969659i | \(0.421389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.48458 | 0.327054 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.9464 | 0.377015 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.6052 | −0.468033 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.9617 | 0.822363 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.00791271 | −0.000271244 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.6813 | 0.502677 | 0.251338 | − | 0.967899i | \(-0.419129\pi\) | ||||
0.251338 | + | 0.967899i | \(0.419129\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.54222 | −0.292138 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.60916 | −0.123287 | −0.0616433 | − | 0.998098i | \(-0.519634\pi\) | ||||
−0.0616433 | + | 0.998098i | \(0.519634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.9615 | −1.53407 | −0.767033 | − | 0.641607i | \(-0.778268\pi\) | ||||
−0.767033 | + | 0.641607i | \(0.778268\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.52948 | −0.290347 | −0.145173 | − | 0.989406i | \(-0.546374\pi\) | ||||
−0.145173 | + | 0.989406i | \(0.546374\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.7563 | 0.943744 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.0387 | −0.680548 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.38119 | 0.114699 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.3488 | −0.452308 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.74966 | −0.0592171 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.11893 | −0.274157 | −0.137078 | − | 0.990560i | \(-0.543771\pi\) | ||||
−0.137078 | + | 0.990560i | \(0.543771\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.94244 | 0.335350 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.5733 | 1.29957 | 0.649784 | − | 0.760119i | \(-0.274859\pi\) | ||||
0.649784 | + | 0.760119i | \(0.274859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.4122 | −1.25902 | −0.629510 | − | 0.776992i | \(-0.716744\pi\) | ||||
−0.629510 | + | 0.776992i | \(0.716744\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.9775 | −0.436233 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.1258 | 0.709333 | 0.354667 | − | 0.934993i | \(-0.384594\pi\) | ||||
0.354667 | + | 0.934993i | \(0.384594\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.55173 | 0.319995 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.4303 | −0.984848 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.9812 | −0.367061 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.124480 | 0.00415626 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.5223 | −0.617752 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.5687 | 0.551983 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.5951 | −0.917292 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.6698 | −0.653124 | −0.326562 | − | 0.945176i | \(-0.605890\pi\) | ||||
−0.326562 | + | 0.945176i | \(0.605890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.23169 | 0.273028 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.5069 | −1.07700 | −0.538501 | − | 0.842625i | \(-0.681009\pi\) | ||||
−0.538501 | + | 0.842625i | \(0.681009\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.9913 | −0.496140 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.22238 | 0.304882 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.7307 | 1.34358 | 0.671791 | − | 0.740741i | \(-0.265525\pi\) | ||||
0.671791 | + | 0.740741i | \(0.265525\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.0593 | 0.529171 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.6861 | −0.779637 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.366478 | −0.0120497 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.47228 | 0.278266 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.2903 | 0.403231 | 0.201616 | − | 0.979465i | \(-0.435381\pi\) | ||||
0.201616 | + | 0.979465i | \(0.435381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.6936 | 1.16856 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.17071 | 0.201804 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.2280 | −1.86956 | −0.934779 | − | 0.355229i | \(-0.884403\pi\) | ||||
−0.934779 | + | 0.355229i | \(0.884403\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.99129 | −0.0976172 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.96786 | 0.0967496 | 0.0483748 | − | 0.998829i | \(-0.484596\pi\) | ||||
0.0483748 | + | 0.998829i | \(0.484596\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0405520 | −0.00132055 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.66991 | 0.314230 | 0.157115 | − | 0.987580i | \(-0.449781\pi\) | ||||
0.157115 | + | 0.987580i | \(0.449781\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.3126 | 0.919067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.9515 | −1.23066 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.5269 | −0.470574 | −0.235287 | − | 0.971926i | \(-0.575603\pi\) | ||||
−0.235287 | + | 0.971926i | \(0.575603\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.70970 | −0.249480 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.5741 | −0.665067 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0854 | −0.712433 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.2665 | 0.459730 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.7988 | −0.862685 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.5318 | 1.39989 | 0.699944 | − | 0.714198i | \(-0.253208\pi\) | ||||
0.699944 | + | 0.714198i | \(0.253208\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.40675 | −0.237939 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.9986 | 0.705969 | 0.352985 | − | 0.935629i | \(-0.385167\pi\) | ||||
0.352985 | + | 0.935629i | \(0.385167\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.76529 | 0.184637 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.7930 | 0.473271 | 0.236636 | − | 0.971598i | \(-0.423955\pi\) | ||||
0.236636 | + | 0.971598i | \(0.423955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.562280 | 0.0179706 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.68936 | 0.0858646 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.5499 | −1.42092 | −0.710460 | − | 0.703738i | \(-0.751513\pi\) | ||||
−0.710460 | + | 0.703738i | \(0.751513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.66879 | −0.244348 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0485266 | 0.00154306 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.6446 | −0.560500 | −0.280250 | − | 0.959927i | \(-0.590417\pi\) | ||||
−0.280250 | + | 0.959927i | \(0.590417\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.65010 | 0.179301 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.43220 | 0.172212 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.7934 | 1.76699 | 0.883497 | − | 0.468437i | \(-0.155183\pi\) | ||||
0.883497 | + | 0.468437i | \(0.155183\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.09849 | −0.0347546 |
(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 | 8036.2.a.m.1.6 | 8 | ||
7.2 | even | 3 | 1148.2.i.d.165.3 | ✓ | 16 | ||
7.4 | even | 3 | 1148.2.i.d.821.3 | yes | 16 | ||
7.6 | odd | 2 | 8036.2.a.n.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.d.165.3 | ✓ | 16 | 7.2 | even | 3 | ||
1148.2.i.d.821.3 | yes | 16 | 7.4 | even | 3 | ||
8036.2.a.m.1.6 | 8 | 1.1 | even | 1 | trivial | ||
8036.2.a.n.1.3 | 8 | 7.6 | odd | 2 |