Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1341,2,Mod(1,1341)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1341, 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("1341.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1341 = 3^{2} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1341.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: | \(10.7079389111\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 6x^{7} + 37x^{6} - 3x^{5} - 101x^{4} + 49x^{3} + 72x^{2} - 21x - 13 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 447) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.720171\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1341.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.720171 | 0.509238 | 0.254619 | − | 0.967042i | \(-0.418050\pi\) | ||||
0.254619 | + | 0.967042i | \(0.418050\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.48135 | −0.740677 | ||||||||
\(5\) | 3.36155 | 1.50333 | 0.751665 | − | 0.659545i | \(-0.229251\pi\) | ||||
0.751665 | + | 0.659545i | \(0.229251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.451528 | 0.170662 | 0.0853308 | − | 0.996353i | \(-0.472805\pi\) | ||||
0.0853308 | + | 0.996353i | \(0.472805\pi\) | |||||||
\(8\) | −2.50717 | −0.886418 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.42089 | 0.765552 | ||||||||
\(11\) | −5.21771 | −1.57320 | −0.786599 | − | 0.617464i | \(-0.788160\pi\) | ||||
−0.786599 | + | 0.617464i | \(0.788160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.16313 | −1.43199 | −0.715997 | − | 0.698103i | \(-0.754028\pi\) | ||||
−0.715997 | + | 0.698103i | \(0.754028\pi\) | |||||||
\(14\) | 0.325177 | 0.0869072 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.15712 | 0.289280 | ||||||||
\(17\) | −7.12598 | −1.72830 | −0.864152 | − | 0.503230i | \(-0.832145\pi\) | ||||
−0.864152 | + | 0.503230i | \(0.832145\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.740583 | −0.169901 | −0.0849507 | − | 0.996385i | \(-0.527073\pi\) | ||||
−0.0849507 | + | 0.996385i | \(0.527073\pi\) | |||||||
\(20\) | −4.97965 | −1.11348 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.75764 | −0.801132 | ||||||||
\(23\) | −7.26909 | −1.51571 | −0.757855 | − | 0.652423i | \(-0.773753\pi\) | ||||
−0.757855 | + | 0.652423i | \(0.773753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.30002 | 1.26000 | ||||||||
\(26\) | −3.71833 | −0.729225 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.668873 | −0.126405 | ||||||||
\(29\) | −0.897164 | −0.166599 | −0.0832996 | − | 0.996525i | \(-0.526546\pi\) | ||||
−0.0832996 | + | 0.996525i | \(0.526546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.36414 | 1.14303 | 0.571517 | − | 0.820590i | \(-0.306355\pi\) | ||||
0.571517 | + | 0.820590i | \(0.306355\pi\) | |||||||
\(32\) | 5.84766 | 1.03373 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.13192 | −0.880118 | ||||||||
\(35\) | 1.51783 | 0.256561 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.200318 | 0.0329321 | 0.0164661 | − | 0.999864i | \(-0.494758\pi\) | ||||
0.0164661 | + | 0.999864i | \(0.494758\pi\) | |||||||
\(38\) | −0.533346 | −0.0865202 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.42797 | −1.33258 | ||||||||
\(41\) | 5.33009 | 0.832420 | 0.416210 | − | 0.909269i | \(-0.363358\pi\) | ||||
0.416210 | + | 0.909269i | \(0.363358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.16561 | 0.940246 | 0.470123 | − | 0.882601i | \(-0.344210\pi\) | ||||
0.470123 | + | 0.882601i | \(0.344210\pi\) | |||||||
\(44\) | 7.72928 | 1.16523 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.23499 | −0.771857 | ||||||||
\(47\) | −8.69209 | −1.26787 | −0.633936 | − | 0.773386i | \(-0.718562\pi\) | ||||
−0.633936 | + | 0.773386i | \(0.718562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.79612 | −0.970875 | ||||||||
\(50\) | 4.53709 | 0.641641 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.64842 | 1.06065 | ||||||||
\(53\) | 12.3472 | 1.69602 | 0.848010 | − | 0.529981i | \(-0.177801\pi\) | ||||
0.848010 | + | 0.529981i | \(0.177801\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.5396 | −2.36504 | ||||||||
\(56\) | −1.13206 | −0.151277 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.646111 | −0.0848386 | ||||||||
\(59\) | −6.95828 | −0.905890 | −0.452945 | − | 0.891538i | \(-0.649627\pi\) | ||||
−0.452945 | + | 0.891538i | \(0.649627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.55490 | −0.327122 | −0.163561 | − | 0.986533i | \(-0.552298\pi\) | ||||
−0.163561 | + | 0.986533i | \(0.552298\pi\) | |||||||
\(62\) | 4.58327 | 0.582076 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.89708 | 0.237134 | ||||||||
\(65\) | −17.3561 | −2.15276 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.74020 | 0.334769 | 0.167384 | − | 0.985892i | \(-0.446468\pi\) | ||||
0.167384 | + | 0.985892i | \(0.446468\pi\) | |||||||
\(68\) | 10.5561 | 1.28012 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.09310 | 0.130650 | ||||||||
\(71\) | −8.88925 | −1.05496 | −0.527480 | − | 0.849567i | \(-0.676863\pi\) | ||||
−0.527480 | + | 0.849567i | \(0.676863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.10321 | 0.363203 | 0.181602 | − | 0.983372i | \(-0.441872\pi\) | ||||
0.181602 | + | 0.983372i | \(0.441872\pi\) | |||||||
\(74\) | 0.144263 | 0.0167703 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.09707 | 0.125842 | ||||||||
\(77\) | −2.35594 | −0.268484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.613299 | −0.0690016 | −0.0345008 | − | 0.999405i | \(-0.510984\pi\) | ||||
−0.0345008 | + | 0.999405i | \(0.510984\pi\) | |||||||
\(80\) | 3.88971 | 0.434883 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.83857 | 0.423899 | ||||||||
\(83\) | −0.114313 | −0.0125475 | −0.00627376 | − | 0.999980i | \(-0.501997\pi\) | ||||
−0.00627376 | + | 0.999980i | \(0.501997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.9543 | −2.59821 | ||||||||
\(86\) | 4.44029 | 0.478809 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.0817 | 1.39451 | ||||||||
\(89\) | −7.68351 | −0.814451 | −0.407225 | − | 0.913328i | \(-0.633504\pi\) | ||||
−0.407225 | + | 0.913328i | \(0.633504\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.33130 | −0.244386 | ||||||||
\(92\) | 10.7681 | 1.12265 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.25979 | −0.645648 | ||||||||
\(95\) | −2.48951 | −0.255418 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.73173 | −0.683504 | −0.341752 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341752 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(98\) | −4.89437 | −0.494406 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.33256 | −0.933256 | ||||||||
\(101\) | 13.9525 | 1.38833 | 0.694164 | − | 0.719817i | \(-0.255774\pi\) | ||||
0.694164 | + | 0.719817i | \(0.255774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.55565 | −0.153283 | −0.0766413 | − | 0.997059i | \(-0.524420\pi\) | ||||
−0.0766413 | + | 0.997059i | \(0.524420\pi\) | |||||||
\(104\) | 12.9448 | 1.26935 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.89210 | 0.863677 | ||||||||
\(107\) | 5.70887 | 0.551897 | 0.275949 | − | 0.961172i | \(-0.411008\pi\) | ||||
0.275949 | + | 0.961172i | \(0.411008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.602118 | −0.0576725 | −0.0288362 | − | 0.999584i | \(-0.509180\pi\) | ||||
−0.0288362 | + | 0.999584i | \(0.509180\pi\) | |||||||
\(110\) | −12.6315 | −1.20437 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.522472 | 0.0493689 | ||||||||
\(113\) | 8.04301 | 0.756622 | 0.378311 | − | 0.925678i | \(-0.376505\pi\) | ||||
0.378311 | + | 0.925678i | \(0.376505\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.4354 | −2.27861 | ||||||||
\(116\) | 1.32902 | 0.123396 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.01115 | −0.461313 | ||||||||
\(119\) | −3.21758 | −0.294955 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.2245 | 1.47495 | ||||||||
\(122\) | −1.83997 | −0.166583 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.42755 | −0.846619 | ||||||||
\(125\) | 4.37007 | 0.390871 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0237 | 1.42187 | 0.710937 | − | 0.703256i | \(-0.248271\pi\) | ||||
0.710937 | + | 0.703256i | \(0.248271\pi\) | |||||||
\(128\) | −10.3291 | −0.912972 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.4994 | −1.09627 | ||||||||
\(131\) | −20.5714 | −1.79733 | −0.898664 | − | 0.438637i | \(-0.855461\pi\) | ||||
−0.898664 | + | 0.438637i | \(0.855461\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.334394 | −0.0289956 | ||||||||
\(134\) | 1.97341 | 0.170477 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.8660 | 1.53200 | ||||||||
\(137\) | −14.8831 | −1.27155 | −0.635773 | − | 0.771876i | \(-0.719318\pi\) | ||||
−0.635773 | + | 0.771876i | \(0.719318\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8984 | −1.68776 | −0.843881 | − | 0.536531i | \(-0.819734\pi\) | ||||
−0.843881 | + | 0.536531i | \(0.819734\pi\) | |||||||
\(140\) | −2.24845 | −0.190029 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.40178 | −0.537225 | ||||||||
\(143\) | 26.9397 | 2.25281 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.01586 | −0.250454 | ||||||||
\(146\) | 2.23484 | 0.184957 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.296743 | −0.0243921 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4528 | −0.932019 | −0.466009 | − | 0.884780i | \(-0.654309\pi\) | ||||
−0.466009 | + | 0.884780i | \(0.654309\pi\) | |||||||
\(152\) | 1.85677 | 0.150604 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.69668 | −0.136722 | ||||||||
\(155\) | 21.3934 | 1.71836 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.01945 | 0.719830 | 0.359915 | − | 0.932985i | \(-0.382806\pi\) | ||||
0.359915 | + | 0.932985i | \(0.382806\pi\) | |||||||
\(158\) | −0.441680 | −0.0351382 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 19.6572 | 1.55404 | ||||||||
\(161\) | −3.28220 | −0.258673 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.75071 | −0.215452 | −0.107726 | − | 0.994181i | \(-0.534357\pi\) | ||||
−0.107726 | + | 0.994181i | \(0.534357\pi\) | |||||||
\(164\) | −7.89575 | −0.616554 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0823251 | −0.00638967 | ||||||||
\(167\) | 11.4623 | 0.886976 | 0.443488 | − | 0.896280i | \(-0.353741\pi\) | ||||
0.443488 | + | 0.896280i | \(0.353741\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.6579 | 1.05061 | ||||||||
\(170\) | −17.2512 | −1.32311 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.13345 | −0.696419 | ||||||||
\(173\) | 23.8734 | 1.81506 | 0.907530 | − | 0.419987i | \(-0.137965\pi\) | ||||
0.907530 | + | 0.419987i | \(0.137965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.84463 | 0.215034 | ||||||||
\(176\) | −6.03751 | −0.455095 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.53344 | −0.414749 | ||||||||
\(179\) | 1.33357 | 0.0996754 | 0.0498377 | − | 0.998757i | \(-0.484130\pi\) | ||||
0.0498377 | + | 0.998757i | \(0.484130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3268 | 0.841916 | 0.420958 | − | 0.907080i | \(-0.361694\pi\) | ||||
0.420958 | + | 0.907080i | \(0.361694\pi\) | |||||||
\(182\) | −1.67893 | −0.124451 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.2248 | 1.34355 | ||||||||
\(185\) | 0.673380 | 0.0495079 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 37.1813 | 2.71897 | ||||||||
\(188\) | 12.8761 | 0.939083 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.79287 | −0.130068 | ||||||||
\(191\) | −16.8660 | −1.22038 | −0.610192 | − | 0.792254i | \(-0.708908\pi\) | ||||
−0.610192 | + | 0.792254i | \(0.708908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.7723 | 0.919372 | 0.459686 | − | 0.888081i | \(-0.347962\pi\) | ||||
0.459686 | + | 0.888081i | \(0.347962\pi\) | |||||||
\(194\) | −4.84800 | −0.348066 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.0675 | 0.719105 | ||||||||
\(197\) | −19.9874 | −1.42404 | −0.712022 | − | 0.702157i | \(-0.752221\pi\) | ||||
−0.712022 | + | 0.702157i | \(0.752221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.2196 | −1.64599 | −0.822997 | − | 0.568046i | \(-0.807699\pi\) | ||||
−0.822997 | + | 0.568046i | \(0.807699\pi\) | |||||||
\(200\) | −15.7952 | −1.11689 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0482 | 0.706989 | ||||||||
\(203\) | −0.405095 | −0.0284321 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.9174 | 1.25140 | ||||||||
\(206\) | −1.12033 | −0.0780573 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.97435 | −0.414247 | ||||||||
\(209\) | 3.86415 | 0.267289 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5749 | 1.34759 | 0.673795 | − | 0.738919i | \(-0.264663\pi\) | ||||
0.673795 | + | 0.738919i | \(0.264663\pi\) | |||||||
\(212\) | −18.2906 | −1.25620 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.11136 | 0.281047 | ||||||||
\(215\) | 20.7260 | 1.41350 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.87359 | 0.195072 | ||||||||
\(218\) | −0.433628 | −0.0293690 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.9824 | 1.75173 | ||||||||
\(221\) | 36.7924 | 2.47492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.2663 | −1.08927 | −0.544636 | − | 0.838673i | \(-0.683332\pi\) | ||||
−0.544636 | + | 0.838673i | \(0.683332\pi\) | |||||||
\(224\) | 2.64038 | 0.176418 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.79234 | 0.385300 | ||||||||
\(227\) | −12.1842 | −0.808692 | −0.404346 | − | 0.914606i | \(-0.632501\pi\) | ||||
−0.404346 | + | 0.914606i | \(0.632501\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6463 | −0.769610 | −0.384805 | − | 0.922998i | \(-0.625731\pi\) | ||||
−0.384805 | + | 0.922998i | \(0.625731\pi\) | |||||||
\(230\) | −17.5977 | −1.16036 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.24934 | 0.147677 | ||||||||
\(233\) | −7.59598 | −0.497629 | −0.248815 | − | 0.968551i | \(-0.580041\pi\) | ||||
−0.248815 | + | 0.968551i | \(0.580041\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.2189 | −1.90603 | ||||||||
\(236\) | 10.3077 | 0.670972 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.31721 | −0.150202 | ||||||||
\(239\) | 7.68084 | 0.496832 | 0.248416 | − | 0.968653i | \(-0.420090\pi\) | ||||
0.248416 | + | 0.968653i | \(0.420090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.20603 | 0.399766 | 0.199883 | − | 0.979820i | \(-0.435944\pi\) | ||||
0.199883 | + | 0.979820i | \(0.435944\pi\) | |||||||
\(242\) | 11.6844 | 0.751102 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.78472 | 0.242292 | ||||||||
\(245\) | −22.8455 | −1.45955 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.82372 | 0.243298 | ||||||||
\(248\) | −15.9560 | −1.01321 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.14720 | 0.199046 | ||||||||
\(251\) | −4.16240 | −0.262729 | −0.131364 | − | 0.991334i | \(-0.541936\pi\) | ||||
−0.131364 | + | 0.991334i | \(0.541936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.9280 | 2.38451 | ||||||||
\(254\) | 11.5398 | 0.724071 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.2329 | −0.702054 | ||||||||
\(257\) | 29.0645 | 1.81300 | 0.906498 | − | 0.422210i | \(-0.138745\pi\) | ||||
0.906498 | + | 0.422210i | \(0.138745\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0904494 | 0.00562025 | ||||||||
\(260\) | 25.7105 | 1.59450 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.8149 | −0.915267 | ||||||||
\(263\) | −19.4771 | −1.20101 | −0.600504 | − | 0.799622i | \(-0.705033\pi\) | ||||
−0.600504 | + | 0.799622i | \(0.705033\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.5058 | 2.54968 | ||||||||
\(266\) | −0.240821 | −0.0147657 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.05921 | −0.247956 | ||||||||
\(269\) | 21.4119 | 1.30550 | 0.652752 | − | 0.757571i | \(-0.273614\pi\) | ||||
0.652752 | + | 0.757571i | \(0.273614\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.02455 | −0.305220 | −0.152610 | − | 0.988287i | \(-0.548768\pi\) | ||||
−0.152610 | + | 0.988287i | \(0.548768\pi\) | |||||||
\(272\) | −8.24561 | −0.499964 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.7183 | −0.647518 | ||||||||
\(275\) | −32.8717 | −1.98224 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.2845 | −1.87970 | −0.939850 | − | 0.341586i | \(-0.889036\pi\) | ||||
−0.939850 | + | 0.341586i | \(0.889036\pi\) | |||||||
\(278\) | −14.3303 | −0.859471 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.80547 | −0.227420 | ||||||||
\(281\) | 24.0698 | 1.43589 | 0.717943 | − | 0.696102i | \(-0.245084\pi\) | ||||
0.717943 | + | 0.696102i | \(0.245084\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.2762 | 0.610856 | 0.305428 | − | 0.952215i | \(-0.401200\pi\) | ||||
0.305428 | + | 0.952215i | \(0.401200\pi\) | |||||||
\(284\) | 13.1681 | 0.781385 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.4012 | 1.14722 | ||||||||
\(287\) | 2.40668 | 0.142062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.7796 | 1.98704 | ||||||||
\(290\) | −2.17193 | −0.127540 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.59695 | −0.269016 | ||||||||
\(293\) | −22.0220 | −1.28654 | −0.643270 | − | 0.765640i | \(-0.722423\pi\) | ||||
−0.643270 | + | 0.765640i | \(0.722423\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.3906 | −1.36185 | ||||||||
\(296\) | −0.502232 | −0.0291917 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.720171 | 0.0417184 | ||||||||
\(299\) | 37.5313 | 2.17049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.78394 | 0.160464 | ||||||||
\(302\) | −8.24800 | −0.474619 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.856943 | −0.0491490 | ||||||||
\(305\) | −8.58843 | −0.491772 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8201 | 1.13119 | 0.565597 | − | 0.824682i | \(-0.308646\pi\) | ||||
0.565597 | + | 0.824682i | \(0.308646\pi\) | |||||||
\(308\) | 3.48998 | 0.198860 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.4069 | 0.875052 | ||||||||
\(311\) | 9.75657 | 0.553244 | 0.276622 | − | 0.960979i | \(-0.410785\pi\) | ||||
0.276622 | + | 0.960979i | \(0.410785\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.21602 | 0.351350 | 0.175675 | − | 0.984448i | \(-0.443789\pi\) | ||||
0.175675 | + | 0.984448i | \(0.443789\pi\) | |||||||
\(314\) | 6.49554 | 0.366564 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.908513 | 0.0511079 | ||||||||
\(317\) | −23.5747 | −1.32409 | −0.662043 | − | 0.749466i | \(-0.730310\pi\) | ||||
−0.662043 | + | 0.749466i | \(0.730310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.68114 | 0.262094 | ||||||||
\(320\) | 6.37711 | 0.356492 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.36374 | −0.131726 | ||||||||
\(323\) | 5.27738 | 0.293641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.5278 | −1.80432 | ||||||||
\(326\) | −1.98098 | −0.109716 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.3634 | −0.737872 | ||||||||
\(329\) | −3.92472 | −0.216377 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.6167 | −1.79278 | −0.896389 | − | 0.443268i | \(-0.853819\pi\) | ||||
−0.896389 | + | 0.443268i | \(0.853819\pi\) | |||||||
\(332\) | 0.169339 | 0.00929366 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.25478 | 0.451681 | ||||||||
\(335\) | 9.21132 | 0.503268 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2181 | 0.774511 | 0.387256 | − | 0.921972i | \(-0.373423\pi\) | ||||
0.387256 | + | 0.921972i | \(0.373423\pi\) | |||||||
\(338\) | 9.83601 | 0.535008 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 35.4849 | 1.92444 | ||||||||
\(341\) | −33.2062 | −1.79822 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.22933 | −0.336352 | ||||||||
\(344\) | −15.4582 | −0.833451 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.1929 | 0.924297 | ||||||||
\(347\) | 13.4582 | 0.722476 | 0.361238 | − | 0.932474i | \(-0.382354\pi\) | ||||
0.361238 | + | 0.932474i | \(0.382354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.78661 | −0.523865 | −0.261933 | − | 0.965086i | \(-0.584360\pi\) | ||||
−0.261933 | + | 0.965086i | \(0.584360\pi\) | |||||||
\(350\) | 2.04862 | 0.109503 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −30.5114 | −1.62626 | ||||||||
\(353\) | 11.2306 | 0.597747 | 0.298873 | − | 0.954293i | \(-0.403389\pi\) | ||||
0.298873 | + | 0.954293i | \(0.403389\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.8817 | −1.58595 | ||||||||
\(356\) | 11.3820 | 0.603245 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.960395 | 0.0507585 | ||||||||
\(359\) | −12.6694 | −0.668663 | −0.334331 | − | 0.942456i | \(-0.608510\pi\) | ||||
−0.334331 | + | 0.942456i | \(0.608510\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4515 | −0.971134 | ||||||||
\(362\) | 8.15724 | 0.428735 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.45348 | 0.181011 | ||||||||
\(365\) | 10.4316 | 0.546015 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5529 | −1.22945 | −0.614726 | − | 0.788741i | \(-0.710733\pi\) | ||||
−0.614726 | + | 0.788741i | \(0.710733\pi\) | |||||||
\(368\) | −8.41121 | −0.438464 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.484949 | 0.0252113 | ||||||||
\(371\) | 5.57511 | 0.289445 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.7862 | −0.817379 | −0.408690 | − | 0.912673i | \(-0.634014\pi\) | ||||
−0.408690 | + | 0.912673i | \(0.634014\pi\) | |||||||
\(374\) | 26.7769 | 1.38460 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.7925 | 1.12386 | ||||||||
\(377\) | 4.63217 | 0.238569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.59277 | −0.390014 | −0.195007 | − | 0.980802i | \(-0.562473\pi\) | ||||
−0.195007 | + | 0.980802i | \(0.562473\pi\) | |||||||
\(380\) | 3.68784 | 0.189182 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.1464 | −0.621465 | ||||||||
\(383\) | −16.6497 | −0.850762 | −0.425381 | − | 0.905014i | \(-0.639860\pi\) | ||||
−0.425381 | + | 0.905014i | \(0.639860\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.91962 | −0.403621 | ||||||||
\(386\) | 9.19826 | 0.468179 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.97208 | 0.506256 | ||||||||
\(389\) | −30.0408 | −1.52313 | −0.761564 | − | 0.648090i | \(-0.775568\pi\) | ||||
−0.761564 | + | 0.648090i | \(0.775568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51.7994 | 2.61961 | ||||||||
\(392\) | 17.0390 | 0.860601 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.3944 | −0.725177 | ||||||||
\(395\) | −2.06164 | −0.103732 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.5365 | 0.779753 | 0.389877 | − | 0.920867i | \(-0.372518\pi\) | ||||
0.389877 | + | 0.920867i | \(0.372518\pi\) | |||||||
\(398\) | −16.7221 | −0.838202 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.28987 | 0.364494 | ||||||||
\(401\) | 29.5840 | 1.47736 | 0.738678 | − | 0.674058i | \(-0.235450\pi\) | ||||
0.738678 | + | 0.674058i | \(0.235450\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.8589 | −1.63682 | ||||||||
\(404\) | −20.6686 | −1.02830 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.291737 | −0.0144787 | ||||||||
\(407\) | −1.04520 | −0.0518088 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.5908 | −0.721470 | −0.360735 | − | 0.932668i | \(-0.617474\pi\) | ||||
−0.360735 | + | 0.932668i | \(0.617474\pi\) | |||||||
\(410\) | 12.9036 | 0.637261 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.30447 | 0.113533 | ||||||||
\(413\) | −3.14186 | −0.154601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.384270 | −0.0188631 | ||||||||
\(416\) | −30.1922 | −1.48030 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.78285 | 0.136113 | ||||||||
\(419\) | −9.01986 | −0.440649 | −0.220325 | − | 0.975427i | \(-0.570712\pi\) | ||||
−0.220325 | + | 0.975427i | \(0.570712\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.78157 | −0.330514 | −0.165257 | − | 0.986251i | \(-0.552845\pi\) | ||||
−0.165257 | + | 0.986251i | \(0.552845\pi\) | |||||||
\(422\) | 14.0972 | 0.686243 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.9565 | −1.50338 | ||||||||
\(425\) | −44.8938 | −2.17767 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.15361 | −0.0558271 | ||||||||
\(428\) | −8.45686 | −0.408778 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.9263 | 0.719808 | ||||||||
\(431\) | 0.0835960 | 0.00402668 | 0.00201334 | − | 0.999998i | \(-0.499359\pi\) | ||||
0.00201334 | + | 0.999998i | \(0.499359\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.5942 | −0.509127 | −0.254564 | − | 0.967056i | \(-0.581932\pi\) | ||||
−0.254564 | + | 0.967056i | \(0.581932\pi\) | |||||||
\(434\) | 2.06947 | 0.0993379 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.891950 | 0.0427167 | ||||||||
\(437\) | 5.38337 | 0.257521 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.1030 | −1.19810 | −0.599051 | − | 0.800711i | \(-0.704455\pi\) | ||||
−0.599051 | + | 0.800711i | \(0.704455\pi\) | |||||||
\(440\) | 43.9747 | 2.09641 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.4968 | 1.26032 | ||||||||
\(443\) | −37.0991 | −1.76263 | −0.881315 | − | 0.472529i | \(-0.843341\pi\) | ||||
−0.881315 | + | 0.472529i | \(0.843341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.8285 | −1.22439 | ||||||||
\(446\) | −11.7145 | −0.554698 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.856583 | 0.0404697 | ||||||||
\(449\) | 20.7464 | 0.979083 | 0.489541 | − | 0.871980i | \(-0.337164\pi\) | ||||
0.489541 | + | 0.871980i | \(0.337164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.8109 | −1.30956 | ||||||||
\(452\) | −11.9145 | −0.560413 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.77468 | −0.411816 | ||||||||
\(455\) | −7.83677 | −0.367393 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.8934 | 1.44513 | 0.722566 | − | 0.691302i | \(-0.242962\pi\) | ||||
0.722566 | + | 0.691302i | \(0.242962\pi\) | |||||||
\(458\) | −8.38733 | −0.391914 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 36.1975 | 1.68772 | ||||||||
\(461\) | 11.5978 | 0.540165 | 0.270082 | − | 0.962837i | \(-0.412949\pi\) | ||||
0.270082 | + | 0.962837i | \(0.412949\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4892 | 1.37048 | 0.685239 | − | 0.728319i | \(-0.259698\pi\) | ||||
0.685239 | + | 0.728319i | \(0.259698\pi\) | |||||||
\(464\) | −1.03813 | −0.0481938 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.47040 | −0.253411 | ||||||||
\(467\) | 30.8781 | 1.42887 | 0.714433 | − | 0.699704i | \(-0.246685\pi\) | ||||
0.714433 | + | 0.699704i | \(0.246685\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.23728 | 0.0571322 | ||||||||
\(470\) | −21.0426 | −0.970622 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.4456 | 0.802998 | ||||||||
\(473\) | −32.1703 | −1.47919 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.66569 | −0.214076 | ||||||||
\(476\) | 4.76638 | 0.218466 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.53152 | 0.253006 | ||||||||
\(479\) | 2.60033 | 0.118812 | 0.0594060 | − | 0.998234i | \(-0.481079\pi\) | ||||
0.0594060 | + | 0.998234i | \(0.481079\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.03427 | −0.0471586 | ||||||||
\(482\) | 4.46940 | 0.203576 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24.0342 | −1.09247 | ||||||||
\(485\) | −22.6291 | −1.02753 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.06798 | −0.0483949 | −0.0241975 | − | 0.999707i | \(-0.507703\pi\) | ||||
−0.0241975 | + | 0.999707i | \(0.507703\pi\) | |||||||
\(488\) | 6.40557 | 0.289967 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.4527 | −0.743255 | ||||||||
\(491\) | 39.9095 | 1.80109 | 0.900545 | − | 0.434763i | \(-0.143168\pi\) | ||||
0.900545 | + | 0.434763i | \(0.143168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.39318 | 0.287934 | ||||||||
\(494\) | 2.75373 | 0.123896 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.36407 | 0.330656 | ||||||||
\(497\) | −4.01375 | −0.180041 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.3923 | −1.49484 | −0.747422 | − | 0.664349i | \(-0.768709\pi\) | ||||
−0.747422 | + | 0.664349i | \(0.768709\pi\) | |||||||
\(500\) | −6.47363 | −0.289509 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.99764 | −0.133791 | ||||||||
\(503\) | 31.9976 | 1.42670 | 0.713352 | − | 0.700806i | \(-0.247176\pi\) | ||||
0.713352 | + | 0.700806i | \(0.247176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 46.9021 | 2.08712 | ||||||||
\(506\) | 27.3146 | 1.21428 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.7368 | −1.05315 | ||||||||
\(509\) | 3.52569 | 0.156274 | 0.0781368 | − | 0.996943i | \(-0.475103\pi\) | ||||
0.0781368 | + | 0.996943i | \(0.475103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.40119 | 0.0619848 | ||||||||
\(512\) | 12.5686 | 0.555460 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.9314 | 0.923246 | ||||||||
\(515\) | −5.22939 | −0.230435 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.3528 | 1.99461 | ||||||||
\(518\) | 0.0651390 | 0.00286204 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 43.5147 | 1.90825 | ||||||||
\(521\) | 32.4565 | 1.42194 | 0.710972 | − | 0.703221i | \(-0.248255\pi\) | ||||
0.710972 | + | 0.703221i | \(0.248255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.10090 | −0.0918658 | −0.0459329 | − | 0.998945i | \(-0.514626\pi\) | ||||
−0.0459329 | + | 0.998945i | \(0.514626\pi\) | |||||||
\(524\) | 30.4735 | 1.33124 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0268 | −0.611599 | ||||||||
\(527\) | −45.3508 | −1.97551 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.8397 | 1.29738 | ||||||||
\(530\) | 29.8912 | 1.29839 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.495356 | 0.0214764 | ||||||||
\(533\) | −27.5199 | −1.19202 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.1906 | 0.829684 | ||||||||
\(536\) | −6.87015 | −0.296745 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.4202 | 0.664812 | ||||||||
\(539\) | 35.4602 | 1.52738 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.8044 | −1.36738 | −0.683689 | − | 0.729773i | \(-0.739626\pi\) | ||||
−0.683689 | + | 0.729773i | \(0.739626\pi\) | |||||||
\(542\) | −3.61853 | −0.155429 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −41.6703 | −1.78660 | ||||||||
\(545\) | −2.02405 | −0.0867008 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.4548 | −1.43042 | −0.715212 | − | 0.698908i | \(-0.753670\pi\) | ||||
−0.715212 | + | 0.698908i | \(0.753670\pi\) | |||||||
\(548\) | 22.0471 | 0.941804 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.6732 | −1.00943 | ||||||||
\(551\) | 0.664424 | 0.0283054 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.276922 | −0.0117759 | ||||||||
\(554\) | −22.5301 | −0.957214 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 29.4766 | 1.25009 | ||||||||
\(557\) | 16.7773 | 0.710877 | 0.355439 | − | 0.934700i | \(-0.384331\pi\) | ||||
0.355439 | + | 0.934700i | \(0.384331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.8338 | −1.34643 | ||||||||
\(560\) | 1.75631 | 0.0742178 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.3344 | 0.731207 | ||||||||
\(563\) | −9.47252 | −0.399219 | −0.199609 | − | 0.979876i | \(-0.563967\pi\) | ||||
−0.199609 | + | 0.979876i | \(0.563967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.0370 | 1.13745 | ||||||||
\(566\) | 7.40061 | 0.311071 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22.2869 | 0.935136 | ||||||||
\(569\) | −7.93748 | −0.332756 | −0.166378 | − | 0.986062i | \(-0.553207\pi\) | ||||
−0.166378 | + | 0.986062i | \(0.553207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.16768 | 0.299958 | 0.149979 | − | 0.988689i | \(-0.452079\pi\) | ||||
0.149979 | + | 0.988689i | \(0.452079\pi\) | |||||||
\(572\) | −39.9072 | −1.66861 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.73322 | 0.0723433 | ||||||||
\(575\) | −45.7954 | −1.90980 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.222271 | 0.00925327 | 0.00462664 | − | 0.999989i | \(-0.498527\pi\) | ||||
0.00462664 | + | 0.999989i | \(0.498527\pi\) | |||||||
\(578\) | 24.3271 | 1.01187 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.46756 | 0.185505 | ||||||||
\(581\) | −0.0516157 | −0.00214138 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −64.4242 | −2.66818 | ||||||||
\(584\) | −7.78027 | −0.321950 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.8596 | −0.655154 | ||||||||
\(587\) | −13.0374 | −0.538113 | −0.269056 | − | 0.963124i | \(-0.586712\pi\) | ||||
−0.269056 | + | 0.963124i | \(0.586712\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.71317 | −0.194203 | ||||||||
\(590\) | −16.8452 | −0.693507 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.231792 | 0.00952660 | ||||||||
\(593\) | −19.5281 | −0.801921 | −0.400960 | − | 0.916095i | \(-0.631324\pi\) | ||||
−0.400960 | + | 0.916095i | \(0.631324\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.8161 | −0.443415 | ||||||||
\(596\) | −1.48135 | −0.0606786 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 27.0289 | 1.10529 | ||||||||
\(599\) | 15.5924 | 0.637088 | 0.318544 | − | 0.947908i | \(-0.396806\pi\) | ||||
0.318544 | + | 0.947908i | \(0.396806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.3793 | −0.586544 | −0.293272 | − | 0.956029i | \(-0.594744\pi\) | ||||
−0.293272 | + | 0.956029i | \(0.594744\pi\) | |||||||
\(602\) | 2.00491 | 0.0817142 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.9657 | 0.690325 | ||||||||
\(605\) | 54.5395 | 2.21734 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.3377 | 1.51549 | 0.757745 | − | 0.652550i | \(-0.226301\pi\) | ||||
0.757745 | + | 0.652550i | \(0.226301\pi\) | |||||||
\(608\) | −4.33068 | −0.175632 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.18514 | −0.250429 | ||||||||
\(611\) | 44.8784 | 1.81558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.2650 | 1.74746 | 0.873728 | − | 0.486415i | \(-0.161696\pi\) | ||||
0.873728 | + | 0.486415i | \(0.161696\pi\) | |||||||
\(614\) | 14.2739 | 0.576047 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.90674 | 0.237990 | ||||||||
\(617\) | 34.0698 | 1.37160 | 0.685799 | − | 0.727791i | \(-0.259453\pi\) | ||||
0.685799 | + | 0.727791i | \(0.259453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.8451 | −1.44074 | −0.720368 | − | 0.693592i | \(-0.756027\pi\) | ||||
−0.720368 | + | 0.693592i | \(0.756027\pi\) | |||||||
\(620\) | −31.6912 | −1.27275 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.02640 | 0.281733 | ||||||||
\(623\) | −3.46932 | −0.138995 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.8099 | −0.672395 | ||||||||
\(626\) | 4.47660 | 0.178921 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.3610 | −0.533162 | ||||||||
\(629\) | −1.42747 | −0.0569168 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.20445 | −0.286805 | −0.143402 | − | 0.989664i | \(-0.545804\pi\) | ||||
−0.143402 | + | 0.989664i | \(0.545804\pi\) | |||||||
\(632\) | 1.53764 | 0.0611642 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.9778 | −0.674274 | ||||||||
\(635\) | 53.8645 | 2.13755 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.0892 | 1.39029 | ||||||||
\(638\) | 3.37122 | 0.133468 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −34.7218 | −1.37250 | ||||||||
\(641\) | −29.1170 | −1.15005 | −0.575027 | − | 0.818135i | \(-0.695008\pi\) | ||||
−0.575027 | + | 0.818135i | \(0.695008\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.88797 | −0.271635 | −0.135818 | − | 0.990734i | \(-0.543366\pi\) | ||||
−0.135818 | + | 0.990734i | \(0.543366\pi\) | |||||||
\(644\) | 4.86210 | 0.191594 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.80061 | 0.149533 | ||||||||
\(647\) | −2.96107 | −0.116412 | −0.0582058 | − | 0.998305i | \(-0.518538\pi\) | ||||
−0.0582058 | + | 0.998305i | \(0.518538\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.3063 | 1.42515 | ||||||||
\(650\) | −23.4256 | −0.918826 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.07477 | 0.159580 | ||||||||
\(653\) | −31.2447 | −1.22270 | −0.611350 | − | 0.791360i | \(-0.709373\pi\) | ||||
−0.611350 | + | 0.791360i | \(0.709373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −69.1517 | −2.70198 | ||||||||
\(656\) | 6.16755 | 0.240802 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.82647 | −0.110187 | ||||||||
\(659\) | 17.4557 | 0.679977 | 0.339989 | − | 0.940430i | \(-0.389577\pi\) | ||||
0.339989 | + | 0.940430i | \(0.389577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8896 | −0.501349 | −0.250674 | − | 0.968071i | \(-0.580652\pi\) | ||||
−0.250674 | + | 0.968071i | \(0.580652\pi\) | |||||||
\(662\) | −23.4896 | −0.912950 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.286603 | 0.0111223 | ||||||||
\(665\) | −1.12408 | −0.0435900 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.52157 | 0.252516 | ||||||||
\(668\) | −16.9797 | −0.656963 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.63372 | 0.256283 | ||||||||
\(671\) | 13.3307 | 0.514627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.0072 | −1.73490 | −0.867450 | − | 0.497525i | \(-0.834242\pi\) | ||||
−0.867450 | + | 0.497525i | \(0.834242\pi\) | |||||||
\(674\) | 10.2395 | 0.394410 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.2322 | −0.778160 | ||||||||
\(677\) | 24.0367 | 0.923806 | 0.461903 | − | 0.886931i | \(-0.347167\pi\) | ||||
0.461903 | + | 0.886931i | \(0.347167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.03957 | −0.116648 | ||||||||
\(680\) | 60.0576 | 2.30310 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −23.9142 | −0.915721 | ||||||||
\(683\) | −5.10700 | −0.195414 | −0.0977070 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977070 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50.0301 | −1.91155 | ||||||||
\(686\) | −4.48618 | −0.171283 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.13434 | 0.271994 | ||||||||
\(689\) | −63.7502 | −2.42869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.3702 | 1.53575 | 0.767877 | − | 0.640598i | \(-0.221313\pi\) | ||||
0.767877 | + | 0.640598i | \(0.221313\pi\) | |||||||
\(692\) | −35.3649 | −1.34437 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.69222 | 0.367912 | ||||||||
\(695\) | −66.8895 | −2.53726 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.9821 | −1.43868 | ||||||||
\(698\) | −7.04803 | −0.266772 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.21391 | −0.159271 | ||||||||
\(701\) | −5.21867 | −0.197106 | −0.0985532 | − | 0.995132i | \(-0.531421\pi\) | ||||
−0.0985532 | + | 0.995132i | \(0.531421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.148352 | −0.00559522 | ||||||||
\(704\) | −9.89839 | −0.373060 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.08798 | 0.304395 | ||||||||
\(707\) | 6.29996 | 0.236934 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1327 | −0.868765 | −0.434383 | − | 0.900728i | \(-0.643033\pi\) | ||||
−0.434383 | + | 0.900728i | \(0.643033\pi\) | |||||||
\(710\) | −21.5199 | −0.807627 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.2639 | 0.721944 | ||||||||
\(713\) | −46.2615 | −1.73251 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 90.5592 | 3.38672 | ||||||||
\(716\) | −1.97548 | −0.0738273 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.12409 | −0.340508 | ||||||||
\(719\) | −34.3541 | −1.28119 | −0.640597 | − | 0.767878i | \(-0.721313\pi\) | ||||
−0.640597 | + | 0.767878i | \(0.721313\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.702419 | −0.0261594 | ||||||||
\(722\) | −13.2883 | −0.494538 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.7790 | −0.623588 | ||||||||
\(725\) | −5.65215 | −0.209916 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.9315 | 1.36971 | 0.684857 | − | 0.728677i | \(-0.259865\pi\) | ||||
0.684857 | + | 0.728677i | \(0.259865\pi\) | |||||||
\(728\) | 5.84495 | 0.216628 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.51253 | 0.278051 | ||||||||
\(731\) | −43.9360 | −1.62503 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.3451 | 0.603718 | 0.301859 | − | 0.953353i | \(-0.402393\pi\) | ||||
0.301859 | + | 0.953353i | \(0.402393\pi\) | |||||||
\(734\) | −16.9621 | −0.626083 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −42.5072 | −1.56684 | ||||||||
\(737\) | −14.2976 | −0.526658 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.5073 | 0.570446 | 0.285223 | − | 0.958461i | \(-0.407932\pi\) | ||||
0.285223 | + | 0.958461i | \(0.407932\pi\) | |||||||
\(740\) | −0.997515 | −0.0366694 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.01503 | 0.147396 | ||||||||
\(743\) | 27.5884 | 1.01212 | 0.506059 | − | 0.862499i | \(-0.331102\pi\) | ||||
0.506059 | + | 0.862499i | \(0.331102\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.36155 | 0.123158 | ||||||||
\(746\) | −11.3688 | −0.416240 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −55.0787 | −2.01388 | ||||||||
\(749\) | 2.57771 | 0.0941876 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00340 | 0.0731050 | 0.0365525 | − | 0.999332i | \(-0.488362\pi\) | ||||
0.0365525 | + | 0.999332i | \(0.488362\pi\) | |||||||
\(752\) | −10.0578 | −0.366770 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.33595 | 0.121488 | ||||||||
\(755\) | −38.4993 | −1.40113 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.30957 | −0.265671 | −0.132835 | − | 0.991138i | \(-0.542408\pi\) | ||||
−0.132835 | + | 0.991138i | \(0.542408\pi\) | |||||||
\(758\) | −5.46809 | −0.198610 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.24161 | 0.226407 | ||||||||
\(761\) | −35.0825 | −1.27174 | −0.635870 | − | 0.771796i | \(-0.719359\pi\) | ||||
−0.635870 | + | 0.771796i | \(0.719359\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.271873 | −0.00984247 | ||||||||
\(764\) | 24.9846 | 0.903911 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.9907 | −0.433240 | ||||||||
\(767\) | 35.9265 | 1.29723 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.9301 | −1.62022 | −0.810111 | − | 0.586277i | \(-0.800593\pi\) | ||||
−0.810111 | + | 0.586277i | \(0.800593\pi\) | |||||||
\(770\) | −5.70347 | −0.205539 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.9203 | −0.680958 | ||||||||
\(773\) | −7.86001 | −0.282705 | −0.141353 | − | 0.989959i | \(-0.545145\pi\) | ||||
−0.141353 | + | 0.989959i | \(0.545145\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.0942 | 1.44023 | ||||||||
\(776\) | 16.8776 | 0.605870 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.6345 | −0.775634 | ||||||||
\(779\) | −3.94737 | −0.141429 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.3815 | 1.65966 | ||||||||
\(782\) | 37.3044 | 1.33400 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.86392 | −0.280854 | ||||||||
\(785\) | 30.3193 | 1.08214 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.7998 | −0.848373 | −0.424186 | − | 0.905575i | \(-0.639440\pi\) | ||||
−0.424186 | + | 0.905575i | \(0.639440\pi\) | |||||||
\(788\) | 29.6085 | 1.05476 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.48473 | −0.0528243 | ||||||||
\(791\) | 3.63164 | 0.129126 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.1913 | 0.468436 | ||||||||
\(794\) | 11.1889 | 0.397080 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34.3964 | 1.21915 | ||||||||
\(797\) | −25.2752 | −0.895295 | −0.447647 | − | 0.894210i | \(-0.647738\pi\) | ||||
−0.447647 | + | 0.894210i | \(0.647738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.9397 | 2.19127 | ||||||||
\(800\) | 36.8404 | 1.30250 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.3056 | 0.752325 | ||||||||
\(803\) | −16.1916 | −0.571391 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.0333 | −0.388872 | ||||||||
\(806\) | −23.6640 | −0.833529 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −34.9813 | −1.23064 | ||||||||
\(809\) | −23.0247 | −0.809505 | −0.404752 | − | 0.914426i | \(-0.632642\pi\) | ||||
−0.404752 | + | 0.914426i | \(0.632642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.4750 | 0.438058 | 0.219029 | − | 0.975718i | \(-0.429711\pi\) | ||||
0.219029 | + | 0.975718i | \(0.429711\pi\) | |||||||
\(812\) | 0.600089 | 0.0210590 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.752725 | −0.0263830 | ||||||||
\(815\) | −9.24664 | −0.323896 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.56614 | −0.159749 | ||||||||
\(818\) | −10.5079 | −0.367400 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.5420 | −0.926885 | ||||||||
\(821\) | 6.26577 | 0.218677 | 0.109338 | − | 0.994005i | \(-0.465127\pi\) | ||||
0.109338 | + | 0.994005i | \(0.465127\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.06515 | −0.315991 | −0.157996 | − | 0.987440i | \(-0.550503\pi\) | ||||
−0.157996 | + | 0.987440i | \(0.550503\pi\) | |||||||
\(824\) | 3.90027 | 0.135873 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.26267 | −0.0787284 | ||||||||
\(827\) | 10.2760 | 0.357331 | 0.178666 | − | 0.983910i | \(-0.442822\pi\) | ||||
0.178666 | + | 0.983910i | \(0.442822\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.4179 | −0.743874 | −0.371937 | − | 0.928258i | \(-0.621306\pi\) | ||||
−0.371937 | + | 0.928258i | \(0.621306\pi\) | |||||||
\(830\) | −0.276740 | −0.00960578 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.79484 | −0.339575 | ||||||||
\(833\) | 48.4291 | 1.67797 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.5309 | 1.33342 | ||||||||
\(836\) | −5.72417 | −0.197975 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.49584 | −0.224395 | ||||||||
\(839\) | −14.4573 | −0.499120 | −0.249560 | − | 0.968359i | \(-0.580286\pi\) | ||||
−0.249560 | + | 0.968359i | \(0.580286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1951 | −0.972245 | ||||||||
\(842\) | −4.88389 | −0.168310 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.9973 | −0.998128 | ||||||||
\(845\) | 45.9117 | 1.57941 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.32581 | 0.251718 | ||||||||
\(848\) | 14.2872 | 0.490624 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −32.3312 | −1.10895 | ||||||||
\(851\) | −1.45613 | −0.0499156 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.9262 | −0.579544 | −0.289772 | − | 0.957096i | \(-0.593579\pi\) | ||||
−0.289772 | + | 0.957096i | \(0.593579\pi\) | |||||||
\(854\) | −0.830796 | −0.0284292 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.3131 | −0.489212 | ||||||||
\(857\) | 27.3260 | 0.933440 | 0.466720 | − | 0.884405i | \(-0.345436\pi\) | ||||
0.466720 | + | 0.884405i | \(0.345436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.63516 | 0.0899106 | 0.0449553 | − | 0.998989i | \(-0.485685\pi\) | ||||
0.0449553 | + | 0.998989i | \(0.485685\pi\) | |||||||
\(860\) | −30.7025 | −1.04695 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.0602034 | 0.00205054 | ||||||||
\(863\) | −34.5485 | −1.17604 | −0.588022 | − | 0.808845i | \(-0.700093\pi\) | ||||
−0.588022 | + | 0.808845i | \(0.700093\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 80.2516 | 2.72864 | ||||||||
\(866\) | −7.62967 | −0.259267 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.25680 | −0.144485 | ||||||||
\(869\) | 3.20002 | 0.108553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.1480 | −0.479387 | ||||||||
\(872\) | 1.50961 | 0.0511219 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.87694 | 0.131140 | ||||||||
\(875\) | 1.97321 | 0.0667067 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.3766 | 1.43096 | 0.715479 | − | 0.698635i | \(-0.246209\pi\) | ||||
0.715479 | + | 0.698635i | \(0.246209\pi\) | |||||||
\(878\) | −18.0785 | −0.610119 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20.2954 | −0.684158 | ||||||||
\(881\) | −0.414494 | −0.0139646 | −0.00698232 | − | 0.999976i | \(-0.502223\pi\) | ||||
−0.00698232 | + | 0.999976i | \(0.502223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.4216 | 0.922810 | 0.461405 | − | 0.887190i | \(-0.347346\pi\) | ||||
0.461405 | + | 0.887190i | \(0.347346\pi\) | |||||||
\(884\) | −54.5025 | −1.83312 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.7177 | −0.897597 | ||||||||
\(887\) | 32.6899 | 1.09762 | 0.548809 | − | 0.835948i | \(-0.315081\pi\) | ||||
0.548809 | + | 0.835948i | \(0.315081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.23515 | 0.242659 | ||||||||
\(890\) | −18.6009 | −0.623505 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.0961 | 0.806799 | ||||||||
\(893\) | 6.43721 | 0.215413 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.48285 | 0.149845 | ||||||||
\(896\) | −4.66388 | −0.155809 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.9409 | 0.498586 | ||||||||
\(899\) | −5.70968 | −0.190428 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −87.9860 | −2.93124 | ||||||||
\(902\) | −20.0286 | −0.666878 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.1652 | −0.670684 | ||||||||
\(905\) | 38.0757 | 1.26568 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.5627 | 0.715977 | 0.357989 | − | 0.933726i | \(-0.383463\pi\) | ||||
0.357989 | + | 0.933726i | \(0.383463\pi\) | |||||||
\(908\) | 18.0491 | 0.598980 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.64381 | −0.187090 | ||||||||
\(911\) | −38.6529 | −1.28063 | −0.640314 | − | 0.768114i | \(-0.721196\pi\) | ||||
−0.640314 | + | 0.768114i | \(0.721196\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.596454 | 0.0197397 | ||||||||
\(914\) | 22.2485 | 0.735916 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.2523 | 0.570033 | ||||||||
\(917\) | −9.28854 | −0.306735 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.2187 | −0.633968 | −0.316984 | − | 0.948431i | \(-0.602670\pi\) | ||||
−0.316984 | + | 0.948431i | \(0.602670\pi\) | |||||||
\(920\) | 61.2637 | 2.01981 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.35242 | 0.275072 | ||||||||
\(923\) | 45.8963 | 1.51070 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.26201 | 0.0414946 | ||||||||
\(926\) | 21.2372 | 0.697898 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.24631 | −0.172219 | ||||||||
\(929\) | −28.3944 | −0.931591 | −0.465795 | − | 0.884892i | \(-0.654232\pi\) | ||||
−0.465795 | + | 0.884892i | \(0.654232\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.03309 | 0.164953 | ||||||||
\(932\) | 11.2523 | 0.368582 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.2375 | 0.727632 | ||||||||
\(935\) | 124.987 | 4.08751 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.3272 | −1.77479 | −0.887396 | − | 0.461007i | \(-0.847488\pi\) | ||||
−0.887396 | + | 0.461007i | \(0.847488\pi\) | |||||||
\(938\) | 0.891051 | 0.0290938 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 43.2835 | 1.41175 | ||||||||
\(941\) | 17.4042 | 0.567359 | 0.283680 | − | 0.958919i | \(-0.408445\pi\) | ||||
0.283680 | + | 0.958919i | \(0.408445\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.7449 | −1.26171 | ||||||||
\(944\) | −8.05155 | −0.262056 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.1681 | −0.753261 | ||||||||
\(947\) | 11.9576 | 0.388571 | 0.194285 | − | 0.980945i | \(-0.437761\pi\) | ||||
0.194285 | + | 0.980945i | \(0.437761\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.0223 | −0.520105 | ||||||||
\(950\) | −3.36009 | −0.109016 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.06702 | 0.261454 | ||||||||
\(953\) | 35.3150 | 1.14396 | 0.571982 | − | 0.820266i | \(-0.306175\pi\) | ||||
0.571982 | + | 0.820266i | \(0.306175\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −56.6960 | −1.83464 | ||||||||
\(956\) | −11.3781 | −0.367992 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.87268 | 0.0605035 | ||||||||
\(959\) | −6.72011 | −0.217004 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.50229 | 0.306526 | ||||||||
\(962\) | −0.744851 | −0.0240149 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.19333 | −0.296097 | ||||||||
\(965\) | 42.9348 | 1.38212 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.8426 | −1.50635 | −0.753177 | − | 0.657817i | \(-0.771480\pi\) | ||||
−0.753177 | + | 0.657817i | \(0.771480\pi\) | |||||||
\(968\) | −40.6776 | −1.30743 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.2968 | −0.523258 | ||||||||
\(971\) | −40.1836 | −1.28955 | −0.644776 | − | 0.764371i | \(-0.723050\pi\) | ||||
−0.644776 | + | 0.764371i | \(0.723050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.98469 | −0.288036 | ||||||||
\(974\) | −0.769130 | −0.0246445 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.95633 | −0.0946297 | ||||||||
\(977\) | −45.5671 | −1.45782 | −0.728911 | − | 0.684609i | \(-0.759973\pi\) | ||||
−0.728911 | + | 0.684609i | \(0.759973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.0903 | 1.28129 | ||||||||
\(980\) | 33.8423 | 1.08105 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 28.7416 | 0.917182 | ||||||||
\(983\) | −60.9266 | −1.94326 | −0.971628 | − | 0.236514i | \(-0.923995\pi\) | ||||
−0.971628 | + | 0.236514i | \(0.923995\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −67.1887 | −2.14081 | ||||||||
\(986\) | 4.60418 | 0.146627 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.66429 | −0.180205 | ||||||||
\(989\) | −44.8184 | −1.42514 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.5041 | 0.587803 | 0.293902 | − | 0.955836i | \(-0.405046\pi\) | ||||
0.293902 | + | 0.955836i | \(0.405046\pi\) | |||||||
\(992\) | 37.2153 | 1.18159 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.89058 | −0.0916837 | ||||||||
\(995\) | −78.0538 | −2.47447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.3876 | −1.12074 | −0.560369 | − | 0.828243i | \(-0.689341\pi\) | ||||
−0.560369 | + | 0.828243i | \(0.689341\pi\) | |||||||
\(998\) | −24.0481 | −0.761231 | ||||||||
\(999\) | 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 | 1341.2.a.d.1.7 | 9 | ||
3.2 | odd | 2 | 447.2.a.c.1.3 | ✓ | 9 | ||
12.11 | even | 2 | 7152.2.a.z.1.1 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
447.2.a.c.1.3 | ✓ | 9 | 3.2 | odd | 2 | ||
1341.2.a.d.1.7 | 9 | 1.1 | even | 1 | trivial | ||
7152.2.a.z.1.1 | 9 | 12.11 | even | 2 |