Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 42 x^{12} + 70 x^{11} + 680 x^{10} - 882 x^{9} - 5559 x^{8} + 5066 x^{7} + \cdots - 7083 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.04034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.04034 | 0.912466 | 0.456233 | − | 0.889860i | \(-0.349198\pi\) | ||||
0.456233 | + | 0.889860i | \(0.349198\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.45177 | 0.926683 | 0.463342 | − | 0.886180i | \(-0.346650\pi\) | ||||
0.463342 | + | 0.886180i | \(0.346650\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.04034 | 0.645211 | ||||||||
\(11\) | 0.203477 | 0.0613506 | 0.0306753 | − | 0.999529i | \(-0.490234\pi\) | ||||
0.0306753 | + | 0.999529i | \(0.490234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.95618 | 1.09725 | 0.548623 | − | 0.836070i | \(-0.315152\pi\) | ||||
0.548623 | + | 0.836070i | \(0.315152\pi\) | |||||||
\(14\) | 2.45177 | 0.655264 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.98757 | 0.724591 | 0.362296 | − | 0.932063i | \(-0.381993\pi\) | ||||
0.362296 | + | 0.932063i | \(0.381993\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.08465 | 1.39591 | 0.697957 | − | 0.716140i | \(-0.254093\pi\) | ||||
0.697957 | + | 0.716140i | \(0.254093\pi\) | |||||||
\(20\) | 2.04034 | 0.456233 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.203477 | 0.0433814 | ||||||||
\(23\) | −0.149808 | −0.0312372 | −0.0156186 | − | 0.999878i | \(-0.504972\pi\) | ||||
−0.0156186 | + | 0.999878i | \(0.504972\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.837025 | −0.167405 | ||||||||
\(26\) | 3.95618 | 0.775870 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.45177 | 0.463342 | ||||||||
\(29\) | 1.18201 | 0.219494 | 0.109747 | − | 0.993960i | \(-0.464996\pi\) | ||||
0.109747 | + | 0.993960i | \(0.464996\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.40369 | 0.252111 | 0.126055 | − | 0.992023i | \(-0.459768\pi\) | ||||
0.126055 | + | 0.992023i | \(0.459768\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.98757 | 0.512363 | ||||||||
\(35\) | 5.00245 | 0.845568 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.56672 | −0.586365 | −0.293182 | − | 0.956057i | \(-0.594714\pi\) | ||||
−0.293182 | + | 0.956057i | \(0.594714\pi\) | |||||||
\(38\) | 6.08465 | 0.987060 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.04034 | 0.322606 | ||||||||
\(41\) | −4.57686 | −0.714785 | −0.357393 | − | 0.933954i | \(-0.616334\pi\) | ||||
−0.357393 | + | 0.933954i | \(0.616334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1987 | 1.55528 | 0.777640 | − | 0.628709i | \(-0.216417\pi\) | ||||
0.777640 | + | 0.628709i | \(0.216417\pi\) | |||||||
\(44\) | 0.203477 | 0.0306753 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.149808 | −0.0220880 | ||||||||
\(47\) | −8.79796 | −1.28331 | −0.641657 | − | 0.766991i | \(-0.721753\pi\) | ||||
−0.641657 | + | 0.766991i | \(0.721753\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.988805 | −0.141258 | ||||||||
\(50\) | −0.837025 | −0.118373 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.95618 | 0.548623 | ||||||||
\(53\) | 8.68416 | 1.19286 | 0.596431 | − | 0.802664i | \(-0.296585\pi\) | ||||
0.596431 | + | 0.802664i | \(0.296585\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.415161 | 0.0559804 | ||||||||
\(56\) | 2.45177 | 0.327632 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.18201 | 0.155205 | ||||||||
\(59\) | −5.65615 | −0.736367 | −0.368184 | − | 0.929753i | \(-0.620020\pi\) | ||||
−0.368184 | + | 0.929753i | \(0.620020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.79078 | −1.12554 | −0.562772 | − | 0.826612i | \(-0.690265\pi\) | ||||
−0.562772 | + | 0.826612i | \(0.690265\pi\) | |||||||
\(62\) | 1.40369 | 0.178269 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.07193 | 1.00120 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.11318 | −0.135996 | −0.0679980 | − | 0.997685i | \(-0.521661\pi\) | ||||
−0.0679980 | + | 0.997685i | \(0.521661\pi\) | |||||||
\(68\) | 2.98757 | 0.362296 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.00245 | 0.597907 | ||||||||
\(71\) | −6.56830 | −0.779513 | −0.389757 | − | 0.920918i | \(-0.627441\pi\) | ||||
−0.389757 | + | 0.920918i | \(0.627441\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.7120 | 1.95599 | 0.977995 | − | 0.208629i | \(-0.0669000\pi\) | ||||
0.977995 | + | 0.208629i | \(0.0669000\pi\) | |||||||
\(74\) | −3.56672 | −0.414622 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.08465 | 0.697957 | ||||||||
\(77\) | 0.498879 | 0.0568526 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.54460 | −0.511307 | −0.255653 | − | 0.966768i | \(-0.582291\pi\) | ||||
−0.255653 | + | 0.966768i | \(0.582291\pi\) | |||||||
\(80\) | 2.04034 | 0.228117 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.57686 | −0.505429 | ||||||||
\(83\) | −2.21378 | −0.242994 | −0.121497 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121497 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.09564 | 0.661165 | ||||||||
\(86\) | 10.1987 | 1.09975 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.203477 | 0.0216907 | ||||||||
\(89\) | −10.6761 | −1.13166 | −0.565830 | − | 0.824522i | \(-0.691444\pi\) | ||||
−0.565830 | + | 0.824522i | \(0.691444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.69965 | 1.01680 | ||||||||
\(92\) | −0.149808 | −0.0156186 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.79796 | −0.907440 | ||||||||
\(95\) | 12.4147 | 1.27372 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.22556 | −0.835179 | −0.417590 | − | 0.908636i | \(-0.637125\pi\) | ||||
−0.417590 | + | 0.908636i | \(0.637125\pi\) | |||||||
\(98\) | −0.988805 | −0.0998844 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.837025 | −0.0837025 | ||||||||
\(101\) | −1.19588 | −0.118994 | −0.0594972 | − | 0.998228i | \(-0.518950\pi\) | ||||
−0.0594972 | + | 0.998228i | \(0.518950\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.95892 | −0.390084 | −0.195042 | − | 0.980795i | \(-0.562484\pi\) | ||||
−0.195042 | + | 0.980795i | \(0.562484\pi\) | |||||||
\(104\) | 3.95618 | 0.387935 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.68416 | 0.843481 | ||||||||
\(107\) | −5.27886 | −0.510326 | −0.255163 | − | 0.966898i | \(-0.582129\pi\) | ||||
−0.255163 | + | 0.966898i | \(0.582129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.5318 | −1.20033 | −0.600163 | − | 0.799878i | \(-0.704898\pi\) | ||||
−0.600163 | + | 0.799878i | \(0.704898\pi\) | |||||||
\(110\) | 0.415161 | 0.0395841 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.45177 | 0.231671 | ||||||||
\(113\) | 5.30005 | 0.498587 | 0.249293 | − | 0.968428i | \(-0.419802\pi\) | ||||
0.249293 | + | 0.968428i | \(0.419802\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.305659 | −0.0285029 | ||||||||
\(116\) | 1.18201 | 0.109747 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.65615 | −0.520690 | ||||||||
\(119\) | 7.32484 | 0.671467 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9586 | −0.996236 | ||||||||
\(122\) | −8.79078 | −0.795880 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.40369 | 0.126055 | ||||||||
\(125\) | −11.9095 | −1.06522 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.45202 | 0.395053 | 0.197526 | − | 0.980298i | \(-0.436709\pi\) | ||||
0.197526 | + | 0.980298i | \(0.436709\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.07193 | 0.707955 | ||||||||
\(131\) | −12.2984 | −1.07451 | −0.537256 | − | 0.843419i | \(-0.680539\pi\) | ||||
−0.537256 | + | 0.843419i | \(0.680539\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.9182 | 1.29357 | ||||||||
\(134\) | −1.11318 | −0.0961637 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.98757 | 0.256182 | ||||||||
\(137\) | 18.7145 | 1.59889 | 0.799445 | − | 0.600740i | \(-0.205127\pi\) | ||||
0.799445 | + | 0.600740i | \(0.205127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.98547 | −0.677319 | −0.338659 | − | 0.940909i | \(-0.609973\pi\) | ||||
−0.338659 | + | 0.940909i | \(0.609973\pi\) | |||||||
\(140\) | 5.00245 | 0.422784 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.56830 | −0.551199 | ||||||||
\(143\) | 0.804990 | 0.0673167 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.41170 | 0.200281 | ||||||||
\(146\) | 16.7120 | 1.38309 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.56672 | −0.293182 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5737 | 1.02324 | 0.511619 | − | 0.859213i | \(-0.329046\pi\) | ||||
0.511619 | + | 0.859213i | \(0.329046\pi\) | |||||||
\(152\) | 6.08465 | 0.493530 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.498879 | 0.0402008 | ||||||||
\(155\) | 2.86401 | 0.230043 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.13867 | 0.569728 | 0.284864 | − | 0.958568i | \(-0.408052\pi\) | ||||
0.284864 | + | 0.958568i | \(0.408052\pi\) | |||||||
\(158\) | −4.54460 | −0.361549 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.04034 | 0.161303 | ||||||||
\(161\) | −0.367296 | −0.0289470 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.08015 | 0.0846039 | 0.0423019 | − | 0.999105i | \(-0.486531\pi\) | ||||
0.0423019 | + | 0.999105i | \(0.486531\pi\) | |||||||
\(164\) | −4.57686 | −0.357393 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.21378 | −0.171823 | ||||||||
\(167\) | 17.8060 | 1.37787 | 0.688936 | − | 0.724822i | \(-0.258078\pi\) | ||||
0.688936 | + | 0.724822i | \(0.258078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.65133 | 0.203948 | ||||||||
\(170\) | 6.09564 | 0.467514 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.1987 | 0.777640 | ||||||||
\(173\) | 18.3462 | 1.39484 | 0.697419 | − | 0.716664i | \(-0.254332\pi\) | ||||
0.697419 | + | 0.716664i | \(0.254332\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.05219 | −0.155131 | ||||||||
\(176\) | 0.203477 | 0.0153376 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.6761 | −0.800205 | ||||||||
\(179\) | −16.2742 | −1.21639 | −0.608194 | − | 0.793788i | \(-0.708106\pi\) | ||||
−0.608194 | + | 0.793788i | \(0.708106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.27919 | 0.466729 | 0.233364 | − | 0.972389i | \(-0.425027\pi\) | ||||
0.233364 | + | 0.972389i | \(0.425027\pi\) | |||||||
\(182\) | 9.69965 | 0.718986 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.149808 | −0.0110440 | ||||||||
\(185\) | −7.27730 | −0.535038 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.607901 | 0.0444541 | ||||||||
\(188\) | −8.79796 | −0.641657 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.4147 | 0.900660 | ||||||||
\(191\) | −15.9069 | −1.15099 | −0.575493 | − | 0.817807i | \(-0.695190\pi\) | ||||
−0.575493 | + | 0.817807i | \(0.695190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.9415 | −1.07552 | −0.537758 | − | 0.843099i | \(-0.680729\pi\) | ||||
−0.537758 | + | 0.843099i | \(0.680729\pi\) | |||||||
\(194\) | −8.22556 | −0.590561 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.988805 | −0.0706289 | ||||||||
\(197\) | −6.88235 | −0.490347 | −0.245174 | − | 0.969479i | \(-0.578845\pi\) | ||||
−0.245174 | + | 0.969479i | \(0.578845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.62978 | −0.611749 | −0.305875 | − | 0.952072i | \(-0.598949\pi\) | ||||
−0.305875 | + | 0.952072i | \(0.598949\pi\) | |||||||
\(200\) | −0.837025 | −0.0591866 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.19588 | −0.0841418 | ||||||||
\(203\) | 2.89802 | 0.203401 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.33833 | −0.652217 | ||||||||
\(206\) | −3.95892 | −0.275831 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.95618 | 0.274311 | ||||||||
\(209\) | 1.23809 | 0.0856402 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9484 | 0.822564 | 0.411282 | − | 0.911508i | \(-0.365081\pi\) | ||||
0.411282 | + | 0.911508i | \(0.365081\pi\) | |||||||
\(212\) | 8.68416 | 0.596431 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.27886 | −0.360855 | ||||||||
\(215\) | 20.8087 | 1.41914 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.44154 | 0.233627 | ||||||||
\(218\) | −12.5318 | −0.848759 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.415161 | 0.0279902 | ||||||||
\(221\) | 11.8193 | 0.795055 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.3096 | 1.09217 | 0.546087 | − | 0.837729i | \(-0.316117\pi\) | ||||
0.546087 | + | 0.837729i | \(0.316117\pi\) | |||||||
\(224\) | 2.45177 | 0.163816 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.30005 | 0.352554 | ||||||||
\(227\) | −25.9668 | −1.72348 | −0.861739 | − | 0.507352i | \(-0.830624\pi\) | ||||
−0.861739 | + | 0.507352i | \(0.830624\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.1880 | −1.13581 | −0.567907 | − | 0.823093i | \(-0.692247\pi\) | ||||
−0.567907 | + | 0.823093i | \(0.692247\pi\) | |||||||
\(230\) | −0.305659 | −0.0201546 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.18201 | 0.0776027 | ||||||||
\(233\) | 11.7241 | 0.768070 | 0.384035 | − | 0.923319i | \(-0.374534\pi\) | ||||
0.384035 | + | 0.923319i | \(0.374534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.9508 | −1.17098 | ||||||||
\(236\) | −5.65615 | −0.368184 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.32484 | 0.474799 | ||||||||
\(239\) | 11.3448 | 0.733833 | 0.366917 | − | 0.930254i | \(-0.380413\pi\) | ||||
0.366917 | + | 0.930254i | \(0.380413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.7772 | 0.823054 | 0.411527 | − | 0.911398i | \(-0.364996\pi\) | ||||
0.411527 | + | 0.911398i | \(0.364996\pi\) | |||||||
\(242\) | −10.9586 | −0.704445 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.79078 | −0.562772 | ||||||||
\(245\) | −2.01749 | −0.128893 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.0719 | 1.53166 | ||||||||
\(248\) | 1.40369 | 0.0891346 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.9095 | −0.753223 | ||||||||
\(251\) | 20.9749 | 1.32392 | 0.661961 | − | 0.749538i | \(-0.269724\pi\) | ||||
0.661961 | + | 0.749538i | \(0.269724\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0304825 | −0.00191642 | ||||||||
\(254\) | 4.45202 | 0.279344 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.1377 | −0.632373 | −0.316186 | − | 0.948697i | \(-0.602402\pi\) | ||||
−0.316186 | + | 0.948697i | \(0.602402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.74478 | −0.543374 | ||||||||
\(260\) | 8.07193 | 0.500600 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.2984 | −0.759795 | ||||||||
\(263\) | 2.00396 | 0.123569 | 0.0617847 | − | 0.998090i | \(-0.480321\pi\) | ||||
0.0617847 | + | 0.998090i | \(0.480321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.7186 | 1.08845 | ||||||||
\(266\) | 14.9182 | 0.914693 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.11318 | −0.0679980 | ||||||||
\(269\) | −1.93175 | −0.117781 | −0.0588904 | − | 0.998264i | \(-0.518756\pi\) | ||||
−0.0588904 | + | 0.998264i | \(0.518756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0451 | 1.46064 | 0.730318 | − | 0.683108i | \(-0.239372\pi\) | ||||
0.730318 | + | 0.683108i | \(0.239372\pi\) | |||||||
\(272\) | 2.98757 | 0.181148 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.7145 | 1.13059 | ||||||||
\(275\) | −0.170315 | −0.0102704 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0962 | 0.666706 | 0.333353 | − | 0.942802i | \(-0.391820\pi\) | ||||
0.333353 | + | 0.942802i | \(0.391820\pi\) | |||||||
\(278\) | −7.98547 | −0.478937 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.00245 | 0.298953 | ||||||||
\(281\) | −16.2571 | −0.969819 | −0.484909 | − | 0.874564i | \(-0.661147\pi\) | ||||
−0.484909 | + | 0.874564i | \(0.661147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.215180 | 0.0127911 | 0.00639555 | − | 0.999980i | \(-0.497964\pi\) | ||||
0.00639555 | + | 0.999980i | \(0.497964\pi\) | |||||||
\(284\) | −6.56830 | −0.389757 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.804990 | 0.0476001 | ||||||||
\(287\) | −11.2214 | −0.662379 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.07445 | −0.474967 | ||||||||
\(290\) | 2.41170 | 0.141620 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.7120 | 0.977995 | ||||||||
\(293\) | −17.9241 | −1.04714 | −0.523570 | − | 0.851983i | \(-0.675400\pi\) | ||||
−0.523570 | + | 0.851983i | \(0.675400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.5404 | −0.671911 | ||||||||
\(296\) | −3.56672 | −0.207311 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −0.592667 | −0.0342748 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.0048 | 1.44125 | ||||||||
\(302\) | 12.5737 | 0.723538 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.08465 | 0.348979 | ||||||||
\(305\) | −17.9362 | −1.02702 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.70157 | 0.496625 | 0.248312 | − | 0.968680i | \(-0.420124\pi\) | ||||
0.248312 | + | 0.968680i | \(0.420124\pi\) | |||||||
\(308\) | 0.498879 | 0.0284263 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.86401 | 0.162665 | ||||||||
\(311\) | 5.96807 | 0.338418 | 0.169209 | − | 0.985580i | \(-0.445879\pi\) | ||||
0.169209 | + | 0.985580i | \(0.445879\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.0096 | 0.678821 | 0.339410 | − | 0.940638i | \(-0.389772\pi\) | ||||
0.339410 | + | 0.940638i | \(0.389772\pi\) | |||||||
\(314\) | 7.13867 | 0.402858 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.54460 | −0.255653 | ||||||||
\(317\) | −9.00626 | −0.505842 | −0.252921 | − | 0.967487i | \(-0.581391\pi\) | ||||
−0.252921 | + | 0.967487i | \(0.581391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.240512 | 0.0134661 | ||||||||
\(320\) | 2.04034 | 0.114058 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.367296 | −0.0204686 | ||||||||
\(323\) | 18.1783 | 1.01147 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.31142 | −0.183684 | ||||||||
\(326\) | 1.08015 | 0.0598240 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.57686 | −0.252715 | ||||||||
\(329\) | −21.5706 | −1.18923 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.9340 | −1.20560 | −0.602802 | − | 0.797891i | \(-0.705949\pi\) | ||||
−0.602802 | + | 0.797891i | \(0.705949\pi\) | |||||||
\(332\) | −2.21378 | −0.121497 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.8060 | 0.974303 | ||||||||
\(335\) | −2.27125 | −0.124092 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.33234 | 0.344944 | 0.172472 | − | 0.985014i | \(-0.444824\pi\) | ||||
0.172472 | + | 0.985014i | \(0.444824\pi\) | |||||||
\(338\) | 2.65133 | 0.144213 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.09564 | 0.330583 | ||||||||
\(341\) | 0.285619 | 0.0154671 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5867 | −1.05758 | ||||||||
\(344\) | 10.1987 | 0.549875 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.3462 | 0.986299 | ||||||||
\(347\) | −17.8450 | −0.957969 | −0.478984 | − | 0.877823i | \(-0.658995\pi\) | ||||
−0.478984 | + | 0.877823i | \(0.658995\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.18716 | 0.224134 | 0.112067 | − | 0.993701i | \(-0.464253\pi\) | ||||
0.112067 | + | 0.993701i | \(0.464253\pi\) | |||||||
\(350\) | −2.05219 | −0.109694 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.203477 | 0.0108454 | ||||||||
\(353\) | −13.9825 | −0.744214 | −0.372107 | − | 0.928190i | \(-0.621365\pi\) | ||||
−0.372107 | + | 0.928190i | \(0.621365\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.4015 | −0.711280 | ||||||||
\(356\) | −10.6761 | −0.565830 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.2742 | −0.860116 | ||||||||
\(359\) | −3.55787 | −0.187777 | −0.0938886 | − | 0.995583i | \(-0.529930\pi\) | ||||
−0.0938886 | + | 0.995583i | \(0.529930\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0230 | 0.948576 | ||||||||
\(362\) | 6.27919 | 0.330027 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.69965 | 0.508400 | ||||||||
\(365\) | 34.0981 | 1.78478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0206 | 1.46267 | 0.731333 | − | 0.682021i | \(-0.238899\pi\) | ||||
0.731333 | + | 0.682021i | \(0.238899\pi\) | |||||||
\(368\) | −0.149808 | −0.00780929 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.27730 | −0.378329 | ||||||||
\(371\) | 21.2916 | 1.10541 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.6903 | −1.33020 | −0.665098 | − | 0.746756i | \(-0.731610\pi\) | ||||
−0.665098 | + | 0.746756i | \(0.731610\pi\) | |||||||
\(374\) | 0.607901 | 0.0314338 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.79796 | −0.453720 | ||||||||
\(377\) | 4.67624 | 0.240838 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.3594 | 1.40536 | 0.702679 | − | 0.711507i | \(-0.251987\pi\) | ||||
0.702679 | + | 0.711507i | \(0.251987\pi\) | |||||||
\(380\) | 12.4147 | 0.636862 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.9069 | −0.813870 | ||||||||
\(383\) | 23.6995 | 1.21099 | 0.605493 | − | 0.795851i | \(-0.292976\pi\) | ||||
0.605493 | + | 0.795851i | \(0.292976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.01788 | 0.0518761 | ||||||||
\(386\) | −14.9415 | −0.760504 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.22556 | −0.417590 | ||||||||
\(389\) | 12.0397 | 0.610435 | 0.305217 | − | 0.952283i | \(-0.401271\pi\) | ||||
0.305217 | + | 0.952283i | \(0.401271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.447562 | −0.0226342 | ||||||||
\(392\) | −0.988805 | −0.0499422 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.88235 | −0.346728 | ||||||||
\(395\) | −9.27251 | −0.466550 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.93861 | −0.398428 | −0.199214 | − | 0.979956i | \(-0.563839\pi\) | ||||
−0.199214 | + | 0.979956i | \(0.563839\pi\) | |||||||
\(398\) | −8.62978 | −0.432572 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.837025 | −0.0418512 | ||||||||
\(401\) | 20.3167 | 1.01457 | 0.507285 | − | 0.861779i | \(-0.330649\pi\) | ||||
0.507285 | + | 0.861779i | \(0.330649\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.55326 | 0.276628 | ||||||||
\(404\) | −1.19588 | −0.0594972 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.89802 | 0.143826 | ||||||||
\(407\) | −0.725744 | −0.0359738 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.10081 | −0.0544318 | −0.0272159 | − | 0.999630i | \(-0.508664\pi\) | ||||
−0.0272159 | + | 0.999630i | \(0.508664\pi\) | |||||||
\(410\) | −9.33833 | −0.461187 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.95892 | −0.195042 | ||||||||
\(413\) | −13.8676 | −0.682380 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.51685 | −0.221724 | ||||||||
\(416\) | 3.95618 | 0.193967 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.23809 | 0.0605567 | ||||||||
\(419\) | −10.2288 | −0.499710 | −0.249855 | − | 0.968283i | \(-0.580383\pi\) | ||||
−0.249855 | + | 0.968283i | \(0.580383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.7435 | −0.816028 | −0.408014 | − | 0.912976i | \(-0.633779\pi\) | ||||
−0.408014 | + | 0.912976i | \(0.633779\pi\) | |||||||
\(422\) | 11.9484 | 0.581640 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.68416 | 0.421740 | ||||||||
\(425\) | −2.50067 | −0.121300 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.5530 | −1.04302 | ||||||||
\(428\) | −5.27886 | −0.255163 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.8087 | 1.00348 | ||||||||
\(431\) | −24.2430 | −1.16774 | −0.583871 | − | 0.811846i | \(-0.698463\pi\) | ||||
−0.583871 | + | 0.811846i | \(0.698463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.4417 | 1.31877 | 0.659383 | − | 0.751807i | \(-0.270818\pi\) | ||||
0.659383 | + | 0.751807i | \(0.270818\pi\) | |||||||
\(434\) | 3.44154 | 0.165199 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.5318 | −0.600163 | ||||||||
\(437\) | −0.911530 | −0.0436044 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7342 | 1.03732 | 0.518658 | − | 0.854982i | \(-0.326432\pi\) | ||||
0.518658 | + | 0.854982i | \(0.326432\pi\) | |||||||
\(440\) | 0.415161 | 0.0197920 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.8193 | 0.562189 | ||||||||
\(443\) | −12.5322 | −0.595424 | −0.297712 | − | 0.954656i | \(-0.596224\pi\) | ||||
−0.297712 | + | 0.954656i | \(0.596224\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.7828 | −1.03260 | ||||||||
\(446\) | 16.3096 | 0.772283 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.45177 | 0.115835 | ||||||||
\(449\) | −18.9161 | −0.892704 | −0.446352 | − | 0.894857i | \(-0.647277\pi\) | ||||
−0.446352 | + | 0.894857i | \(0.647277\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.931285 | −0.0438525 | ||||||||
\(452\) | 5.30005 | 0.249293 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −25.9668 | −1.21868 | ||||||||
\(455\) | 19.7906 | 0.927795 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.15610 | −0.381526 | −0.190763 | − | 0.981636i | \(-0.561096\pi\) | ||||
−0.190763 | + | 0.981636i | \(0.561096\pi\) | |||||||
\(458\) | −17.1880 | −0.803142 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.305659 | −0.0142514 | ||||||||
\(461\) | −16.2395 | −0.756351 | −0.378176 | − | 0.925734i | \(-0.623448\pi\) | ||||
−0.378176 | + | 0.925734i | \(0.623448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.8238 | 0.688922 | 0.344461 | − | 0.938801i | \(-0.388062\pi\) | ||||
0.344461 | + | 0.938801i | \(0.388062\pi\) | |||||||
\(464\) | 1.18201 | 0.0548734 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.7241 | 0.543107 | ||||||||
\(467\) | 15.7271 | 0.727766 | 0.363883 | − | 0.931445i | \(-0.381451\pi\) | ||||
0.363883 | + | 0.931445i | \(0.381451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.72926 | −0.126025 | ||||||||
\(470\) | −17.9508 | −0.828009 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.65615 | −0.260345 | ||||||||
\(473\) | 2.07519 | 0.0954174 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.09300 | −0.233683 | ||||||||
\(476\) | 7.32484 | 0.335733 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.3448 | 0.518899 | ||||||||
\(479\) | −23.6260 | −1.07950 | −0.539749 | − | 0.841826i | \(-0.681481\pi\) | ||||
−0.539749 | + | 0.841826i | \(0.681481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.1106 | −0.643386 | ||||||||
\(482\) | 12.7772 | 0.581987 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9586 | −0.498118 | ||||||||
\(485\) | −16.7829 | −0.762073 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.8503 | 1.44328 | 0.721638 | − | 0.692271i | \(-0.243389\pi\) | ||||
0.721638 | + | 0.692271i | \(0.243389\pi\) | |||||||
\(488\) | −8.79078 | −0.397940 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.01749 | −0.0911411 | ||||||||
\(491\) | −8.22229 | −0.371067 | −0.185533 | − | 0.982638i | \(-0.559401\pi\) | ||||
−0.185533 | + | 0.982638i | \(0.559401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.53133 | 0.159043 | ||||||||
\(494\) | 24.0719 | 1.08305 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.40369 | 0.0630277 | ||||||||
\(497\) | −16.1040 | −0.722362 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.4260 | 1.54112 | 0.770560 | − | 0.637367i | \(-0.219976\pi\) | ||||
0.770560 | + | 0.637367i | \(0.219976\pi\) | |||||||
\(500\) | −11.9095 | −0.532609 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.9749 | 0.936155 | ||||||||
\(503\) | −7.44402 | −0.331913 | −0.165956 | − | 0.986133i | \(-0.553071\pi\) | ||||
−0.165956 | + | 0.986133i | \(0.553071\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.44000 | −0.108578 | ||||||||
\(506\) | −0.0304825 | −0.00135511 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.45202 | 0.197526 | ||||||||
\(509\) | −23.1214 | −1.02484 | −0.512418 | − | 0.858736i | \(-0.671250\pi\) | ||||
−0.512418 | + | 0.858736i | \(0.671250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.9740 | 1.81258 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.1377 | −0.447155 | ||||||||
\(515\) | −8.07753 | −0.355939 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.79018 | −0.0787321 | ||||||||
\(518\) | −8.74478 | −0.384224 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.07193 | 0.353978 | ||||||||
\(521\) | −8.90428 | −0.390104 | −0.195052 | − | 0.980793i | \(-0.562487\pi\) | ||||
−0.195052 | + | 0.980793i | \(0.562487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.7942 | 0.778084 | 0.389042 | − | 0.921220i | \(-0.372806\pi\) | ||||
0.389042 | + | 0.921220i | \(0.372806\pi\) | |||||||
\(524\) | −12.2984 | −0.537256 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00396 | 0.0873767 | ||||||||
\(527\) | 4.19363 | 0.182677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9776 | −0.999024 | ||||||||
\(530\) | 17.7186 | 0.769648 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.9182 | 0.646785 | ||||||||
\(533\) | −18.1069 | −0.784295 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.7706 | −0.465656 | ||||||||
\(536\) | −1.11318 | −0.0480819 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.93175 | −0.0832836 | ||||||||
\(539\) | −0.201199 | −0.00866625 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.335476 | −0.0144232 | −0.00721161 | − | 0.999974i | \(-0.502296\pi\) | ||||
−0.00721161 | + | 0.999974i | \(0.502296\pi\) | |||||||
\(542\) | 24.0451 | 1.03283 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.98757 | 0.128091 | ||||||||
\(545\) | −25.5690 | −1.09526 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.81996 | −0.120573 | −0.0602864 | − | 0.998181i | \(-0.519201\pi\) | ||||
−0.0602864 | + | 0.998181i | \(0.519201\pi\) | |||||||
\(548\) | 18.7145 | 0.799445 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.170315 | −0.00726226 | ||||||||
\(551\) | 7.19211 | 0.306394 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1423 | −0.473820 | ||||||||
\(554\) | 11.0962 | 0.471432 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.98547 | −0.338659 | ||||||||
\(557\) | −17.2759 | −0.732004 | −0.366002 | − | 0.930614i | \(-0.619274\pi\) | ||||
−0.366002 | + | 0.930614i | \(0.619274\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.3477 | 1.70653 | ||||||||
\(560\) | 5.00245 | 0.211392 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.2571 | −0.685766 | ||||||||
\(563\) | 23.2936 | 0.981709 | 0.490854 | − | 0.871242i | \(-0.336685\pi\) | ||||
0.490854 | + | 0.871242i | \(0.336685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.8139 | 0.454944 | ||||||||
\(566\) | 0.215180 | 0.00904468 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.56830 | −0.275600 | ||||||||
\(569\) | 5.17932 | 0.217129 | 0.108564 | − | 0.994089i | \(-0.465375\pi\) | ||||
0.108564 | + | 0.994089i | \(0.465375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.3418 | −1.68825 | −0.844126 | − | 0.536145i | \(-0.819880\pi\) | ||||
−0.844126 | + | 0.536145i | \(0.819880\pi\) | |||||||
\(572\) | 0.804990 | 0.0336583 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.2214 | −0.468373 | ||||||||
\(575\) | 0.125393 | 0.00522925 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.0244 | 1.79113 | 0.895564 | − | 0.444932i | \(-0.146772\pi\) | ||||
0.895564 | + | 0.444932i | \(0.146772\pi\) | |||||||
\(578\) | −8.07445 | −0.335853 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.41170 | 0.100140 | ||||||||
\(581\) | −5.42768 | −0.225178 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.76703 | 0.0731828 | ||||||||
\(584\) | 16.7120 | 0.691547 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.9241 | −0.740439 | ||||||||
\(587\) | −35.9418 | −1.48348 | −0.741738 | − | 0.670689i | \(-0.765998\pi\) | ||||
−0.741738 | + | 0.670689i | \(0.765998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.54098 | 0.351925 | ||||||||
\(590\) | −11.5404 | −0.475113 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.56672 | −0.146591 | ||||||||
\(593\) | −8.28724 | −0.340316 | −0.170158 | − | 0.985417i | \(-0.554428\pi\) | ||||
−0.170158 | + | 0.985417i | \(0.554428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9451 | 0.612691 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.592667 | −0.0242360 | ||||||||
\(599\) | 38.7266 | 1.58233 | 0.791164 | − | 0.611605i | \(-0.209476\pi\) | ||||
0.791164 | + | 0.611605i | \(0.209476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0216 | 0.857490 | 0.428745 | − | 0.903426i | \(-0.358956\pi\) | ||||
0.428745 | + | 0.903426i | \(0.358956\pi\) | |||||||
\(602\) | 25.0048 | 1.01912 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.5737 | 0.511619 | ||||||||
\(605\) | −22.3592 | −0.909032 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.91848 | −0.280812 | −0.140406 | − | 0.990094i | \(-0.544841\pi\) | ||||
−0.140406 | + | 0.990094i | \(0.544841\pi\) | |||||||
\(608\) | 6.08465 | 0.246765 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.9362 | −0.726214 | ||||||||
\(611\) | −34.8063 | −1.40811 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.1798 | −0.693885 | −0.346943 | − | 0.937886i | \(-0.612780\pi\) | ||||
−0.346943 | + | 0.937886i | \(0.612780\pi\) | |||||||
\(614\) | 8.70157 | 0.351167 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.498879 | 0.0201004 | ||||||||
\(617\) | 29.4917 | 1.18729 | 0.593646 | − | 0.804726i | \(-0.297688\pi\) | ||||
0.593646 | + | 0.804726i | \(0.297688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8981 | 0.799772 | 0.399886 | − | 0.916565i | \(-0.369050\pi\) | ||||
0.399886 | + | 0.916565i | \(0.369050\pi\) | |||||||
\(620\) | 2.86401 | 0.115021 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.96807 | 0.239298 | ||||||||
\(623\) | −26.1753 | −1.04869 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.1143 | −0.804571 | ||||||||
\(626\) | 12.0096 | 0.479999 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.13867 | 0.284864 | ||||||||
\(629\) | −10.6558 | −0.424875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8054 | 1.42539 | 0.712696 | − | 0.701473i | \(-0.247474\pi\) | ||||
0.712696 | + | 0.701473i | \(0.247474\pi\) | |||||||
\(632\) | −4.54460 | −0.180774 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.00626 | −0.357684 | ||||||||
\(635\) | 9.08362 | 0.360472 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.91189 | −0.154995 | ||||||||
\(638\) | 0.240512 | 0.00952194 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.04034 | 0.0806514 | ||||||||
\(641\) | −23.1561 | −0.914611 | −0.457305 | − | 0.889310i | \(-0.651185\pi\) | ||||
−0.457305 | + | 0.889310i | \(0.651185\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.9119 | 0.469761 | 0.234880 | − | 0.972024i | \(-0.424530\pi\) | ||||
0.234880 | + | 0.972024i | \(0.424530\pi\) | |||||||
\(644\) | −0.367296 | −0.0144735 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.1783 | 0.715215 | ||||||||
\(647\) | −0.801674 | −0.0315171 | −0.0157585 | − | 0.999876i | \(-0.505016\pi\) | ||||
−0.0157585 | + | 0.999876i | \(0.505016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.15089 | −0.0451766 | ||||||||
\(650\) | −3.31142 | −0.129884 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.08015 | 0.0423019 | ||||||||
\(653\) | −14.6278 | −0.572431 | −0.286215 | − | 0.958165i | \(-0.592397\pi\) | ||||
−0.286215 | + | 0.958165i | \(0.592397\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.0928 | −0.980456 | ||||||||
\(656\) | −4.57686 | −0.178696 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −21.5706 | −0.840910 | ||||||||
\(659\) | 36.8855 | 1.43686 | 0.718428 | − | 0.695601i | \(-0.244862\pi\) | ||||
0.718428 | + | 0.695601i | \(0.244862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.83682 | −0.188130 | −0.0940652 | − | 0.995566i | \(-0.529986\pi\) | ||||
−0.0940652 | + | 0.995566i | \(0.529986\pi\) | |||||||
\(662\) | −21.9340 | −0.852491 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.21378 | −0.0859113 | ||||||||
\(665\) | 30.4381 | 1.18034 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.177075 | −0.00685636 | ||||||||
\(668\) | 17.8060 | 0.688936 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.27125 | −0.0877462 | ||||||||
\(671\) | −1.78872 | −0.0690528 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.43783 | −0.0554245 | −0.0277122 | − | 0.999616i | \(-0.508822\pi\) | ||||
−0.0277122 | + | 0.999616i | \(0.508822\pi\) | |||||||
\(674\) | 6.33234 | 0.243913 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.65133 | 0.101974 | ||||||||
\(677\) | 51.4167 | 1.97610 | 0.988052 | − | 0.154123i | \(-0.0492552\pi\) | ||||
0.988052 | + | 0.154123i | \(0.0492552\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.1672 | −0.773947 | ||||||||
\(680\) | 6.09564 | 0.233757 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.285619 | 0.0109369 | ||||||||
\(683\) | 36.2412 | 1.38673 | 0.693365 | − | 0.720586i | \(-0.256127\pi\) | ||||
0.693365 | + | 0.720586i | \(0.256127\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.1839 | 1.45893 | ||||||||
\(686\) | −19.5867 | −0.747825 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.1987 | 0.388820 | ||||||||
\(689\) | 34.3561 | 1.30886 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.2663 | 0.428589 | 0.214294 | − | 0.976769i | \(-0.431255\pi\) | ||||
0.214294 | + | 0.976769i | \(0.431255\pi\) | |||||||
\(692\) | 18.3462 | 0.697419 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.8450 | −0.677386 | ||||||||
\(695\) | −16.2931 | −0.618031 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.6737 | −0.517927 | ||||||||
\(698\) | 4.18716 | 0.158486 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.05219 | −0.0775657 | ||||||||
\(701\) | −22.6248 | −0.854526 | −0.427263 | − | 0.904127i | \(-0.640522\pi\) | ||||
−0.427263 | + | 0.904127i | \(0.640522\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.7022 | −0.818515 | ||||||||
\(704\) | 0.203477 | 0.00766882 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.9825 | −0.526239 | ||||||||
\(707\) | −2.93203 | −0.110270 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.7184 | 0.890763 | 0.445381 | − | 0.895341i | \(-0.353068\pi\) | ||||
0.445381 | + | 0.895341i | \(0.353068\pi\) | |||||||
\(710\) | −13.4015 | −0.502951 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.6761 | −0.400102 | ||||||||
\(713\) | −0.210285 | −0.00787523 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.64245 | 0.0614242 | ||||||||
\(716\) | −16.2742 | −0.608194 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.55787 | −0.132778 | ||||||||
\(719\) | −7.15270 | −0.266751 | −0.133375 | − | 0.991066i | \(-0.542582\pi\) | ||||
−0.133375 | + | 0.991066i | \(0.542582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.70638 | −0.361485 | ||||||||
\(722\) | 18.0230 | 0.670745 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.27919 | 0.233364 | ||||||||
\(725\) | −0.989371 | −0.0367443 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.45384 | −0.350623 | −0.175312 | − | 0.984513i | \(-0.556093\pi\) | ||||
−0.175312 | + | 0.984513i | \(0.556093\pi\) | |||||||
\(728\) | 9.69965 | 0.359493 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 34.0981 | 1.26203 | ||||||||
\(731\) | 30.4692 | 1.12694 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.1192 | −1.03860 | −0.519302 | − | 0.854591i | \(-0.673808\pi\) | ||||
−0.519302 | + | 0.854591i | \(0.673808\pi\) | |||||||
\(734\) | 28.0206 | 1.03426 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.149808 | −0.00552200 | ||||||||
\(737\) | −0.226506 | −0.00834344 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.7960 | 1.61106 | 0.805532 | − | 0.592553i | \(-0.201880\pi\) | ||||
0.805532 | + | 0.592553i | \(0.201880\pi\) | |||||||
\(740\) | −7.27730 | −0.267519 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.2916 | 0.781639 | ||||||||
\(743\) | −37.3780 | −1.37126 | −0.685632 | − | 0.727948i | \(-0.740474\pi\) | ||||
−0.685632 | + | 0.727948i | \(0.740474\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.04034 | 0.0747522 | ||||||||
\(746\) | −25.6903 | −0.940590 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.607901 | 0.0222270 | ||||||||
\(749\) | −12.9426 | −0.472911 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4139 | −0.452989 | −0.226495 | − | 0.974012i | \(-0.572727\pi\) | ||||
−0.226495 | + | 0.974012i | \(0.572727\pi\) | |||||||
\(752\) | −8.79796 | −0.320829 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.67624 | 0.170298 | ||||||||
\(755\) | 25.6547 | 0.933670 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.7545 | −0.827028 | −0.413514 | − | 0.910498i | \(-0.635699\pi\) | ||||
−0.413514 | + | 0.910498i | \(0.635699\pi\) | |||||||
\(758\) | 27.3594 | 0.993738 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.4147 | 0.450330 | ||||||||
\(761\) | −32.3320 | −1.17204 | −0.586018 | − | 0.810298i | \(-0.699305\pi\) | ||||
−0.586018 | + | 0.810298i | \(0.699305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.7251 | −1.11232 | ||||||||
\(764\) | −15.9069 | −0.575493 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.6995 | 0.856296 | ||||||||
\(767\) | −22.3767 | −0.807976 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.9719 | −0.648083 | −0.324041 | − | 0.946043i | \(-0.605042\pi\) | ||||
−0.324041 | + | 0.946043i | \(0.605042\pi\) | |||||||
\(770\) | 1.01788 | 0.0366819 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.9415 | −0.537758 | ||||||||
\(773\) | −8.22939 | −0.295990 | −0.147995 | − | 0.988988i | \(-0.547282\pi\) | ||||
−0.147995 | + | 0.988988i | \(0.547282\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.17493 | −0.0422046 | ||||||||
\(776\) | −8.22556 | −0.295281 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.0397 | 0.431642 | ||||||||
\(779\) | −27.8486 | −0.997779 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.33650 | −0.0478236 | ||||||||
\(782\) | −0.447562 | −0.0160048 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.988805 | −0.0353145 | ||||||||
\(785\) | 14.5653 | 0.519857 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.8243 | 1.31264 | 0.656322 | − | 0.754481i | \(-0.272111\pi\) | ||||
0.656322 | + | 0.754481i | \(0.272111\pi\) | |||||||
\(788\) | −6.88235 | −0.245174 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.27251 | −0.329901 | ||||||||
\(791\) | 12.9945 | 0.462032 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.7779 | −1.23500 | ||||||||
\(794\) | −7.93861 | −0.281731 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.62978 | −0.305875 | ||||||||
\(797\) | 45.4961 | 1.61156 | 0.805778 | − | 0.592217i | \(-0.201747\pi\) | ||||
0.805778 | + | 0.592217i | \(0.201747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.2845 | −0.929879 | ||||||||
\(800\) | −0.837025 | −0.0295933 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.3167 | 0.717409 | ||||||||
\(803\) | 3.40050 | 0.120001 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.749407 | −0.0264131 | ||||||||
\(806\) | 5.55326 | 0.195605 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.19588 | −0.0420709 | ||||||||
\(809\) | 42.0253 | 1.47753 | 0.738766 | − | 0.673962i | \(-0.235409\pi\) | ||||
0.738766 | + | 0.673962i | \(0.235409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.5255 | 1.17724 | 0.588619 | − | 0.808411i | \(-0.299672\pi\) | ||||
0.588619 | + | 0.808411i | \(0.299672\pi\) | |||||||
\(812\) | 2.89802 | 0.101701 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.725744 | −0.0254373 | ||||||||
\(815\) | 2.20387 | 0.0771982 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 62.0552 | 2.17104 | ||||||||
\(818\) | −1.10081 | −0.0384891 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.33833 | −0.326109 | ||||||||
\(821\) | −10.1280 | −0.353470 | −0.176735 | − | 0.984258i | \(-0.556554\pi\) | ||||
−0.176735 | + | 0.984258i | \(0.556554\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.5274 | 1.20355 | 0.601775 | − | 0.798666i | \(-0.294461\pi\) | ||||
0.601775 | + | 0.798666i | \(0.294461\pi\) | |||||||
\(824\) | −3.95892 | −0.137916 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.8676 | −0.482515 | ||||||||
\(827\) | 12.0445 | 0.418827 | 0.209414 | − | 0.977827i | \(-0.432845\pi\) | ||||
0.209414 | + | 0.977827i | \(0.432845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.4078 | 0.778257 | 0.389128 | − | 0.921184i | \(-0.372776\pi\) | ||||
0.389128 | + | 0.921184i | \(0.372776\pi\) | |||||||
\(830\) | −4.51685 | −0.156782 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.95618 | 0.137156 | ||||||||
\(833\) | −2.95412 | −0.102354 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.3303 | 1.25726 | ||||||||
\(836\) | 1.23809 | 0.0428201 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.2288 | −0.353348 | ||||||||
\(839\) | −34.9694 | −1.20728 | −0.603640 | − | 0.797257i | \(-0.706283\pi\) | ||||
−0.603640 | + | 0.797257i | \(0.706283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6029 | −0.951823 | ||||||||
\(842\) | −16.7435 | −0.577019 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.9484 | 0.411282 | ||||||||
\(845\) | 5.40961 | 0.186096 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.8680 | −0.923195 | ||||||||
\(848\) | 8.68416 | 0.298215 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.50067 | −0.0857721 | ||||||||
\(851\) | 0.534323 | 0.0183164 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.7366 | 1.49751 | 0.748756 | − | 0.662846i | \(-0.230652\pi\) | ||||
0.748756 | + | 0.662846i | \(0.230652\pi\) | |||||||
\(854\) | −21.5530 | −0.737529 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.27886 | −0.180428 | ||||||||
\(857\) | 47.8442 | 1.63433 | 0.817163 | − | 0.576407i | \(-0.195546\pi\) | ||||
0.817163 | + | 0.576407i | \(0.195546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.60137 | 0.293475 | 0.146737 | − | 0.989175i | \(-0.453123\pi\) | ||||
0.146737 | + | 0.989175i | \(0.453123\pi\) | |||||||
\(860\) | 20.8087 | 0.709571 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.2430 | −0.825719 | ||||||||
\(863\) | −19.0673 | −0.649059 | −0.324529 | − | 0.945876i | \(-0.605206\pi\) | ||||
−0.324529 | + | 0.945876i | \(0.605206\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.4325 | 1.27274 | ||||||||
\(866\) | 27.4417 | 0.932509 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.44154 | 0.116813 | ||||||||
\(869\) | −0.924720 | −0.0313690 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.40392 | −0.149221 | ||||||||
\(872\) | −12.5318 | −0.424379 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.911530 | −0.0308330 | ||||||||
\(875\) | −29.1994 | −0.987120 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.2798 | −0.988708 | −0.494354 | − | 0.869261i | \(-0.664595\pi\) | ||||
−0.494354 | + | 0.869261i | \(0.664595\pi\) | |||||||
\(878\) | 21.7342 | 0.733494 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.415161 | 0.0139951 | ||||||||
\(881\) | −15.2528 | −0.513881 | −0.256940 | − | 0.966427i | \(-0.582714\pi\) | ||||
−0.256940 | + | 0.966427i | \(0.582714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4516 | −0.755557 | −0.377778 | − | 0.925896i | \(-0.623312\pi\) | ||||
−0.377778 | + | 0.925896i | \(0.623312\pi\) | |||||||
\(884\) | 11.8193 | 0.397527 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.5322 | −0.421028 | ||||||||
\(887\) | −19.7620 | −0.663544 | −0.331772 | − | 0.943360i | \(-0.607647\pi\) | ||||
−0.331772 | + | 0.943360i | \(0.607647\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9153 | 0.366089 | ||||||||
\(890\) | −21.7828 | −0.730160 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.3096 | 0.546087 | ||||||||
\(893\) | −53.5325 | −1.79140 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.2048 | −1.10991 | ||||||||
\(896\) | 2.45177 | 0.0819080 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.9161 | −0.631237 | ||||||||
\(899\) | 1.65918 | 0.0553367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.9445 | 0.864337 | ||||||||
\(902\) | −0.931285 | −0.0310084 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.30005 | 0.176277 | ||||||||
\(905\) | 12.8117 | 0.425874 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.9011 | −1.55733 | −0.778663 | − | 0.627443i | \(-0.784102\pi\) | ||||
−0.778663 | + | 0.627443i | \(0.784102\pi\) | |||||||
\(908\) | −25.9668 | −0.861739 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 19.7906 | 0.656050 | ||||||||
\(911\) | −32.7025 | −1.08348 | −0.541742 | − | 0.840545i | \(-0.682235\pi\) | ||||
−0.541742 | + | 0.840545i | \(0.682235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.450453 | −0.0149078 | ||||||||
\(914\) | −8.15610 | −0.269780 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.1880 | −0.567907 | ||||||||
\(917\) | −30.1528 | −0.995732 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.93251 | 0.195696 | 0.0978478 | − | 0.995201i | \(-0.468804\pi\) | ||||
0.0978478 | + | 0.995201i | \(0.468804\pi\) | |||||||
\(920\) | −0.305659 | −0.0100773 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.2395 | −0.534821 | ||||||||
\(923\) | −25.9853 | −0.855318 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.98543 | 0.0981603 | ||||||||
\(926\) | 14.8238 | 0.487141 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.18201 | 0.0388013 | ||||||||
\(929\) | −4.38637 | −0.143912 | −0.0719560 | − | 0.997408i | \(-0.522924\pi\) | ||||
−0.0719560 | + | 0.997408i | \(0.522924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.01653 | −0.197184 | ||||||||
\(932\) | 11.7241 | 0.384035 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.7271 | 0.514608 | ||||||||
\(935\) | 1.24032 | 0.0405629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.8270 | −0.745726 | −0.372863 | − | 0.927886i | \(-0.621624\pi\) | ||||
−0.372863 | + | 0.927886i | \(0.621624\pi\) | |||||||
\(938\) | −2.72926 | −0.0891133 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.9508 | −0.585491 | ||||||||
\(941\) | 13.3308 | 0.434571 | 0.217285 | − | 0.976108i | \(-0.430280\pi\) | ||||
0.217285 | + | 0.976108i | \(0.430280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.685651 | 0.0223279 | ||||||||
\(944\) | −5.65615 | −0.184092 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.07519 | 0.0674703 | ||||||||
\(947\) | −51.2535 | −1.66552 | −0.832758 | − | 0.553637i | \(-0.813239\pi\) | ||||
−0.832758 | + | 0.553637i | \(0.813239\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 66.1156 | 2.14620 | ||||||||
\(950\) | −5.09300 | −0.165239 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.32484 | 0.237399 | ||||||||
\(953\) | −1.57768 | −0.0511061 | −0.0255531 | − | 0.999673i | \(-0.508135\pi\) | ||||
−0.0255531 | + | 0.999673i | \(0.508135\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.4555 | −1.05024 | ||||||||
\(956\) | 11.3448 | 0.366917 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.6260 | −0.763320 | ||||||||
\(959\) | 45.8838 | 1.48166 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0296 | −0.936440 | ||||||||
\(962\) | −14.1106 | −0.454943 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.7772 | 0.411527 | ||||||||
\(965\) | −30.4858 | −0.981372 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.8568 | −0.992287 | −0.496143 | − | 0.868241i | \(-0.665251\pi\) | ||||
−0.496143 | + | 0.868241i | \(0.665251\pi\) | |||||||
\(968\) | −10.9586 | −0.352223 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.7829 | −0.538867 | ||||||||
\(971\) | 30.6296 | 0.982952 | 0.491476 | − | 0.870891i | \(-0.336458\pi\) | ||||
0.491476 | + | 0.870891i | \(0.336458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.5786 | −0.627660 | ||||||||
\(974\) | 31.8503 | 1.02055 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.79078 | −0.281386 | ||||||||
\(977\) | 19.6525 | 0.628738 | 0.314369 | − | 0.949301i | \(-0.398207\pi\) | ||||
0.314369 | + | 0.949301i | \(0.398207\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.17233 | −0.0694280 | ||||||||
\(980\) | −2.01749 | −0.0644465 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.22229 | −0.262384 | ||||||||
\(983\) | −27.1718 | −0.866646 | −0.433323 | − | 0.901239i | \(-0.642659\pi\) | ||||
−0.433323 | + | 0.901239i | \(0.642659\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.0423 | −0.447425 | ||||||||
\(986\) | 3.53133 | 0.112460 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.0719 | 0.765831 | ||||||||
\(989\) | −1.52784 | −0.0485825 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.8356 | 1.26542 | 0.632711 | − | 0.774388i | \(-0.281942\pi\) | ||||
0.632711 | + | 0.774388i | \(0.281942\pi\) | |||||||
\(992\) | 1.40369 | 0.0445673 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.1040 | −0.510787 | ||||||||
\(995\) | −17.6077 | −0.558201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.3388 | 0.644137 | 0.322068 | − | 0.946716i | \(-0.395622\pi\) | ||||
0.322068 | + | 0.946716i | \(0.395622\pi\) | |||||||
\(998\) | 34.4260 | 1.08974 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.r.1.10 | yes | 14 | |
3.2 | odd | 2 | 8046.2.a.q.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.q.1.5 | ✓ | 14 | 3.2 | odd | 2 | ||
8046.2.a.r.1.10 | yes | 14 | 1.1 | even | 1 | trivial |