Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.19898000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.935683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | −0.935683 | −0.540217 | −0.270109 | − | 0.962830i | \(-0.587060\pi\) | ||||
−0.270109 | + | 0.962830i | \(0.587060\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.935683 | −0.381991 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.12450 | −0.708165 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.935683 | −0.270109 | ||||||||
\(13\) | 2.51397 | 0.697249 | 0.348625 | − | 0.937262i | \(-0.386649\pi\) | ||||
0.348625 | + | 0.937262i | \(0.386649\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.935683 | −0.241592 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.68602 | −1.13653 | −0.568263 | − | 0.822847i | \(-0.692384\pi\) | ||||
−0.568263 | + | 0.822847i | \(0.692384\pi\) | |||||||
\(18\) | −2.12450 | −0.500749 | ||||||||
\(19\) | −4.05554 | −0.930405 | −0.465203 | − | 0.885204i | \(-0.654018\pi\) | ||||
−0.465203 | + | 0.885204i | \(0.654018\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.935683 | 0.204183 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.46945 | −0.723431 | −0.361716 | − | 0.932289i | \(-0.617809\pi\) | ||||
−0.361716 | + | 0.932289i | \(0.617809\pi\) | |||||||
\(24\) | −0.935683 | −0.190996 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.51397 | 0.493030 | ||||||||
\(27\) | 4.79491 | 0.922780 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 7.46463 | 1.38615 | 0.693074 | − | 0.720867i | \(-0.256256\pi\) | ||||
0.693074 | + | 0.720867i | \(0.256256\pi\) | |||||||
\(30\) | −0.935683 | −0.170832 | ||||||||
\(31\) | 1.54591 | 0.277654 | 0.138827 | − | 0.990317i | \(-0.455667\pi\) | ||||
0.138827 | + | 0.990317i | \(0.455667\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.68602 | −0.803645 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.12450 | −0.354083 | ||||||||
\(37\) | −4.92622 | −0.809866 | −0.404933 | − | 0.914346i | \(-0.632705\pi\) | ||||
−0.404933 | + | 0.914346i | \(0.632705\pi\) | |||||||
\(38\) | −4.05554 | −0.657896 | ||||||||
\(39\) | −2.35228 | −0.376666 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.65079 | −0.257810 | −0.128905 | − | 0.991657i | \(-0.541146\pi\) | ||||
−0.128905 | + | 0.991657i | \(0.541146\pi\) | |||||||
\(42\) | 0.935683 | 0.144379 | ||||||||
\(43\) | 7.97092 | 1.21555 | 0.607777 | − | 0.794108i | \(-0.292061\pi\) | ||||
0.607777 | + | 0.794108i | \(0.292061\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.12450 | −0.316701 | ||||||||
\(46\) | −3.46945 | −0.511543 | ||||||||
\(47\) | 1.77448 | 0.258834 | 0.129417 | − | 0.991590i | \(-0.458689\pi\) | ||||
0.129417 | + | 0.991590i | \(0.458689\pi\) | |||||||
\(48\) | −0.935683 | −0.135054 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.38463 | 0.613971 | ||||||||
\(52\) | 2.51397 | 0.348625 | ||||||||
\(53\) | 7.14297 | 0.981162 | 0.490581 | − | 0.871395i | \(-0.336784\pi\) | ||||
0.490581 | + | 0.871395i | \(0.336784\pi\) | |||||||
\(54\) | 4.79491 | 0.652504 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 3.79470 | 0.502621 | ||||||||
\(58\) | 7.46463 | 0.980154 | ||||||||
\(59\) | −0.426837 | −0.0555694 | −0.0277847 | − | 0.999614i | \(-0.508845\pi\) | ||||
−0.0277847 | + | 0.999614i | \(0.508845\pi\) | |||||||
\(60\) | −0.935683 | −0.120796 | ||||||||
\(61\) | −6.15201 | −0.787684 | −0.393842 | − | 0.919178i | \(-0.628854\pi\) | ||||
−0.393842 | + | 0.919178i | \(0.628854\pi\) | |||||||
\(62\) | 1.54591 | 0.196331 | ||||||||
\(63\) | 2.12450 | 0.267661 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.51397 | 0.311819 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.99409 | −0.732295 | −0.366147 | − | 0.930557i | \(-0.619323\pi\) | ||||
−0.366147 | + | 0.930557i | \(0.619323\pi\) | |||||||
\(68\) | −4.68602 | −0.568263 | ||||||||
\(69\) | 3.24631 | 0.390810 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 6.53922 | 0.776063 | 0.388031 | − | 0.921646i | \(-0.373155\pi\) | ||||
0.388031 | + | 0.921646i | \(0.373155\pi\) | |||||||
\(72\) | −2.12450 | −0.250374 | ||||||||
\(73\) | 0.855372 | 0.100114 | 0.0500568 | − | 0.998746i | \(-0.484060\pi\) | ||||
0.0500568 | + | 0.998746i | \(0.484060\pi\) | |||||||
\(74\) | −4.92622 | −0.572662 | ||||||||
\(75\) | −0.935683 | −0.108043 | ||||||||
\(76\) | −4.05554 | −0.465203 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.35228 | −0.266343 | ||||||||
\(79\) | 9.86178 | 1.10954 | 0.554768 | − | 0.832005i | \(-0.312807\pi\) | ||||
0.554768 | + | 0.832005i | \(0.312807\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.88697 | 0.209664 | ||||||||
\(82\) | −1.65079 | −0.182300 | ||||||||
\(83\) | 8.15674 | 0.895319 | 0.447659 | − | 0.894204i | \(-0.352258\pi\) | ||||
0.447659 | + | 0.894204i | \(0.352258\pi\) | |||||||
\(84\) | 0.935683 | 0.102091 | ||||||||
\(85\) | −4.68602 | −0.508270 | ||||||||
\(86\) | 7.97092 | 0.859526 | ||||||||
\(87\) | −6.98453 | −0.748820 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00048 | 0.106051 | 0.0530255 | − | 0.998593i | \(-0.483114\pi\) | ||||
0.0530255 | + | 0.998593i | \(0.483114\pi\) | |||||||
\(90\) | −2.12450 | −0.223942 | ||||||||
\(91\) | −2.51397 | −0.263535 | ||||||||
\(92\) | −3.46945 | −0.361716 | ||||||||
\(93\) | −1.44649 | −0.149994 | ||||||||
\(94\) | 1.77448 | 0.183023 | ||||||||
\(95\) | −4.05554 | −0.416090 | ||||||||
\(96\) | −0.935683 | −0.0954978 | ||||||||
\(97\) | 11.3338 | 1.15078 | 0.575388 | − | 0.817880i | \(-0.304851\pi\) | ||||
0.575388 | + | 0.817880i | \(0.304851\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −3.16660 | −0.315088 | −0.157544 | − | 0.987512i | \(-0.550358\pi\) | ||||
−0.157544 | + | 0.987512i | \(0.550358\pi\) | |||||||
\(102\) | 4.38463 | 0.434143 | ||||||||
\(103\) | 15.0475 | 1.48267 | 0.741335 | − | 0.671135i | \(-0.234193\pi\) | ||||
0.741335 | + | 0.671135i | \(0.234193\pi\) | |||||||
\(104\) | 2.51397 | 0.246515 | ||||||||
\(105\) | 0.935683 | 0.0913134 | ||||||||
\(106\) | 7.14297 | 0.693787 | ||||||||
\(107\) | 14.4377 | 1.39574 | 0.697872 | − | 0.716222i | \(-0.254130\pi\) | ||||
0.697872 | + | 0.716222i | \(0.254130\pi\) | |||||||
\(108\) | 4.79491 | 0.461390 | ||||||||
\(109\) | 12.1869 | 1.16729 | 0.583646 | − | 0.812008i | \(-0.301626\pi\) | ||||
0.583646 | + | 0.812008i | \(0.301626\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.60938 | 0.437503 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −11.7294 | −1.10341 | −0.551706 | − | 0.834039i | \(-0.686023\pi\) | ||||
−0.551706 | + | 0.834039i | \(0.686023\pi\) | |||||||
\(114\) | 3.79470 | 0.355407 | ||||||||
\(115\) | −3.46945 | −0.323528 | ||||||||
\(116\) | 7.46463 | 0.693074 | ||||||||
\(117\) | −5.34092 | −0.493768 | ||||||||
\(118\) | −0.426837 | −0.0392935 | ||||||||
\(119\) | 4.68602 | 0.429567 | ||||||||
\(120\) | −0.935683 | −0.0854158 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −6.15201 | −0.556977 | ||||||||
\(123\) | 1.54462 | 0.139274 | ||||||||
\(124\) | 1.54591 | 0.138827 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.12450 | 0.189265 | ||||||||
\(127\) | −3.68316 | −0.326828 | −0.163414 | − | 0.986558i | \(-0.552251\pi\) | ||||
−0.163414 | + | 0.986558i | \(0.552251\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.45826 | −0.656663 | ||||||||
\(130\) | 2.51397 | 0.220490 | ||||||||
\(131\) | −8.57781 | −0.749447 | −0.374724 | − | 0.927137i | \(-0.622262\pi\) | ||||
−0.374724 | + | 0.927137i | \(0.622262\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.05554 | 0.351660 | ||||||||
\(134\) | −5.99409 | −0.517811 | ||||||||
\(135\) | 4.79491 | 0.412680 | ||||||||
\(136\) | −4.68602 | −0.401823 | ||||||||
\(137\) | 1.63086 | 0.139334 | 0.0696671 | − | 0.997570i | \(-0.477806\pi\) | ||||
0.0696671 | + | 0.997570i | \(0.477806\pi\) | |||||||
\(138\) | 3.24631 | 0.276344 | ||||||||
\(139\) | 23.1799 | 1.96609 | 0.983046 | − | 0.183360i | \(-0.0586974\pi\) | ||||
0.983046 | + | 0.183360i | \(0.0586974\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −1.66035 | −0.139827 | ||||||||
\(142\) | 6.53922 | 0.548759 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.12450 | −0.177041 | ||||||||
\(145\) | 7.46463 | 0.619904 | ||||||||
\(146\) | 0.855372 | 0.0707911 | ||||||||
\(147\) | −0.935683 | −0.0771739 | ||||||||
\(148\) | −4.92622 | −0.404933 | ||||||||
\(149\) | 1.43386 | 0.117466 | 0.0587332 | − | 0.998274i | \(-0.481294\pi\) | ||||
0.0587332 | + | 0.998274i | \(0.481294\pi\) | |||||||
\(150\) | −0.935683 | −0.0763982 | ||||||||
\(151\) | −17.7952 | −1.44815 | −0.724075 | − | 0.689722i | \(-0.757733\pi\) | ||||
−0.724075 | + | 0.689722i | \(0.757733\pi\) | |||||||
\(152\) | −4.05554 | −0.328948 | ||||||||
\(153\) | 9.95543 | 0.804849 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.54591 | 0.124171 | ||||||||
\(156\) | −2.35228 | −0.188333 | ||||||||
\(157\) | −7.29144 | −0.581920 | −0.290960 | − | 0.956735i | \(-0.593975\pi\) | ||||
−0.290960 | + | 0.956735i | \(0.593975\pi\) | |||||||
\(158\) | 9.86178 | 0.784561 | ||||||||
\(159\) | −6.68356 | −0.530041 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 3.46945 | 0.273431 | ||||||||
\(162\) | 1.88697 | 0.148255 | ||||||||
\(163\) | 9.41304 | 0.737286 | 0.368643 | − | 0.929571i | \(-0.379822\pi\) | ||||
0.368643 | + | 0.929571i | \(0.379822\pi\) | |||||||
\(164\) | −1.65079 | −0.128905 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.15674 | 0.633086 | ||||||||
\(167\) | 0.289918 | 0.0224345 | 0.0112173 | − | 0.999937i | \(-0.496429\pi\) | ||||
0.0112173 | + | 0.999937i | \(0.496429\pi\) | |||||||
\(168\) | 0.935683 | 0.0721895 | ||||||||
\(169\) | −6.67997 | −0.513844 | ||||||||
\(170\) | −4.68602 | −0.359401 | ||||||||
\(171\) | 8.61598 | 0.658881 | ||||||||
\(172\) | 7.97092 | 0.607777 | ||||||||
\(173\) | 10.4188 | 0.792126 | 0.396063 | − | 0.918223i | \(-0.370376\pi\) | ||||
0.396063 | + | 0.918223i | \(0.370376\pi\) | |||||||
\(174\) | −6.98453 | −0.529496 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.399384 | 0.0300196 | ||||||||
\(178\) | 1.00048 | 0.0749893 | ||||||||
\(179\) | −14.9115 | −1.11454 | −0.557270 | − | 0.830331i | \(-0.688151\pi\) | ||||
−0.557270 | + | 0.830331i | \(0.688151\pi\) | |||||||
\(180\) | −2.12450 | −0.158351 | ||||||||
\(181\) | 4.37330 | 0.325065 | 0.162533 | − | 0.986703i | \(-0.448034\pi\) | ||||
0.162533 | + | 0.986703i | \(0.448034\pi\) | |||||||
\(182\) | −2.51397 | −0.186348 | ||||||||
\(183\) | 5.75633 | 0.425520 | ||||||||
\(184\) | −3.46945 | −0.255772 | ||||||||
\(185\) | −4.92622 | −0.362183 | ||||||||
\(186\) | −1.44649 | −0.106062 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.77448 | 0.129417 | ||||||||
\(189\) | −4.79491 | −0.348778 | ||||||||
\(190\) | −4.05554 | −0.294220 | ||||||||
\(191\) | −10.6197 | −0.768416 | −0.384208 | − | 0.923246i | \(-0.625526\pi\) | ||||
−0.384208 | + | 0.923246i | \(0.625526\pi\) | |||||||
\(192\) | −0.935683 | −0.0675271 | ||||||||
\(193\) | −7.98145 | −0.574517 | −0.287259 | − | 0.957853i | \(-0.592744\pi\) | ||||
−0.287259 | + | 0.957853i | \(0.592744\pi\) | |||||||
\(194\) | 11.3338 | 0.813722 | ||||||||
\(195\) | −2.35228 | −0.168450 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 7.28621 | 0.519121 | 0.259560 | − | 0.965727i | \(-0.416422\pi\) | ||||
0.259560 | + | 0.965727i | \(0.416422\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.1853 | 1.00557 | 0.502783 | − | 0.864413i | \(-0.332309\pi\) | ||||
0.502783 | + | 0.864413i | \(0.332309\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 5.60857 | 0.395598 | ||||||||
\(202\) | −3.16660 | −0.222801 | ||||||||
\(203\) | −7.46463 | −0.523914 | ||||||||
\(204\) | 4.38463 | 0.306985 | ||||||||
\(205\) | −1.65079 | −0.115296 | ||||||||
\(206\) | 15.0475 | 1.04841 | ||||||||
\(207\) | 7.37084 | 0.512309 | ||||||||
\(208\) | 2.51397 | 0.174312 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.935683 | 0.0645683 | ||||||||
\(211\) | 23.2770 | 1.60246 | 0.801229 | − | 0.598358i | \(-0.204180\pi\) | ||||
0.801229 | + | 0.598358i | \(0.204180\pi\) | |||||||
\(212\) | 7.14297 | 0.490581 | ||||||||
\(213\) | −6.11864 | −0.419242 | ||||||||
\(214\) | 14.4377 | 0.986940 | ||||||||
\(215\) | 7.97092 | 0.543612 | ||||||||
\(216\) | 4.79491 | 0.326252 | ||||||||
\(217\) | −1.54591 | −0.104943 | ||||||||
\(218\) | 12.1869 | 0.825400 | ||||||||
\(219\) | −0.800357 | −0.0540831 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.7805 | −0.792442 | ||||||||
\(222\) | 4.60938 | 0.309362 | ||||||||
\(223\) | −8.09748 | −0.542248 | −0.271124 | − | 0.962544i | \(-0.587395\pi\) | ||||
−0.271124 | + | 0.962544i | \(0.587395\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.12450 | −0.141633 | ||||||||
\(226\) | −11.7294 | −0.780230 | ||||||||
\(227\) | 18.8354 | 1.25015 | 0.625074 | − | 0.780565i | \(-0.285069\pi\) | ||||
0.625074 | + | 0.780565i | \(0.285069\pi\) | |||||||
\(228\) | 3.79470 | 0.251310 | ||||||||
\(229\) | 10.8721 | 0.718451 | 0.359225 | − | 0.933251i | \(-0.383041\pi\) | ||||
0.359225 | + | 0.933251i | \(0.383041\pi\) | |||||||
\(230\) | −3.46945 | −0.228769 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.46463 | 0.490077 | ||||||||
\(233\) | 8.97639 | 0.588063 | 0.294031 | − | 0.955796i | \(-0.405003\pi\) | ||||
0.294031 | + | 0.955796i | \(0.405003\pi\) | |||||||
\(234\) | −5.34092 | −0.349147 | ||||||||
\(235\) | 1.77448 | 0.115754 | ||||||||
\(236\) | −0.426837 | −0.0277847 | ||||||||
\(237\) | −9.22750 | −0.599391 | ||||||||
\(238\) | 4.68602 | 0.303749 | ||||||||
\(239\) | 9.78125 | 0.632696 | 0.316348 | − | 0.948643i | \(-0.397543\pi\) | ||||
0.316348 | + | 0.948643i | \(0.397543\pi\) | |||||||
\(240\) | −0.935683 | −0.0603981 | ||||||||
\(241\) | −23.3855 | −1.50639 | −0.753195 | − | 0.657797i | \(-0.771488\pi\) | ||||
−0.753195 | + | 0.657797i | \(0.771488\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1503 | −1.03604 | ||||||||
\(244\) | −6.15201 | −0.393842 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 1.54462 | 0.0984813 | ||||||||
\(247\) | −10.1955 | −0.648724 | ||||||||
\(248\) | 1.54591 | 0.0981656 | ||||||||
\(249\) | −7.63213 | −0.483666 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 26.0939 | 1.64703 | 0.823517 | − | 0.567291i | \(-0.192009\pi\) | ||||
0.823517 | + | 0.567291i | \(0.192009\pi\) | |||||||
\(252\) | 2.12450 | 0.133831 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.68316 | −0.231102 | ||||||||
\(255\) | 4.38463 | 0.274576 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.51935 | 0.344287 | 0.172144 | − | 0.985072i | \(-0.444931\pi\) | ||||
0.172144 | + | 0.985072i | \(0.444931\pi\) | |||||||
\(258\) | −7.45826 | −0.464331 | ||||||||
\(259\) | 4.92622 | 0.306101 | ||||||||
\(260\) | 2.51397 | 0.155910 | ||||||||
\(261\) | −15.8586 | −0.981622 | ||||||||
\(262\) | −8.57781 | −0.529939 | ||||||||
\(263\) | 27.1823 | 1.67613 | 0.838067 | − | 0.545568i | \(-0.183686\pi\) | ||||
0.838067 | + | 0.545568i | \(0.183686\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.14297 | 0.438789 | ||||||||
\(266\) | 4.05554 | 0.248661 | ||||||||
\(267\) | −0.936135 | −0.0572905 | ||||||||
\(268\) | −5.99409 | −0.366147 | ||||||||
\(269\) | −8.14480 | −0.496597 | −0.248299 | − | 0.968684i | \(-0.579871\pi\) | ||||
−0.248299 | + | 0.968684i | \(0.579871\pi\) | |||||||
\(270\) | 4.79491 | 0.291809 | ||||||||
\(271\) | 6.30590 | 0.383056 | 0.191528 | − | 0.981487i | \(-0.438656\pi\) | ||||
0.191528 | + | 0.981487i | \(0.438656\pi\) | |||||||
\(272\) | −4.68602 | −0.284132 | ||||||||
\(273\) | 2.35228 | 0.142366 | ||||||||
\(274\) | 1.63086 | 0.0985241 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.24631 | 0.195405 | ||||||||
\(277\) | 26.1396 | 1.57057 | 0.785287 | − | 0.619132i | \(-0.212515\pi\) | ||||
0.785287 | + | 0.619132i | \(0.212515\pi\) | |||||||
\(278\) | 23.1799 | 1.39024 | ||||||||
\(279\) | −3.28429 | −0.196625 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −14.7356 | −0.879055 | −0.439527 | − | 0.898229i | \(-0.644854\pi\) | ||||
−0.439527 | + | 0.898229i | \(0.644854\pi\) | |||||||
\(282\) | −1.66035 | −0.0988723 | ||||||||
\(283\) | −21.5060 | −1.27840 | −0.639199 | − | 0.769041i | \(-0.720734\pi\) | ||||
−0.639199 | + | 0.769041i | \(0.720734\pi\) | |||||||
\(284\) | 6.53922 | 0.388031 | ||||||||
\(285\) | 3.79470 | 0.224779 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.65079 | 0.0974432 | ||||||||
\(288\) | −2.12450 | −0.125187 | ||||||||
\(289\) | 4.95876 | 0.291692 | ||||||||
\(290\) | 7.46463 | 0.438338 | ||||||||
\(291\) | −10.6049 | −0.621669 | ||||||||
\(292\) | 0.855372 | 0.0500568 | ||||||||
\(293\) | 6.11604 | 0.357303 | 0.178651 | − | 0.983912i | \(-0.442827\pi\) | ||||
0.178651 | + | 0.983912i | \(0.442827\pi\) | |||||||
\(294\) | −0.935683 | −0.0545702 | ||||||||
\(295\) | −0.426837 | −0.0248514 | ||||||||
\(296\) | −4.92622 | −0.286331 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.43386 | 0.0830613 | ||||||||
\(299\) | −8.72209 | −0.504412 | ||||||||
\(300\) | −0.935683 | −0.0540217 | ||||||||
\(301\) | −7.97092 | −0.459436 | ||||||||
\(302\) | −17.7952 | −1.02400 | ||||||||
\(303\) | 2.96293 | 0.170216 | ||||||||
\(304\) | −4.05554 | −0.232601 | ||||||||
\(305\) | −6.15201 | −0.352263 | ||||||||
\(306\) | 9.95543 | 0.569114 | ||||||||
\(307\) | −24.8721 | −1.41952 | −0.709762 | − | 0.704441i | \(-0.751198\pi\) | ||||
−0.709762 | + | 0.704441i | \(0.751198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.0797 | −0.800963 | ||||||||
\(310\) | 1.54591 | 0.0878020 | ||||||||
\(311\) | 3.37946 | 0.191632 | 0.0958158 | − | 0.995399i | \(-0.469454\pi\) | ||||
0.0958158 | + | 0.995399i | \(0.469454\pi\) | |||||||
\(312\) | −2.35228 | −0.133172 | ||||||||
\(313\) | −20.7401 | −1.17230 | −0.586150 | − | 0.810203i | \(-0.699357\pi\) | ||||
−0.586150 | + | 0.810203i | \(0.699357\pi\) | |||||||
\(314\) | −7.29144 | −0.411480 | ||||||||
\(315\) | 2.12450 | 0.119702 | ||||||||
\(316\) | 9.86178 | 0.554768 | ||||||||
\(317\) | 7.46200 | 0.419108 | 0.209554 | − | 0.977797i | \(-0.432799\pi\) | ||||
0.209554 | + | 0.977797i | \(0.432799\pi\) | |||||||
\(318\) | −6.68356 | −0.374795 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −13.5091 | −0.754005 | ||||||||
\(322\) | 3.46945 | 0.193345 | ||||||||
\(323\) | 19.0043 | 1.05743 | ||||||||
\(324\) | 1.88697 | 0.104832 | ||||||||
\(325\) | 2.51397 | 0.139450 | ||||||||
\(326\) | 9.41304 | 0.521340 | ||||||||
\(327\) | −11.4031 | −0.630591 | ||||||||
\(328\) | −1.65079 | −0.0911498 | ||||||||
\(329\) | −1.77448 | −0.0978301 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.26702 | −0.454396 | −0.227198 | − | 0.973849i | \(-0.572956\pi\) | ||||
−0.227198 | + | 0.973849i | \(0.572956\pi\) | |||||||
\(332\) | 8.15674 | 0.447659 | ||||||||
\(333\) | 10.4657 | 0.573519 | ||||||||
\(334\) | 0.289918 | 0.0158636 | ||||||||
\(335\) | −5.99409 | −0.327492 | ||||||||
\(336\) | 0.935683 | 0.0510457 | ||||||||
\(337\) | −0.309107 | −0.0168381 | −0.00841906 | − | 0.999965i | \(-0.502680\pi\) | ||||
−0.00841906 | + | 0.999965i | \(0.502680\pi\) | |||||||
\(338\) | −6.67997 | −0.363342 | ||||||||
\(339\) | 10.9750 | 0.596082 | ||||||||
\(340\) | −4.68602 | −0.254135 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 8.61598 | 0.465899 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.97092 | 0.429763 | ||||||||
\(345\) | 3.24631 | 0.174775 | ||||||||
\(346\) | 10.4188 | 0.560118 | ||||||||
\(347\) | 6.12313 | 0.328707 | 0.164353 | − | 0.986402i | \(-0.447446\pi\) | ||||
0.164353 | + | 0.986402i | \(0.447446\pi\) | |||||||
\(348\) | −6.98453 | −0.374410 | ||||||||
\(349\) | −19.7838 | −1.05900 | −0.529501 | − | 0.848309i | \(-0.677621\pi\) | ||||
−0.529501 | + | 0.848309i | \(0.677621\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 12.0542 | 0.643408 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.8256 | −1.64068 | −0.820340 | − | 0.571876i | \(-0.806216\pi\) | ||||
−0.820340 | + | 0.571876i | \(0.806216\pi\) | |||||||
\(354\) | 0.399384 | 0.0212270 | ||||||||
\(355\) | 6.53922 | 0.347066 | ||||||||
\(356\) | 1.00048 | 0.0530255 | ||||||||
\(357\) | −4.38463 | −0.232059 | ||||||||
\(358\) | −14.9115 | −0.788099 | ||||||||
\(359\) | −25.2431 | −1.33228 | −0.666140 | − | 0.745827i | \(-0.732055\pi\) | ||||
−0.666140 | + | 0.745827i | \(0.732055\pi\) | |||||||
\(360\) | −2.12450 | −0.111971 | ||||||||
\(361\) | −2.55258 | −0.134347 | ||||||||
\(362\) | 4.37330 | 0.229856 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.51397 | −0.131768 | ||||||||
\(365\) | 0.855372 | 0.0447722 | ||||||||
\(366\) | 5.75633 | 0.300888 | ||||||||
\(367\) | −8.87025 | −0.463023 | −0.231512 | − | 0.972832i | \(-0.574367\pi\) | ||||
−0.231512 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(368\) | −3.46945 | −0.180858 | ||||||||
\(369\) | 3.50710 | 0.182572 | ||||||||
\(370\) | −4.92622 | −0.256102 | ||||||||
\(371\) | −7.14297 | −0.370845 | ||||||||
\(372\) | −1.44649 | −0.0749968 | ||||||||
\(373\) | 23.0860 | 1.19535 | 0.597675 | − | 0.801739i | \(-0.296091\pi\) | ||||
0.597675 | + | 0.801739i | \(0.296091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.935683 | −0.0483185 | ||||||||
\(376\) | 1.77448 | 0.0915116 | ||||||||
\(377\) | 18.7658 | 0.966490 | ||||||||
\(378\) | −4.79491 | −0.246623 | ||||||||
\(379\) | 31.6315 | 1.62480 | 0.812399 | − | 0.583101i | \(-0.198161\pi\) | ||||
0.812399 | + | 0.583101i | \(0.198161\pi\) | |||||||
\(380\) | −4.05554 | −0.208045 | ||||||||
\(381\) | 3.44627 | 0.176558 | ||||||||
\(382\) | −10.6197 | −0.543352 | ||||||||
\(383\) | 1.84985 | 0.0945228 | 0.0472614 | − | 0.998883i | \(-0.484951\pi\) | ||||
0.0472614 | + | 0.998883i | \(0.484951\pi\) | |||||||
\(384\) | −0.935683 | −0.0477489 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.98145 | −0.406245 | ||||||||
\(387\) | −16.9342 | −0.860813 | ||||||||
\(388\) | 11.3338 | 0.575388 | ||||||||
\(389\) | 15.6624 | 0.794116 | 0.397058 | − | 0.917793i | \(-0.370031\pi\) | ||||
0.397058 | + | 0.917793i | \(0.370031\pi\) | |||||||
\(390\) | −2.35228 | −0.119112 | ||||||||
\(391\) | 16.2579 | 0.822198 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 8.02612 | 0.404864 | ||||||||
\(394\) | 7.28621 | 0.367074 | ||||||||
\(395\) | 9.86178 | 0.496200 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.8207 | −0.743827 | −0.371914 | − | 0.928267i | \(-0.621298\pi\) | ||||
−0.371914 | + | 0.928267i | \(0.621298\pi\) | |||||||
\(398\) | 14.1853 | 0.711043 | ||||||||
\(399\) | −3.79470 | −0.189973 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 14.4322 | 0.720710 | 0.360355 | − | 0.932815i | \(-0.382656\pi\) | ||||
0.360355 | + | 0.932815i | \(0.382656\pi\) | |||||||
\(402\) | 5.60857 | 0.279730 | ||||||||
\(403\) | 3.88638 | 0.193594 | ||||||||
\(404\) | −3.16660 | −0.157544 | ||||||||
\(405\) | 1.88697 | 0.0937645 | ||||||||
\(406\) | −7.46463 | −0.370463 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.38463 | 0.217071 | ||||||||
\(409\) | 38.0339 | 1.88066 | 0.940328 | − | 0.340270i | \(-0.110518\pi\) | ||||
0.940328 | + | 0.340270i | \(0.110518\pi\) | |||||||
\(410\) | −1.65079 | −0.0815268 | ||||||||
\(411\) | −1.52597 | −0.0752707 | ||||||||
\(412\) | 15.0475 | 0.741335 | ||||||||
\(413\) | 0.426837 | 0.0210033 | ||||||||
\(414\) | 7.37084 | 0.362257 | ||||||||
\(415\) | 8.15674 | 0.400399 | ||||||||
\(416\) | 2.51397 | 0.123257 | ||||||||
\(417\) | −21.6890 | −1.06212 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.2138 | 1.18292 | 0.591460 | − | 0.806334i | \(-0.298552\pi\) | ||||
0.591460 | + | 0.806334i | \(0.298552\pi\) | |||||||
\(420\) | 0.935683 | 0.0456567 | ||||||||
\(421\) | 38.6678 | 1.88455 | 0.942276 | − | 0.334837i | \(-0.108681\pi\) | ||||
0.942276 | + | 0.334837i | \(0.108681\pi\) | |||||||
\(422\) | 23.2770 | 1.13311 | ||||||||
\(423\) | −3.76987 | −0.183297 | ||||||||
\(424\) | 7.14297 | 0.346893 | ||||||||
\(425\) | −4.68602 | −0.227305 | ||||||||
\(426\) | −6.11864 | −0.296449 | ||||||||
\(427\) | 6.15201 | 0.297717 | ||||||||
\(428\) | 14.4377 | 0.697872 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.97092 | 0.384392 | ||||||||
\(431\) | 23.6029 | 1.13691 | 0.568455 | − | 0.822714i | \(-0.307541\pi\) | ||||
0.568455 | + | 0.822714i | \(0.307541\pi\) | |||||||
\(432\) | 4.79491 | 0.230695 | ||||||||
\(433\) | −30.6532 | −1.47310 | −0.736550 | − | 0.676384i | \(-0.763546\pi\) | ||||
−0.736550 | + | 0.676384i | \(0.763546\pi\) | |||||||
\(434\) | −1.54591 | −0.0742062 | ||||||||
\(435\) | −6.98453 | −0.334883 | ||||||||
\(436\) | 12.1869 | 0.583646 | ||||||||
\(437\) | 14.0705 | 0.673084 | ||||||||
\(438\) | −0.800357 | −0.0382426 | ||||||||
\(439\) | −23.4152 | −1.11755 | −0.558774 | − | 0.829320i | \(-0.688728\pi\) | ||||
−0.558774 | + | 0.829320i | \(0.688728\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.12450 | −0.101166 | ||||||||
\(442\) | −11.7805 | −0.560341 | ||||||||
\(443\) | 0.833237 | 0.0395883 | 0.0197941 | − | 0.999804i | \(-0.493699\pi\) | ||||
0.0197941 | + | 0.999804i | \(0.493699\pi\) | |||||||
\(444\) | 4.60938 | 0.218752 | ||||||||
\(445\) | 1.00048 | 0.0474274 | ||||||||
\(446\) | −8.09748 | −0.383427 | ||||||||
\(447\) | −1.34164 | −0.0634573 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −5.98030 | −0.282228 | −0.141114 | − | 0.989993i | \(-0.545068\pi\) | ||||
−0.141114 | + | 0.989993i | \(0.545068\pi\) | |||||||
\(450\) | −2.12450 | −0.100150 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −11.7294 | −0.551706 | ||||||||
\(453\) | 16.6506 | 0.782315 | ||||||||
\(454\) | 18.8354 | 0.883989 | ||||||||
\(455\) | −2.51397 | −0.117857 | ||||||||
\(456\) | 3.79470 | 0.177703 | ||||||||
\(457\) | 41.9762 | 1.96356 | 0.981782 | − | 0.190010i | \(-0.0608519\pi\) | ||||
0.981782 | + | 0.190010i | \(0.0608519\pi\) | |||||||
\(458\) | 10.8721 | 0.508021 | ||||||||
\(459\) | −22.4690 | −1.04876 | ||||||||
\(460\) | −3.46945 | −0.161764 | ||||||||
\(461\) | 32.1474 | 1.49725 | 0.748626 | − | 0.662992i | \(-0.230714\pi\) | ||||
0.748626 | + | 0.662992i | \(0.230714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.14625 | −0.378588 | −0.189294 | − | 0.981920i | \(-0.560620\pi\) | ||||
−0.189294 | + | 0.981920i | \(0.560620\pi\) | |||||||
\(464\) | 7.46463 | 0.346537 | ||||||||
\(465\) | −1.44649 | −0.0670792 | ||||||||
\(466\) | 8.97639 | 0.415823 | ||||||||
\(467\) | 7.67994 | 0.355385 | 0.177693 | − | 0.984086i | \(-0.443137\pi\) | ||||
0.177693 | + | 0.984086i | \(0.443137\pi\) | |||||||
\(468\) | −5.34092 | −0.246884 | ||||||||
\(469\) | 5.99409 | 0.276781 | ||||||||
\(470\) | 1.77448 | 0.0818505 | ||||||||
\(471\) | 6.82248 | 0.314363 | ||||||||
\(472\) | −0.426837 | −0.0196468 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −9.22750 | −0.423833 | ||||||||
\(475\) | −4.05554 | −0.186081 | ||||||||
\(476\) | 4.68602 | 0.214783 | ||||||||
\(477\) | −15.1752 | −0.694825 | ||||||||
\(478\) | 9.78125 | 0.447384 | ||||||||
\(479\) | 22.7225 | 1.03822 | 0.519109 | − | 0.854708i | \(-0.326264\pi\) | ||||
0.519109 | + | 0.854708i | \(0.326264\pi\) | |||||||
\(480\) | −0.935683 | −0.0427079 | ||||||||
\(481\) | −12.3844 | −0.564678 | ||||||||
\(482\) | −23.3855 | −1.06518 | ||||||||
\(483\) | −3.24631 | −0.147712 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.3338 | 0.514643 | ||||||||
\(486\) | −16.1503 | −0.732594 | ||||||||
\(487\) | 33.4458 | 1.51557 | 0.757786 | − | 0.652503i | \(-0.226281\pi\) | ||||
0.757786 | + | 0.652503i | \(0.226281\pi\) | |||||||
\(488\) | −6.15201 | −0.278488 | ||||||||
\(489\) | −8.80763 | −0.398295 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −6.10991 | −0.275736 | −0.137868 | − | 0.990451i | \(-0.544025\pi\) | ||||
−0.137868 | + | 0.990451i | \(0.544025\pi\) | |||||||
\(492\) | 1.54462 | 0.0696368 | ||||||||
\(493\) | −34.9794 | −1.57539 | ||||||||
\(494\) | −10.1955 | −0.458717 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.54591 | 0.0694136 | ||||||||
\(497\) | −6.53922 | −0.293324 | ||||||||
\(498\) | −7.63213 | −0.342004 | ||||||||
\(499\) | 21.1193 | 0.945430 | 0.472715 | − | 0.881215i | \(-0.343274\pi\) | ||||
0.472715 | + | 0.881215i | \(0.343274\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −0.271271 | −0.0121195 | ||||||||
\(502\) | 26.0939 | 1.16463 | ||||||||
\(503\) | 25.5325 | 1.13844 | 0.569219 | − | 0.822186i | \(-0.307246\pi\) | ||||
0.569219 | + | 0.822186i | \(0.307246\pi\) | |||||||
\(504\) | 2.12450 | 0.0946326 | ||||||||
\(505\) | −3.16660 | −0.140912 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.25033 | 0.277587 | ||||||||
\(508\) | −3.68316 | −0.163414 | ||||||||
\(509\) | −22.0002 | −0.975144 | −0.487572 | − | 0.873083i | \(-0.662117\pi\) | ||||
−0.487572 | + | 0.873083i | \(0.662117\pi\) | |||||||
\(510\) | 4.38463 | 0.194155 | ||||||||
\(511\) | −0.855372 | −0.0378394 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −19.4459 | −0.858559 | ||||||||
\(514\) | 5.51935 | 0.243448 | ||||||||
\(515\) | 15.0475 | 0.663070 | ||||||||
\(516\) | −7.45826 | −0.328332 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.92622 | 0.216446 | ||||||||
\(519\) | −9.74870 | −0.427920 | ||||||||
\(520\) | 2.51397 | 0.110245 | ||||||||
\(521\) | −27.5451 | −1.20677 | −0.603387 | − | 0.797449i | \(-0.706182\pi\) | ||||
−0.603387 | + | 0.797449i | \(0.706182\pi\) | |||||||
\(522\) | −15.8586 | −0.694111 | ||||||||
\(523\) | −2.58863 | −0.113193 | −0.0565963 | − | 0.998397i | \(-0.518025\pi\) | ||||
−0.0565963 | + | 0.998397i | \(0.518025\pi\) | |||||||
\(524\) | −8.57781 | −0.374724 | ||||||||
\(525\) | 0.935683 | 0.0408366 | ||||||||
\(526\) | 27.1823 | 1.18521 | ||||||||
\(527\) | −7.24418 | −0.315561 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9629 | −0.476647 | ||||||||
\(530\) | 7.14297 | 0.310271 | ||||||||
\(531\) | 0.906814 | 0.0393524 | ||||||||
\(532\) | 4.05554 | 0.175830 | ||||||||
\(533\) | −4.15004 | −0.179758 | ||||||||
\(534\) | −0.936135 | −0.0405105 | ||||||||
\(535\) | 14.4377 | 0.624196 | ||||||||
\(536\) | −5.99409 | −0.258905 | ||||||||
\(537\) | 13.9525 | 0.602094 | ||||||||
\(538\) | −8.14480 | −0.351147 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.79491 | 0.206340 | ||||||||
\(541\) | −16.6493 | −0.715809 | −0.357905 | − | 0.933758i | \(-0.616509\pi\) | ||||
−0.357905 | + | 0.933758i | \(0.616509\pi\) | |||||||
\(542\) | 6.30590 | 0.270861 | ||||||||
\(543\) | −4.09203 | −0.175606 | ||||||||
\(544\) | −4.68602 | −0.200911 | ||||||||
\(545\) | 12.1869 | 0.522029 | ||||||||
\(546\) | 2.35228 | 0.100668 | ||||||||
\(547\) | 32.2258 | 1.37788 | 0.688938 | − | 0.724821i | \(-0.258077\pi\) | ||||
0.688938 | + | 0.724821i | \(0.258077\pi\) | |||||||
\(548\) | 1.63086 | 0.0696671 | ||||||||
\(549\) | 13.0699 | 0.557811 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.2731 | −1.28968 | ||||||||
\(552\) | 3.24631 | 0.138172 | ||||||||
\(553\) | −9.86178 | −0.419366 | ||||||||
\(554\) | 26.1396 | 1.11056 | ||||||||
\(555\) | 4.60938 | 0.195657 | ||||||||
\(556\) | 23.1799 | 0.983046 | ||||||||
\(557\) | 43.4129 | 1.83946 | 0.919732 | − | 0.392548i | \(-0.128406\pi\) | ||||
0.919732 | + | 0.392548i | \(0.128406\pi\) | |||||||
\(558\) | −3.28429 | −0.139035 | ||||||||
\(559\) | 20.0386 | 0.847544 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.7356 | −0.621586 | ||||||||
\(563\) | 12.0403 | 0.507437 | 0.253718 | − | 0.967278i | \(-0.418346\pi\) | ||||
0.253718 | + | 0.967278i | \(0.418346\pi\) | |||||||
\(564\) | −1.66035 | −0.0699133 | ||||||||
\(565\) | −11.7294 | −0.493461 | ||||||||
\(566\) | −21.5060 | −0.903964 | ||||||||
\(567\) | −1.88697 | −0.0792455 | ||||||||
\(568\) | 6.53922 | 0.274380 | ||||||||
\(569\) | 26.3405 | 1.10425 | 0.552126 | − | 0.833761i | \(-0.313817\pi\) | ||||
0.552126 | + | 0.833761i | \(0.313817\pi\) | |||||||
\(570\) | 3.79470 | 0.158943 | ||||||||
\(571\) | −22.2032 | −0.929176 | −0.464588 | − | 0.885527i | \(-0.653797\pi\) | ||||
−0.464588 | + | 0.885527i | \(0.653797\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.93670 | 0.415112 | ||||||||
\(574\) | 1.65079 | 0.0689027 | ||||||||
\(575\) | −3.46945 | −0.144686 | ||||||||
\(576\) | −2.12450 | −0.0885207 | ||||||||
\(577\) | 33.9425 | 1.41304 | 0.706522 | − | 0.707691i | \(-0.250263\pi\) | ||||
0.706522 | + | 0.707691i | \(0.250263\pi\) | |||||||
\(578\) | 4.95876 | 0.206257 | ||||||||
\(579\) | 7.46811 | 0.310364 | ||||||||
\(580\) | 7.46463 | 0.309952 | ||||||||
\(581\) | −8.15674 | −0.338399 | ||||||||
\(582\) | −10.6049 | −0.439587 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.855372 | 0.0353955 | ||||||||
\(585\) | −5.34092 | −0.220820 | ||||||||
\(586\) | 6.11604 | 0.252651 | ||||||||
\(587\) | −10.6550 | −0.439779 | −0.219889 | − | 0.975525i | \(-0.570570\pi\) | ||||
−0.219889 | + | 0.975525i | \(0.570570\pi\) | |||||||
\(588\) | −0.935683 | −0.0385869 | ||||||||
\(589\) | −6.26952 | −0.258331 | ||||||||
\(590\) | −0.426837 | −0.0175726 | ||||||||
\(591\) | −6.81758 | −0.280438 | ||||||||
\(592\) | −4.92622 | −0.202466 | ||||||||
\(593\) | −44.1567 | −1.81330 | −0.906649 | − | 0.421886i | \(-0.861368\pi\) | ||||
−0.906649 | + | 0.421886i | \(0.861368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.68602 | 0.192108 | ||||||||
\(596\) | 1.43386 | 0.0587332 | ||||||||
\(597\) | −13.2729 | −0.543224 | ||||||||
\(598\) | −8.72209 | −0.356673 | ||||||||
\(599\) | 25.7621 | 1.05261 | 0.526306 | − | 0.850295i | \(-0.323577\pi\) | ||||
0.526306 | + | 0.850295i | \(0.323577\pi\) | |||||||
\(600\) | −0.935683 | −0.0381991 | ||||||||
\(601\) | −48.8171 | −1.99129 | −0.995645 | − | 0.0932309i | \(-0.970281\pi\) | ||||
−0.995645 | + | 0.0932309i | \(0.970281\pi\) | |||||||
\(602\) | −7.97092 | −0.324870 | ||||||||
\(603\) | 12.7344 | 0.518586 | ||||||||
\(604\) | −17.7952 | −0.724075 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.96293 | 0.120361 | ||||||||
\(607\) | 23.4113 | 0.950237 | 0.475118 | − | 0.879922i | \(-0.342405\pi\) | ||||
0.475118 | + | 0.879922i | \(0.342405\pi\) | |||||||
\(608\) | −4.05554 | −0.164474 | ||||||||
\(609\) | 6.98453 | 0.283028 | ||||||||
\(610\) | −6.15201 | −0.249088 | ||||||||
\(611\) | 4.46098 | 0.180472 | ||||||||
\(612\) | 9.95543 | 0.402424 | ||||||||
\(613\) | 34.3936 | 1.38914 | 0.694572 | − | 0.719424i | \(-0.255594\pi\) | ||||
0.694572 | + | 0.719424i | \(0.255594\pi\) | |||||||
\(614\) | −24.8721 | −1.00376 | ||||||||
\(615\) | 1.54462 | 0.0622851 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.9149 | −1.36536 | −0.682681 | − | 0.730717i | \(-0.739186\pi\) | ||||
−0.682681 | + | 0.730717i | \(0.739186\pi\) | |||||||
\(618\) | −14.0797 | −0.566367 | ||||||||
\(619\) | −46.5283 | −1.87013 | −0.935066 | − | 0.354474i | \(-0.884660\pi\) | ||||
−0.935066 | + | 0.354474i | \(0.884660\pi\) | |||||||
\(620\) | 1.54591 | 0.0620854 | ||||||||
\(621\) | −16.6357 | −0.667568 | ||||||||
\(622\) | 3.37946 | 0.135504 | ||||||||
\(623\) | −1.00048 | −0.0400835 | ||||||||
\(624\) | −2.35228 | −0.0941665 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −20.7401 | −0.828941 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.29144 | −0.290960 | ||||||||
\(629\) | 23.0844 | 0.920434 | ||||||||
\(630\) | 2.12450 | 0.0846420 | ||||||||
\(631\) | −49.1136 | −1.95518 | −0.977591 | − | 0.210514i | \(-0.932486\pi\) | ||||
−0.977591 | + | 0.210514i | \(0.932486\pi\) | |||||||
\(632\) | 9.86178 | 0.392281 | ||||||||
\(633\) | −21.7799 | −0.865675 | ||||||||
\(634\) | 7.46200 | 0.296354 | ||||||||
\(635\) | −3.68316 | −0.146162 | ||||||||
\(636\) | −6.68356 | −0.265020 | ||||||||
\(637\) | 2.51397 | 0.0996070 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.8926 | −0.549581 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −10.5819 | −0.417959 | −0.208979 | − | 0.977920i | \(-0.567014\pi\) | ||||
−0.208979 | + | 0.977920i | \(0.567014\pi\) | |||||||
\(642\) | −13.5091 | −0.533162 | ||||||||
\(643\) | −27.2101 | −1.07306 | −0.536531 | − | 0.843881i | \(-0.680266\pi\) | ||||
−0.536531 | + | 0.843881i | \(0.680266\pi\) | |||||||
\(644\) | 3.46945 | 0.136716 | ||||||||
\(645\) | −7.45826 | −0.293669 | ||||||||
\(646\) | 19.0043 | 0.747716 | ||||||||
\(647\) | −32.6756 | −1.28461 | −0.642304 | − | 0.766450i | \(-0.722021\pi\) | ||||
−0.642304 | + | 0.766450i | \(0.722021\pi\) | |||||||
\(648\) | 1.88697 | 0.0741273 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.51397 | 0.0986059 | ||||||||
\(651\) | 1.44649 | 0.0566923 | ||||||||
\(652\) | 9.41304 | 0.368643 | ||||||||
\(653\) | −35.8727 | −1.40381 | −0.701904 | − | 0.712272i | \(-0.747666\pi\) | ||||
−0.701904 | + | 0.712272i | \(0.747666\pi\) | |||||||
\(654\) | −11.4031 | −0.445895 | ||||||||
\(655\) | −8.57781 | −0.335163 | ||||||||
\(656\) | −1.65079 | −0.0644526 | ||||||||
\(657\) | −1.81723 | −0.0708971 | ||||||||
\(658\) | −1.77448 | −0.0691763 | ||||||||
\(659\) | 2.91875 | 0.113698 | 0.0568492 | − | 0.998383i | \(-0.481895\pi\) | ||||
0.0568492 | + | 0.998383i | \(0.481895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.9224 | −1.78617 | −0.893087 | − | 0.449883i | \(-0.851466\pi\) | ||||
−0.893087 | + | 0.449883i | \(0.851466\pi\) | |||||||
\(662\) | −8.26702 | −0.321307 | ||||||||
\(663\) | 11.0228 | 0.428091 | ||||||||
\(664\) | 8.15674 | 0.316543 | ||||||||
\(665\) | 4.05554 | 0.157267 | ||||||||
\(666\) | 10.4657 | 0.405539 | ||||||||
\(667\) | −25.8982 | −1.00278 | ||||||||
\(668\) | 0.289918 | 0.0112173 | ||||||||
\(669\) | 7.57668 | 0.292931 | ||||||||
\(670\) | −5.99409 | −0.231572 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.935683 | 0.0360948 | ||||||||
\(673\) | 17.1172 | 0.659818 | 0.329909 | − | 0.944013i | \(-0.392982\pi\) | ||||
0.329909 | + | 0.944013i | \(0.392982\pi\) | |||||||
\(674\) | −0.309107 | −0.0119063 | ||||||||
\(675\) | 4.79491 | 0.184556 | ||||||||
\(676\) | −6.67997 | −0.256922 | ||||||||
\(677\) | 0.309569 | 0.0118977 | 0.00594886 | − | 0.999982i | \(-0.498106\pi\) | ||||
0.00594886 | + | 0.999982i | \(0.498106\pi\) | |||||||
\(678\) | 10.9750 | 0.421494 | ||||||||
\(679\) | −11.3338 | −0.434953 | ||||||||
\(680\) | −4.68602 | −0.179701 | ||||||||
\(681\) | −17.6240 | −0.675352 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.6187 | 1.70729 | 0.853644 | − | 0.520856i | \(-0.174387\pi\) | ||||
0.853644 | + | 0.520856i | \(0.174387\pi\) | |||||||
\(684\) | 8.61598 | 0.329440 | ||||||||
\(685\) | 1.63086 | 0.0623121 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −10.1729 | −0.388119 | ||||||||
\(688\) | 7.97092 | 0.303888 | ||||||||
\(689\) | 17.9572 | 0.684115 | ||||||||
\(690\) | 3.24631 | 0.123585 | ||||||||
\(691\) | 1.84640 | 0.0702406 | 0.0351203 | − | 0.999383i | \(-0.488819\pi\) | ||||
0.0351203 | + | 0.999383i | \(0.488819\pi\) | |||||||
\(692\) | 10.4188 | 0.396063 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.12313 | 0.232431 | ||||||||
\(695\) | 23.1799 | 0.879263 | ||||||||
\(696\) | −6.98453 | −0.264748 | ||||||||
\(697\) | 7.73564 | 0.293008 | ||||||||
\(698\) | −19.7838 | −0.748828 | ||||||||
\(699\) | −8.39906 | −0.317682 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 13.9594 | 0.527240 | 0.263620 | − | 0.964627i | \(-0.415083\pi\) | ||||
0.263620 | + | 0.964627i | \(0.415083\pi\) | |||||||
\(702\) | 12.0542 | 0.454958 | ||||||||
\(703\) | 19.9785 | 0.753503 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.66035 | −0.0625323 | ||||||||
\(706\) | −30.8256 | −1.16014 | ||||||||
\(707\) | 3.16660 | 0.119092 | ||||||||
\(708\) | 0.399384 | 0.0150098 | ||||||||
\(709\) | −12.2455 | −0.459891 | −0.229945 | − | 0.973204i | \(-0.573855\pi\) | ||||
−0.229945 | + | 0.973204i | \(0.573855\pi\) | |||||||
\(710\) | 6.53922 | 0.245413 | ||||||||
\(711\) | −20.9513 | −0.785736 | ||||||||
\(712\) | 1.00048 | 0.0374947 | ||||||||
\(713\) | −5.36348 | −0.200864 | ||||||||
\(714\) | −4.38463 | −0.164091 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.9115 | −0.557270 | ||||||||
\(717\) | −9.15215 | −0.341793 | ||||||||
\(718\) | −25.2431 | −0.942064 | ||||||||
\(719\) | −11.5631 | −0.431230 | −0.215615 | − | 0.976478i | \(-0.569176\pi\) | ||||
−0.215615 | + | 0.976478i | \(0.569176\pi\) | |||||||
\(720\) | −2.12450 | −0.0791753 | ||||||||
\(721\) | −15.0475 | −0.560396 | ||||||||
\(722\) | −2.55258 | −0.0949973 | ||||||||
\(723\) | 21.8814 | 0.813778 | ||||||||
\(724\) | 4.37330 | 0.162533 | ||||||||
\(725\) | 7.46463 | 0.277229 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.2457 | −0.417080 | −0.208540 | − | 0.978014i | \(-0.566871\pi\) | ||||
−0.208540 | + | 0.978014i | \(0.566871\pi\) | |||||||
\(728\) | −2.51397 | −0.0931738 | ||||||||
\(729\) | 9.45068 | 0.350025 | ||||||||
\(730\) | 0.855372 | 0.0316587 | ||||||||
\(731\) | −37.3519 | −1.38151 | ||||||||
\(732\) | 5.75633 | 0.212760 | ||||||||
\(733\) | 13.3226 | 0.492081 | 0.246041 | − | 0.969260i | \(-0.420870\pi\) | ||||
0.246041 | + | 0.969260i | \(0.420870\pi\) | |||||||
\(734\) | −8.87025 | −0.327407 | ||||||||
\(735\) | −0.935683 | −0.0345132 | ||||||||
\(736\) | −3.46945 | −0.127886 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3.50710 | 0.129098 | ||||||||
\(739\) | 42.5012 | 1.56343 | 0.781716 | − | 0.623635i | \(-0.214345\pi\) | ||||
0.781716 | + | 0.623635i | \(0.214345\pi\) | |||||||
\(740\) | −4.92622 | −0.181092 | ||||||||
\(741\) | 9.53976 | 0.350452 | ||||||||
\(742\) | −7.14297 | −0.262227 | ||||||||
\(743\) | −22.0875 | −0.810311 | −0.405156 | − | 0.914248i | \(-0.632783\pi\) | ||||
−0.405156 | + | 0.914248i | \(0.632783\pi\) | |||||||
\(744\) | −1.44649 | −0.0530308 | ||||||||
\(745\) | 1.43386 | 0.0525326 | ||||||||
\(746\) | 23.0860 | 0.845240 | ||||||||
\(747\) | −17.3290 | −0.634034 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.4377 | −0.527542 | ||||||||
\(750\) | −0.935683 | −0.0341663 | ||||||||
\(751\) | 20.2698 | 0.739657 | 0.369829 | − | 0.929100i | \(-0.379416\pi\) | ||||
0.369829 | + | 0.929100i | \(0.379416\pi\) | |||||||
\(752\) | 1.77448 | 0.0647085 | ||||||||
\(753\) | −24.4157 | −0.889756 | ||||||||
\(754\) | 18.7658 | 0.683412 | ||||||||
\(755\) | −17.7952 | −0.647632 | ||||||||
\(756\) | −4.79491 | −0.174389 | ||||||||
\(757\) | −5.51054 | −0.200284 | −0.100142 | − | 0.994973i | \(-0.531930\pi\) | ||||
−0.100142 | + | 0.994973i | \(0.531930\pi\) | |||||||
\(758\) | 31.6315 | 1.14891 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.05554 | −0.147110 | ||||||||
\(761\) | −33.9696 | −1.23140 | −0.615699 | − | 0.787981i | \(-0.711126\pi\) | ||||
−0.615699 | + | 0.787981i | \(0.711126\pi\) | |||||||
\(762\) | 3.44627 | 0.124845 | ||||||||
\(763\) | −12.1869 | −0.441195 | ||||||||
\(764\) | −10.6197 | −0.384208 | ||||||||
\(765\) | 9.95543 | 0.359939 | ||||||||
\(766\) | 1.84985 | 0.0668377 | ||||||||
\(767\) | −1.07305 | −0.0387458 | ||||||||
\(768\) | −0.935683 | −0.0337636 | ||||||||
\(769\) | −0.669422 | −0.0241400 | −0.0120700 | − | 0.999927i | \(-0.503842\pi\) | ||||
−0.0120700 | + | 0.999927i | \(0.503842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.16436 | −0.185990 | ||||||||
\(772\) | −7.98145 | −0.287259 | ||||||||
\(773\) | −32.7311 | −1.17725 | −0.588627 | − | 0.808405i | \(-0.700331\pi\) | ||||
−0.588627 | + | 0.808405i | \(0.700331\pi\) | |||||||
\(774\) | −16.9342 | −0.608687 | ||||||||
\(775\) | 1.54591 | 0.0555309 | ||||||||
\(776\) | 11.3338 | 0.406861 | ||||||||
\(777\) | −4.60938 | −0.165361 | ||||||||
\(778\) | 15.6624 | 0.561525 | ||||||||
\(779\) | 6.69486 | 0.239868 | ||||||||
\(780\) | −2.35228 | −0.0842251 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 16.2579 | 0.581382 | ||||||||
\(783\) | 35.7922 | 1.27911 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −7.29144 | −0.260243 | ||||||||
\(786\) | 8.02612 | 0.286282 | ||||||||
\(787\) | 16.9929 | 0.605732 | 0.302866 | − | 0.953033i | \(-0.402056\pi\) | ||||
0.302866 | + | 0.953033i | \(0.402056\pi\) | |||||||
\(788\) | 7.28621 | 0.259560 | ||||||||
\(789\) | −25.4340 | −0.905476 | ||||||||
\(790\) | 9.86178 | 0.350866 | ||||||||
\(791\) | 11.7294 | 0.417050 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.4659 | −0.549212 | ||||||||
\(794\) | −14.8207 | −0.525965 | ||||||||
\(795\) | −6.68356 | −0.237041 | ||||||||
\(796\) | 14.1853 | 0.502783 | ||||||||
\(797\) | 46.4576 | 1.64561 | 0.822806 | − | 0.568322i | \(-0.192407\pi\) | ||||
0.822806 | + | 0.568322i | \(0.192407\pi\) | |||||||
\(798\) | −3.79470 | −0.134331 | ||||||||
\(799\) | −8.31523 | −0.294172 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −2.12552 | −0.0751016 | ||||||||
\(802\) | 14.4322 | 0.509619 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.60857 | 0.197799 | ||||||||
\(805\) | 3.46945 | 0.122282 | ||||||||
\(806\) | 3.88638 | 0.136892 | ||||||||
\(807\) | 7.62096 | 0.268270 | ||||||||
\(808\) | −3.16660 | −0.111401 | ||||||||
\(809\) | −2.84705 | −0.100097 | −0.0500484 | − | 0.998747i | \(-0.515938\pi\) | ||||
−0.0500484 | + | 0.998747i | \(0.515938\pi\) | |||||||
\(810\) | 1.88697 | 0.0663015 | ||||||||
\(811\) | −1.46624 | −0.0514866 | −0.0257433 | − | 0.999669i | \(-0.508195\pi\) | ||||
−0.0257433 | + | 0.999669i | \(0.508195\pi\) | |||||||
\(812\) | −7.46463 | −0.261957 | ||||||||
\(813\) | −5.90032 | −0.206933 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.41304 | 0.329724 | ||||||||
\(816\) | 4.38463 | 0.153493 | ||||||||
\(817\) | −32.3264 | −1.13096 | ||||||||
\(818\) | 38.0339 | 1.32982 | ||||||||
\(819\) | 5.34092 | 0.186627 | ||||||||
\(820\) | −1.65079 | −0.0576482 | ||||||||
\(821\) | 19.6491 | 0.685757 | 0.342879 | − | 0.939380i | \(-0.388598\pi\) | ||||
0.342879 | + | 0.939380i | \(0.388598\pi\) | |||||||
\(822\) | −1.52597 | −0.0532244 | ||||||||
\(823\) | −17.0752 | −0.595203 | −0.297601 | − | 0.954690i | \(-0.596187\pi\) | ||||
−0.297601 | + | 0.954690i | \(0.596187\pi\) | |||||||
\(824\) | 15.0475 | 0.524203 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.426837 | 0.0148516 | ||||||||
\(827\) | −15.9823 | −0.555759 | −0.277880 | − | 0.960616i | \(-0.589632\pi\) | ||||
−0.277880 | + | 0.960616i | \(0.589632\pi\) | |||||||
\(828\) | 7.37084 | 0.256154 | ||||||||
\(829\) | 17.6458 | 0.612863 | 0.306432 | − | 0.951893i | \(-0.400865\pi\) | ||||
0.306432 | + | 0.951893i | \(0.400865\pi\) | |||||||
\(830\) | 8.15674 | 0.283125 | ||||||||
\(831\) | −24.4584 | −0.848451 | ||||||||
\(832\) | 2.51397 | 0.0871561 | ||||||||
\(833\) | −4.68602 | −0.162361 | ||||||||
\(834\) | −21.6890 | −0.751030 | ||||||||
\(835\) | 0.289918 | 0.0100330 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.41251 | 0.256214 | ||||||||
\(838\) | 24.2138 | 0.836451 | ||||||||
\(839\) | 7.96223 | 0.274887 | 0.137443 | − | 0.990510i | \(-0.456111\pi\) | ||||
0.137443 | + | 0.990510i | \(0.456111\pi\) | |||||||
\(840\) | 0.935683 | 0.0322841 | ||||||||
\(841\) | 26.7207 | 0.921404 | ||||||||
\(842\) | 38.6678 | 1.33258 | ||||||||
\(843\) | 13.7879 | 0.474880 | ||||||||
\(844\) | 23.2770 | 0.801229 | ||||||||
\(845\) | −6.67997 | −0.229798 | ||||||||
\(846\) | −3.76987 | −0.129611 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.14297 | 0.245291 | ||||||||
\(849\) | 20.1228 | 0.690613 | ||||||||
\(850\) | −4.68602 | −0.160729 | ||||||||
\(851\) | 17.0913 | 0.585882 | ||||||||
\(852\) | −6.11864 | −0.209621 | ||||||||
\(853\) | 39.3256 | 1.34648 | 0.673242 | − | 0.739422i | \(-0.264901\pi\) | ||||
0.673242 | + | 0.739422i | \(0.264901\pi\) | |||||||
\(854\) | 6.15201 | 0.210517 | ||||||||
\(855\) | 8.61598 | 0.294660 | ||||||||
\(856\) | 14.4377 | 0.493470 | ||||||||
\(857\) | 42.5288 | 1.45276 | 0.726379 | − | 0.687295i | \(-0.241202\pi\) | ||||
0.726379 | + | 0.687295i | \(0.241202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.8680 | 1.25792 | 0.628960 | − | 0.777438i | \(-0.283481\pi\) | ||||
0.628960 | + | 0.777438i | \(0.283481\pi\) | |||||||
\(860\) | 7.97092 | 0.271806 | ||||||||
\(861\) | −1.54462 | −0.0526405 | ||||||||
\(862\) | 23.6029 | 0.803917 | ||||||||
\(863\) | 25.0975 | 0.854327 | 0.427164 | − | 0.904174i | \(-0.359513\pi\) | ||||
0.427164 | + | 0.904174i | \(0.359513\pi\) | |||||||
\(864\) | 4.79491 | 0.163126 | ||||||||
\(865\) | 10.4188 | 0.354250 | ||||||||
\(866\) | −30.6532 | −1.04164 | ||||||||
\(867\) | −4.63983 | −0.157577 | ||||||||
\(868\) | −1.54591 | −0.0524717 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.98453 | −0.236798 | ||||||||
\(871\) | −15.0690 | −0.510592 | ||||||||
\(872\) | 12.1869 | 0.412700 | ||||||||
\(873\) | −24.0787 | −0.814940 | ||||||||
\(874\) | 14.0705 | 0.475942 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −0.800357 | −0.0270416 | ||||||||
\(877\) | 54.6433 | 1.84517 | 0.922586 | − | 0.385792i | \(-0.126072\pi\) | ||||
0.922586 | + | 0.385792i | \(0.126072\pi\) | |||||||
\(878\) | −23.4152 | −0.790226 | ||||||||
\(879\) | −5.72268 | −0.193021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.1584 | −1.65619 | −0.828094 | − | 0.560590i | \(-0.810575\pi\) | ||||
−0.828094 | + | 0.560590i | \(0.810575\pi\) | |||||||
\(882\) | −2.12450 | −0.0715355 | ||||||||
\(883\) | −26.9252 | −0.906105 | −0.453053 | − | 0.891484i | \(-0.649665\pi\) | ||||
−0.453053 | + | 0.891484i | \(0.649665\pi\) | |||||||
\(884\) | −11.7805 | −0.396221 | ||||||||
\(885\) | 0.399384 | 0.0134252 | ||||||||
\(886\) | 0.833237 | 0.0279931 | ||||||||
\(887\) | −31.8126 | −1.06816 | −0.534082 | − | 0.845433i | \(-0.679342\pi\) | ||||
−0.534082 | + | 0.845433i | \(0.679342\pi\) | |||||||
\(888\) | 4.60938 | 0.154681 | ||||||||
\(889\) | 3.68316 | 0.123529 | ||||||||
\(890\) | 1.00048 | 0.0335363 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.09748 | −0.271124 | ||||||||
\(893\) | −7.19646 | −0.240820 | ||||||||
\(894\) | −1.34164 | −0.0448711 | ||||||||
\(895\) | −14.9115 | −0.498438 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 8.16112 | 0.272492 | ||||||||
\(898\) | −5.98030 | −0.199565 | ||||||||
\(899\) | 11.5397 | 0.384870 | ||||||||
\(900\) | −2.12450 | −0.0708165 | ||||||||
\(901\) | −33.4721 | −1.11512 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.45826 | 0.248195 | ||||||||
\(904\) | −11.7294 | −0.390115 | ||||||||
\(905\) | 4.37330 | 0.145374 | ||||||||
\(906\) | 16.6506 | 0.553180 | ||||||||
\(907\) | 27.8459 | 0.924609 | 0.462304 | − | 0.886721i | \(-0.347023\pi\) | ||||
0.462304 | + | 0.886721i | \(0.347023\pi\) | |||||||
\(908\) | 18.8354 | 0.625074 | ||||||||
\(909\) | 6.72743 | 0.223135 | ||||||||
\(910\) | −2.51397 | −0.0833372 | ||||||||
\(911\) | −54.9974 | −1.82214 | −0.911072 | − | 0.412247i | \(-0.864744\pi\) | ||||
−0.911072 | + | 0.412247i | \(0.864744\pi\) | |||||||
\(912\) | 3.79470 | 0.125655 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 41.9762 | 1.38845 | ||||||||
\(915\) | 5.75633 | 0.190298 | ||||||||
\(916\) | 10.8721 | 0.359225 | ||||||||
\(917\) | 8.57781 | 0.283264 | ||||||||
\(918\) | −22.4690 | −0.741588 | ||||||||
\(919\) | −16.9015 | −0.557529 | −0.278764 | − | 0.960360i | \(-0.589925\pi\) | ||||
−0.278764 | + | 0.960360i | \(0.589925\pi\) | |||||||
\(920\) | −3.46945 | −0.114384 | ||||||||
\(921\) | 23.2724 | 0.766851 | ||||||||
\(922\) | 32.1474 | 1.05872 | ||||||||
\(923\) | 16.4394 | 0.541109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.92622 | −0.161973 | ||||||||
\(926\) | −8.14625 | −0.267702 | ||||||||
\(927\) | −31.9683 | −1.04998 | ||||||||
\(928\) | 7.46463 | 0.245039 | ||||||||
\(929\) | −16.9182 | −0.555069 | −0.277535 | − | 0.960716i | \(-0.589517\pi\) | ||||
−0.277535 | + | 0.960716i | \(0.589517\pi\) | |||||||
\(930\) | −1.44649 | −0.0474321 | ||||||||
\(931\) | −4.05554 | −0.132915 | ||||||||
\(932\) | 8.97639 | 0.294031 | ||||||||
\(933\) | −3.16210 | −0.103523 | ||||||||
\(934\) | 7.67994 | 0.251295 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.34092 | −0.174573 | ||||||||
\(937\) | 5.70923 | 0.186512 | 0.0932562 | − | 0.995642i | \(-0.470272\pi\) | ||||
0.0932562 | + | 0.995642i | \(0.470272\pi\) | |||||||
\(938\) | 5.99409 | 0.195714 | ||||||||
\(939\) | 19.4062 | 0.633297 | ||||||||
\(940\) | 1.77448 | 0.0578770 | ||||||||
\(941\) | 34.2699 | 1.11717 | 0.558584 | − | 0.829448i | \(-0.311345\pi\) | ||||
0.558584 | + | 0.829448i | \(0.311345\pi\) | |||||||
\(942\) | 6.82248 | 0.222288 | ||||||||
\(943\) | 5.72735 | 0.186508 | ||||||||
\(944\) | −0.426837 | −0.0138924 | ||||||||
\(945\) | −4.79491 | −0.155978 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.4856 | −0.958154 | −0.479077 | − | 0.877773i | \(-0.659029\pi\) | ||||
−0.479077 | + | 0.877773i | \(0.659029\pi\) | |||||||
\(948\) | −9.22750 | −0.299695 | ||||||||
\(949\) | 2.15038 | 0.0698042 | ||||||||
\(950\) | −4.05554 | −0.131579 | ||||||||
\(951\) | −6.98207 | −0.226409 | ||||||||
\(952\) | 4.68602 | 0.151875 | ||||||||
\(953\) | 43.8435 | 1.42023 | 0.710116 | − | 0.704085i | \(-0.248643\pi\) | ||||
0.710116 | + | 0.704085i | \(0.248643\pi\) | |||||||
\(954\) | −15.1752 | −0.491316 | ||||||||
\(955\) | −10.6197 | −0.343646 | ||||||||
\(956\) | 9.78125 | 0.316348 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.7225 | 0.734131 | ||||||||
\(959\) | −1.63086 | −0.0526633 | ||||||||
\(960\) | −0.935683 | −0.0301991 | ||||||||
\(961\) | −28.6102 | −0.922908 | ||||||||
\(962\) | −12.3844 | −0.399288 | ||||||||
\(963\) | −30.6728 | −0.988418 | ||||||||
\(964\) | −23.3855 | −0.753195 | ||||||||
\(965\) | −7.98145 | −0.256932 | ||||||||
\(966\) | −3.24631 | −0.104448 | ||||||||
\(967\) | 43.1164 | 1.38653 | 0.693265 | − | 0.720683i | \(-0.256172\pi\) | ||||
0.693265 | + | 0.720683i | \(0.256172\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.7820 | −0.571242 | ||||||||
\(970\) | 11.3338 | 0.363908 | ||||||||
\(971\) | −55.6910 | −1.78721 | −0.893604 | − | 0.448856i | \(-0.851831\pi\) | ||||
−0.893604 | + | 0.448856i | \(0.851831\pi\) | |||||||
\(972\) | −16.1503 | −0.518022 | ||||||||
\(973\) | −23.1799 | −0.743113 | ||||||||
\(974\) | 33.4458 | 1.07167 | ||||||||
\(975\) | −2.35228 | −0.0753332 | ||||||||
\(976\) | −6.15201 | −0.196921 | ||||||||
\(977\) | −9.63540 | −0.308264 | −0.154132 | − | 0.988050i | \(-0.549258\pi\) | ||||
−0.154132 | + | 0.988050i | \(0.549258\pi\) | |||||||
\(978\) | −8.80763 | −0.281637 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −25.8910 | −0.826636 | ||||||||
\(982\) | −6.10991 | −0.194975 | ||||||||
\(983\) | 54.5716 | 1.74056 | 0.870281 | − | 0.492555i | \(-0.163937\pi\) | ||||
0.870281 | + | 0.492555i | \(0.163937\pi\) | |||||||
\(984\) | 1.54462 | 0.0492407 | ||||||||
\(985\) | 7.28621 | 0.232158 | ||||||||
\(986\) | −34.9794 | −1.11397 | ||||||||
\(987\) | 1.66035 | 0.0528495 | ||||||||
\(988\) | −10.1955 | −0.324362 | ||||||||
\(989\) | −27.6547 | −0.879370 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.0492 | −1.58986 | −0.794932 | − | 0.606699i | \(-0.792494\pi\) | ||||
−0.794932 | + | 0.606699i | \(0.792494\pi\) | |||||||
\(992\) | 1.54591 | 0.0490828 | ||||||||
\(993\) | 7.73531 | 0.245473 | ||||||||
\(994\) | −6.53922 | −0.207411 | ||||||||
\(995\) | 14.1853 | 0.449703 | ||||||||
\(996\) | −7.63213 | −0.241833 | ||||||||
\(997\) | −22.8919 | −0.724994 | −0.362497 | − | 0.931985i | \(-0.618076\pi\) | ||||
−0.362497 | + | 0.931985i | \(0.618076\pi\) | |||||||
\(998\) | 21.1193 | 0.668520 | ||||||||
\(999\) | −23.6208 | −0.747328 |
(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 | 8470.2.a.dc.1.3 | 6 | ||
11.7 | odd | 10 | 770.2.n.j.71.2 | ✓ | 12 | ||
11.8 | odd | 10 | 770.2.n.j.141.2 | yes | 12 | ||
11.10 | odd | 2 | 8470.2.a.cw.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.j.71.2 | ✓ | 12 | 11.7 | odd | 10 | ||
770.2.n.j.141.2 | yes | 12 | 11.8 | odd | 10 | ||
8470.2.a.cw.1.3 | 6 | 11.10 | odd | 2 | |||
8470.2.a.dc.1.3 | 6 | 1.1 | even | 1 | trivial |