Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + 4748 x^{12} - 40524 x^{11} - 220 x^{10} + 82500 x^{9} - 21992 x^{8} - 84720 x^{7} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.45978\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.45978 | −1.42016 | −0.710078 | − | 0.704123i | \(-0.751340\pi\) | ||||
−0.710078 | + | 0.704123i | \(0.751340\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.10149 | −0.939816 | −0.469908 | − | 0.882716i | \(-0.655713\pi\) | ||||
−0.469908 | + | 0.882716i | \(0.655713\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.05053 | 1.01684 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.99553 | −0.903186 | −0.451593 | − | 0.892224i | \(-0.649144\pi\) | ||||
−0.451593 | + | 0.892224i | \(0.649144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.922682 | 0.255906 | 0.127953 | − | 0.991780i | \(-0.459159\pi\) | ||||
0.127953 | + | 0.991780i | \(0.459159\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.16921 | 1.33469 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.22399 | 1.50954 | 0.754770 | − | 0.655990i | \(-0.227749\pi\) | ||||
0.754770 | + | 0.655990i | \(0.227749\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.64918 | 1.52543 | 0.762713 | − | 0.646737i | \(-0.223867\pi\) | ||||
0.762713 | + | 0.646737i | \(0.223867\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.34110 | −1.32221 | −0.661106 | − | 0.750293i | \(-0.729912\pi\) | ||||
−0.661106 | + | 0.750293i | \(0.729912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.583733 | −0.116747 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.124300 | −0.0239215 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.64093 | −0.304712 | −0.152356 | − | 0.988326i | \(-0.548686\pi\) | ||||
−0.152356 | + | 0.988326i | \(0.548686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00257 | 0.539278 | 0.269639 | − | 0.962961i | \(-0.413096\pi\) | ||||
0.269639 | + | 0.962961i | \(0.413096\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.36835 | 1.28267 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.04669 | 1.48727 | 0.743634 | − | 0.668587i | \(-0.233101\pi\) | ||||
0.743634 | + | 0.668587i | \(0.233101\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.26960 | −0.363426 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.65476 | 1.16734 | 0.583670 | − | 0.811991i | \(-0.301616\pi\) | ||||
0.583670 | + | 0.811991i | \(0.301616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.41067 | −0.955646 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.66681 | −0.972454 | −0.486227 | − | 0.873833i | \(-0.661627\pi\) | ||||
−0.486227 | + | 0.873833i | \(0.661627\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.3097 | −2.14378 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.74187 | −1.06343 | −0.531714 | − | 0.846924i | \(-0.678452\pi\) | ||||
−0.531714 | + | 0.846924i | \(0.678452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.29508 | 0.848829 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.3555 | −2.16634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.3223 | −1.73442 | −0.867209 | − | 0.497944i | \(-0.834089\pi\) | ||||
−0.867209 | + | 0.497944i | \(0.834089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.83873 | 1.25972 | 0.629860 | − | 0.776708i | \(-0.283112\pi\) | ||||
0.629860 | + | 0.776708i | \(0.283112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.93901 | −0.240504 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.26139 | −1.00929 | −0.504644 | − | 0.863327i | \(-0.668376\pi\) | ||||
−0.504644 | + | 0.863327i | \(0.668376\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.5977 | 1.87775 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.01924 | −0.358317 | −0.179159 | − | 0.983820i | \(-0.557338\pi\) | ||||
−0.179159 | + | 0.983820i | \(0.557338\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.5270 | −1.93434 | −0.967170 | − | 0.254130i | \(-0.918211\pi\) | ||||
−0.967170 | + | 0.254130i | \(0.918211\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.43586 | 0.165799 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.193471 | 0.0217672 | 0.0108836 | − | 0.999941i | \(-0.496536\pi\) | ||||
0.0108836 | + | 0.999941i | \(0.496536\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.84585 | −0.982872 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.85504 | 0.203618 | 0.101809 | − | 0.994804i | \(-0.467537\pi\) | ||||
0.101809 | + | 0.994804i | \(0.467537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.0797 | −1.41869 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.03632 | 0.432739 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.02262 | 0.108397 | 0.0541986 | − | 0.998530i | \(-0.482740\pi\) | ||||
0.0541986 | + | 0.998530i | \(0.482740\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.38568 | −0.765859 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.9732 | −1.43362 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.5072 | 1.77759 | 0.888794 | − | 0.458306i | \(-0.151544\pi\) | ||||
0.888794 | + | 0.458306i | \(0.151544\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.13796 | −0.918400 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3992 | 1.23376 | 0.616882 | − | 0.787055i | \(-0.288395\pi\) | ||||
0.616882 | + | 0.787055i | \(0.288395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7268 | 1.25401 | 0.627003 | − | 0.779017i | \(-0.284281\pi\) | ||||
0.627003 | + | 0.779017i | \(0.284281\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.91995 | −0.475630 | −0.237815 | − | 0.971311i | \(-0.576431\pi\) | ||||
−0.237815 | + | 0.971311i | \(0.576431\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.01906 | −0.863870 | −0.431935 | − | 0.901905i | \(-0.642169\pi\) | ||||
−0.431935 | + | 0.901905i | \(0.642169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.2529 | −2.11215 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0393302 | 0.00369988 | 0.00184994 | − | 0.999998i | \(-0.499411\pi\) | ||||
0.00184994 | + | 0.999998i | \(0.499411\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.3258 | 1.24263 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.81467 | 0.260216 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.02680 | −0.184255 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.45978 | 0.221791 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7342 | 1.04954 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.19318 | −0.372085 | −0.186042 | − | 0.982542i | \(-0.559566\pi\) | ||||
−0.186042 | + | 0.982542i | \(0.559566\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.8291 | −1.65781 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.2344 | −1.85525 | −0.927627 | − | 0.373507i | \(-0.878155\pi\) | ||||
−0.927627 | + | 0.373507i | \(0.878155\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.261215 | 0.0224818 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.642660 | 0.0549061 | 0.0274531 | − | 0.999623i | \(-0.491260\pi\) | ||||
0.0274531 | + | 0.999623i | \(0.491260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.63836 | 0.138964 | 0.0694818 | − | 0.997583i | \(-0.477865\pi\) | ||||
0.0694818 | + | 0.997583i | \(0.477865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.3989 | 1.38104 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.76392 | −0.231131 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.44839 | 0.286373 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.58039 | 0.702933 | 0.351467 | − | 0.936200i | \(-0.385683\pi\) | ||||
0.351467 | + | 0.936200i | \(0.385683\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.84431 | 0.556982 | 0.278491 | − | 0.960439i | \(-0.410166\pi\) | ||||
0.278491 | + | 0.960439i | \(0.410166\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.9865 | 1.53497 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.30988 | −0.506822 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.23915 | 0.737364 | 0.368682 | − | 0.929556i | \(-0.379809\pi\) | ||||
0.368682 | + | 0.929556i | \(0.379809\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.0433 | 1.51023 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7674 | 0.921697 | 0.460848 | − | 0.887479i | \(-0.347545\pi\) | ||||
0.460848 | + | 0.887479i | \(0.347545\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.4845 | −1.20547 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.24447 | −0.328447 | −0.164224 | − | 0.986423i | \(-0.552512\pi\) | ||||
−0.164224 | + | 0.986423i | \(0.552512\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1487 | −0.934512 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.2835 | 1.55112 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.5768 | −1.79251 | −0.896256 | − | 0.443537i | \(-0.853724\pi\) | ||||
−0.896256 | + | 0.443537i | \(0.853724\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.7700 | 2.46315 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.94971 | −0.295215 | −0.147608 | − | 0.989046i | \(-0.547157\pi\) | ||||
−0.147608 | + | 0.989046i | \(0.547157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1826 | 0.905523 | 0.452762 | − | 0.891632i | \(-0.350439\pi\) | ||||
0.452762 | + | 0.891632i | \(0.350439\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.2012 | −1.78900 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.0115 | −1.39776 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.6442 | −1.36340 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.7774 | −0.779823 | −0.389911 | − | 0.920852i | \(-0.627494\pi\) | ||||
−0.389911 | + | 0.920852i | \(0.627494\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.7731 | −1.71122 | −0.855612 | − | 0.517618i | \(-0.826819\pi\) | ||||
−0.855612 | + | 0.517618i | \(0.826819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.76954 | 0.341554 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.3119 | 0.805940 | 0.402970 | − | 0.915213i | \(-0.367978\pi\) | ||||
0.402970 | + | 0.915213i | \(0.367978\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.50514 | −0.177585 | −0.0887924 | − | 0.996050i | \(-0.528301\pi\) | ||||
−0.0887924 | + | 0.996050i | \(0.528301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.3212 | 1.43335 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.10149 | 0.146775 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.3437 | −1.34448 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.9178 | −1.37774 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0504 | 1.17380 | 0.586898 | − | 0.809661i | \(-0.300349\pi\) | ||||
0.586898 | + | 0.809661i | \(0.300349\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.42667 | 0.508867 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0864 | −1.09708 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 40.6529 | 2.74707 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.74276 | 0.386300 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.1839 | −1.88734 | −0.943668 | − | 0.330894i | \(-0.892650\pi\) | ||||
−0.943668 | + | 0.330894i | \(0.892650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.78070 | −0.118713 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.8695 | 0.787810 | 0.393905 | − | 0.919151i | \(-0.371124\pi\) | ||||
0.393905 | + | 0.919151i | \(0.371124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.8424 | −1.31122 | −0.655611 | − | 0.755099i | \(-0.727589\pi\) | ||||
−0.655611 | + | 0.755099i | \(0.727589\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.4298 | 0.748792 | 0.374396 | − | 0.927269i | \(-0.377850\pi\) | ||||
0.374396 | + | 0.927269i | \(0.377850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.0102 | 0.913927 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.475897 | −0.0309128 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.81103 | 0.311199 | 0.155600 | − | 0.987820i | \(-0.450269\pi\) | ||||
0.155600 | + | 0.987820i | \(0.450269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1967 | −0.656825 | −0.328413 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328413 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1318 | 1.41975 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.13507 | 0.390365 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.56301 | −0.289169 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.18649 | −0.201129 | −0.100565 | − | 0.994931i | \(-0.532065\pi\) | ||||
−0.100565 | + | 0.994931i | \(0.532065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.9950 | 1.19420 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32.1731 | 2.01476 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.6691 | 1.47643 | 0.738217 | − | 0.674563i | \(-0.235668\pi\) | ||||
0.738217 | + | 0.674563i | \(0.235668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00570 | −0.309845 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.5035 | −1.07931 | −0.539655 | − | 0.841887i | \(-0.681445\pi\) | ||||
−0.539655 | + | 0.841887i | \(0.681445\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.2695 | 0.999426 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.51541 | −0.153941 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.3533 | 1.48485 | 0.742425 | − | 0.669929i | \(-0.233676\pi\) | ||||
0.742425 | + | 0.669929i | \(0.233676\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.21685 | 0.377647 | 0.188823 | − | 0.982011i | \(-0.439533\pi\) | ||||
0.188823 | + | 0.982011i | \(0.439533\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.74859 | 0.105444 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.77913 | −0.166982 | −0.0834908 | − | 0.996509i | \(-0.526607\pi\) | ||||
−0.0834908 | + | 0.996509i | \(0.526607\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.15945 | 0.548362 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.2802 | 1.26947 | 0.634736 | − | 0.772729i | \(-0.281109\pi\) | ||||
0.634736 | + | 0.772729i | \(0.281109\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5832 | −0.985771 | −0.492886 | − | 0.870094i | \(-0.664058\pi\) | ||||
−0.492886 | + | 0.870094i | \(0.664058\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 34.3710 | 2.03596 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.7381 | 1.27871 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −43.0640 | −2.52445 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.44832 | −0.435135 | −0.217568 | − | 0.976045i | \(-0.569812\pi\) | ||||
−0.217568 | + | 0.976045i | \(0.569812\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.9968 | 1.63003 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.372344 | 0.0216056 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.85082 | −0.338362 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −30.4993 | −1.75214 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.6760 | −1.18391 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2722 | 0.928703 | 0.464351 | − | 0.885651i | \(-0.346287\pi\) | ||||
0.464351 | + | 0.885651i | \(0.346287\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31.3051 | −1.78088 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.1922 | 0.974882 | 0.487441 | − | 0.873156i | \(-0.337930\pi\) | ||||
0.487441 | + | 0.873156i | \(0.337930\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.4997 | 1.44133 | 0.720665 | − | 0.693283i | \(-0.243837\pi\) | ||||
0.720665 | + | 0.693283i | \(0.243837\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.5574 | 0.592964 | 0.296482 | − | 0.955038i | \(-0.404186\pi\) | ||||
0.296482 | + | 0.955038i | \(0.404186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.91544 | 0.275212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.1020 | 0.675469 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.3844 | 2.30269 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.538600 | −0.0298762 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.1849 | 1.22683 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.40506 | 0.461984 | 0.230992 | − | 0.972956i | \(-0.425803\pi\) | ||||
0.230992 | + | 0.972956i | \(0.425803\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.5972 | 1.51232 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.3612 | 0.948545 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1490 | 0.661798 | 0.330899 | − | 0.943666i | \(-0.392648\pi\) | ||||
0.330899 | + | 0.943666i | \(0.392648\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0967438 | −0.00525440 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.99430 | −0.487069 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −32.7785 | −1.76474 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.65522 | 0.303588 | 0.151794 | − | 0.988412i | \(-0.451495\pi\) | ||||
0.151794 | + | 0.988412i | \(0.451495\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.5239 | 0.723917 | 0.361959 | − | 0.932194i | \(-0.382108\pi\) | ||||
0.361959 | + | 0.932194i | \(0.382108\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.114689 | −0.00612166 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.9341 | 1.38033 | 0.690165 | − | 0.723652i | \(-0.257538\pi\) | ||||
0.690165 | + | 0.723652i | \(0.257538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.34490 | 0.336752 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.31446 | 0.333265 | 0.166632 | − | 0.986019i | \(-0.446711\pi\) | ||||
0.166632 | + | 0.986019i | \(0.446711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.2115 | 1.32692 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.98549 | 0.261670 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.7314 | 1.81792 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.45266 | 0.232427 | 0.116213 | − | 0.993224i | \(-0.462924\pi\) | ||||
0.116213 | + | 0.993224i | \(0.462924\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.05053 | −0.158804 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.9550 | −1.91346 | −0.956728 | − | 0.290983i | \(-0.906018\pi\) | ||||
−0.956728 | + | 0.290983i | \(0.906018\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.8635 | −1.49051 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.51405 | −0.0779777 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6482 | 0.906527 | 0.453263 | − | 0.891377i | \(-0.350260\pi\) | ||||
0.453263 | + | 0.891377i | \(0.350260\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.3143 | 0.528418 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.4077 | −1.86035 | −0.930174 | − | 0.367119i | \(-0.880344\pi\) | ||||
−0.930174 | + | 0.367119i | \(0.880344\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.3511 | 1.18700 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.9868 | 1.06407 | 0.532035 | − | 0.846722i | \(-0.321427\pi\) | ||||
0.532035 | + | 0.846722i | \(0.321427\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.4670 | −1.99593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 52.2319 | 2.63475 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.406578 | −0.0204572 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.5486 | 1.28225 | 0.641123 | − | 0.767438i | \(-0.278469\pi\) | ||||
0.641123 | + | 0.767438i | \(0.278469\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.6613 | 1.48121 | 0.740607 | − | 0.671938i | \(-0.234538\pi\) | ||||
0.740607 | + | 0.671938i | \(0.234538\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.77042 | 0.138004 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.5895 | 0.923718 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.0996 | −1.34328 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.74246 | −0.234499 | −0.117250 | − | 0.993102i | \(-0.537408\pi\) | ||||
−0.117250 | + | 0.993102i | \(0.537408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.58080 | −0.0779753 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.89836 | −0.191363 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.03000 | −0.197350 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.3836 | 0.702685 | 0.351342 | − | 0.936247i | \(-0.385725\pi\) | ||||
0.351342 | + | 0.936247i | \(0.385725\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.89043 | −0.482030 | −0.241015 | − | 0.970521i | \(-0.577480\pi\) | ||||
−0.241015 | + | 0.970521i | \(0.577480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.3373 | −0.988834 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.63315 | −0.176234 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.79865 | 0.328242 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.1907 | 0.635375 | 0.317688 | − | 0.948195i | \(-0.397094\pi\) | ||||
0.317688 | + | 0.948195i | \(0.397094\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.8403 | −0.905406 | −0.452703 | − | 0.891661i | \(-0.649540\pi\) | ||||
−0.452703 | + | 0.891661i | \(0.649540\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.48230 | −0.406695 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −42.1631 | −2.01693 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2902 | −0.777487 | −0.388743 | − | 0.921346i | \(-0.627091\pi\) | ||||
−0.388743 | + | 0.921346i | \(0.627091\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.7111 | 1.41162 | 0.705809 | − | 0.708402i | \(-0.250584\pi\) | ||||
0.705809 | + | 0.708402i | \(0.250584\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.14902 | −0.101873 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.1059 | −0.998275 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.26145 | 0.106724 | 0.0533622 | − | 0.998575i | \(-0.483006\pi\) | ||||
0.0533622 | + | 0.998575i | \(0.483006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.99553 | 0.141054 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.8355 | −0.791002 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.65074 | −0.264330 | −0.132165 | − | 0.991228i | \(-0.542193\pi\) | ||||
−0.132165 | + | 0.991228i | \(0.542193\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.773642 | −0.0361105 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.1407 | −0.705171 | −0.352585 | − | 0.935780i | \(-0.614697\pi\) | ||||
−0.352585 | + | 0.935780i | \(0.614697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.3527 | −1.59650 | −0.798252 | − | 0.602324i | \(-0.794242\pi\) | ||||
−0.798252 | + | 0.602324i | \(0.794242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.5209 | 0.719766 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.7199 | 1.42155 | 0.710773 | − | 0.703421i | \(-0.248345\pi\) | ||||
0.710773 | + | 0.703421i | \(0.248345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.7263 | −1.04717 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.9301 | −1.05433 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.88135 | −0.178088 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.6168 | −1.08134 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.91797 | −0.453163 | −0.226582 | − | 0.973992i | \(-0.572755\pi\) | ||||
−0.226582 | + | 0.973992i | \(0.572755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.34722 | 0.380600 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −36.7913 | −1.67061 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.95675 | 0.315240 | 0.157620 | − | 0.987500i | \(-0.449618\pi\) | ||||
0.157620 | + | 0.987500i | \(0.449618\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.9453 | −1.30895 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.26318 | −0.282653 | −0.141327 | − | 0.989963i | \(-0.545137\pi\) | ||||
−0.141327 | + | 0.989963i | \(0.545137\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2131 | −0.459975 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.2034 | 0.863126 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.9396 | −0.534491 | −0.267246 | − | 0.963628i | \(-0.586113\pi\) | ||||
−0.267246 | + | 0.963628i | \(0.586113\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4405 | 0.466447 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.4862 | −0.556731 | −0.278366 | − | 0.960475i | \(-0.589793\pi\) | ||||
−0.278366 | + | 0.960475i | \(0.589793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.0568 | −1.15951 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.8831 | 1.32715 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.0082 | 1.55171 | 0.775856 | − | 0.630910i | \(-0.217318\pi\) | ||||
0.775856 | + | 0.630910i | \(0.217318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.826492 | −0.0364905 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.7452 | −1.17853 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.9706 | 0.878307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.9939 | 2.54565 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.3464 | 1.32950 | 0.664749 | − | 0.747067i | \(-0.268538\pi\) | ||||
0.664749 | + | 0.747067i | \(0.268538\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.2273 | −1.54038 | −0.770191 | − | 0.637813i | \(-0.779839\pi\) | ||||
−0.770191 | + | 0.637813i | \(0.779839\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.6880 | 0.814062 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.2096 | 0.748243 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −40.6402 | −1.76363 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.922682 | −0.0399658 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.3392 | 0.447004 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.71544 | 0.419252 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.5207 | 1.48416 | 0.742079 | − | 0.670312i | \(-0.233840\pi\) | ||||
0.742079 | + | 0.670312i | \(0.233840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.9665 | −1.28598 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.9535 | 0.811878 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.86234 | 0.0796281 | 0.0398141 | − | 0.999207i | \(-0.487323\pi\) | ||||
0.0398141 | + | 0.999207i | \(0.487323\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.0134 | 1.28094 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9108 | −0.464816 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 46.7643 | 1.98503 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.47891 | 0.316892 | 0.158446 | − | 0.987368i | \(-0.449352\pi\) | ||||
0.158446 | + | 0.987368i | \(0.449352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.06291 | 0.298729 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 45.8606 | 1.93623 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.4596 | 1.36801 | 0.684005 | − | 0.729477i | \(-0.260237\pi\) | ||||
0.684005 | + | 0.729477i | \(0.260237\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0826521 | −0.00347720 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.6801 | −1.49579 | −0.747894 | − | 0.663819i | \(-0.768935\pi\) | ||||
−0.747894 | + | 0.663819i | \(0.768935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.06761 | 0.379468 | 0.189734 | − | 0.981836i | \(-0.439237\pi\) | ||||
0.189734 | + | 0.981836i | \(0.439237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.5100 | 1.10747 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.70151 | 0.154364 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.1045 | −0.545548 | −0.272774 | − | 0.962078i | \(-0.587941\pi\) | ||||
−0.272774 | + | 0.962078i | \(0.587941\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 58.4766 | 2.43021 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.1910 | 0.960474 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.91501 | −0.244555 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.7207 | −1.43308 | −0.716538 | − | 0.697548i | \(-0.754274\pi\) | ||||
−0.716538 | + | 0.697548i | \(0.754274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.9646 | 0.822629 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.8248 | −1.14456 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.944182 | 0.0387729 | 0.0193864 | − | 0.999812i | \(-0.493829\pi\) | ||||
0.0193864 | + | 0.999812i | \(0.493829\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.16211 | 0.252198 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.72293 | −0.397268 | −0.198634 | − | 0.980074i | \(-0.563651\pi\) | ||||
−0.198634 | + | 0.980074i | \(0.563651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.61321 | 0.106595 | 0.0532976 | − | 0.998579i | \(-0.483027\pi\) | ||||
0.0532976 | + | 0.998579i | \(0.483027\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.2016 | −1.02629 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.25930 | 0.173165 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.08841 | −0.247121 | −0.123560 | − | 0.992337i | \(-0.539431\pi\) | ||||
−0.123560 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.15134 | −0.248857 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.42610 | −0.0979894 | −0.0489947 | − | 0.998799i | \(-0.515602\pi\) | ||||
−0.0489947 | + | 0.998799i | \(0.515602\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.16921 | −0.208443 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.75936 | 0.111087 | 0.0555437 | − | 0.998456i | \(-0.482311\pi\) | ||||
0.0555437 | + | 0.998456i | \(0.482311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.0572 | 1.40907 | 0.704534 | − | 0.709670i | \(-0.251156\pi\) | ||||
0.704534 | + | 0.709670i | \(0.251156\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.788199 | 0.0316293 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.7406 | −0.869624 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 48.9935 | 1.95661 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 56.3065 | 2.24509 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.2717 | −1.00605 | −0.503026 | − | 0.864271i | \(-0.667780\pi\) | ||||
−0.503026 | + | 0.864271i | \(0.667780\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −41.9402 | −1.66697 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.81193 | 0.349691 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.21028 | −0.364353 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.47393 | 0.176710 | 0.0883548 | − | 0.996089i | \(-0.471839\pi\) | ||||
0.0883548 | + | 0.996089i | \(0.471839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.3398 | 1.23592 | 0.617961 | − | 0.786209i | \(-0.287959\pi\) | ||||
0.617961 | + | 0.786209i | \(0.287959\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 39.5691 | 1.55803 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.1114 | 1.10518 | 0.552588 | − | 0.833455i | \(-0.313640\pi\) | ||||
0.552588 | + | 0.833455i | \(0.313640\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.9074 | 1.56650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.97196 | 0.194568 | 0.0972839 | − | 0.995257i | \(-0.468985\pi\) | ||||
0.0972839 | + | 0.995257i | \(0.468985\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.6238 | 1.74360 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −50.4162 | −1.96692 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.9246 | −0.893014 | −0.446507 | − | 0.894780i | \(-0.647332\pi\) | ||||
−0.446507 | + | 0.894780i | \(0.647332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.1921 | 1.75777 | 0.878884 | − | 0.477036i | \(-0.158289\pi\) | ||||
0.878884 | + | 0.477036i | \(0.158289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.1260 | −0.548607 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4053 | 0.402894 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 69.3264 | 2.68031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.4722 | −1.13776 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.6558 | 1.83700 | 0.918498 | − | 0.395426i | \(-0.129403\pi\) | ||||
0.918498 | + | 0.395426i | \(0.129403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.0725580 | 0.00279276 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.8310 | 0.416270 | 0.208135 | − | 0.978100i | \(-0.433261\pi\) | ||||
0.208135 | + | 0.978100i | \(0.433261\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.1965 | −1.11881 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.1592 | −0.541787 | −0.270893 | − | 0.962609i | \(-0.587319\pi\) | ||||
−0.270893 | + | 0.962609i | \(0.587319\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.35054 | −0.0516016 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 48.8080 | 1.86214 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.14329 | −0.272138 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.50530 | 0.0953061 | 0.0476530 | − | 0.998864i | \(-0.484826\pi\) | ||||
0.0476530 | + | 0.998864i | \(0.484826\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.44299 | −0.130600 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.22399 | −0.235750 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.1149 | −1.06340 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.8134 | −0.446185 | −0.223092 | − | 0.974797i | \(-0.571615\pi\) | ||||
−0.223092 | + | 0.974797i | \(0.571615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.1531 | 2.26872 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.4622 | −1.29792 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.5103 | 0.995614 | 0.497807 | − | 0.867288i | \(-0.334139\pi\) | ||||
0.497807 | + | 0.867288i | \(0.334139\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.590190 | 0.0221339 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.0396 | −0.713040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.80836 | 0.217220 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.8341 | −0.441952 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.0081 | −0.634294 | −0.317147 | − | 0.948376i | \(-0.602725\pi\) | ||||
−0.317147 | + | 0.948376i | \(0.602725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.0816 | 0.932794 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.957864 | 0.0355742 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.07621 | −0.0770025 | −0.0385013 | − | 0.999259i | \(-0.512258\pi\) | ||||
−0.0385013 | + | 0.999259i | \(0.512258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.9018 | −1.03340 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.6432 | 1.76215 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.9911 | −1.18162 | −0.590808 | − | 0.806812i | \(-0.701191\pi\) | ||||
−0.590808 | + | 0.806812i | \(0.701191\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.7472 | 0.911576 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3436 | 0.380494 | 0.190247 | − | 0.981736i | \(-0.439071\pi\) | ||||
0.190247 | + | 0.981736i | \(0.439071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.0910 | −0.554380 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2982 | 0.891415 | 0.445707 | − | 0.895179i | \(-0.352952\pi\) | ||||
0.445707 | + | 0.895179i | \(0.352952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0316 | −0.660628 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.65887 | 0.207047 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.0572 | 1.35224 | 0.676118 | − | 0.736793i | \(-0.263661\pi\) | ||||
0.676118 | + | 0.736793i | \(0.263661\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.83807 | 0.285635 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.3833 | −0.523460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8750 | 0.686023 | 0.343011 | − | 0.939331i | \(-0.388553\pi\) | ||||
0.343011 | + | 0.939331i | \(0.388553\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −46.7235 | −1.69596 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.3925 | 0.847978 | 0.423989 | − | 0.905667i | \(-0.360630\pi\) | ||||
0.423989 | + | 0.905667i | \(0.360630\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −39.8999 | −1.44259 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.2923 | −0.443848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.63351 | 0.0589060 | 0.0294530 | − | 0.999566i | \(-0.490623\pi\) | ||||
0.0294530 | + | 0.999566i | \(0.490623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −58.2207 | −2.09677 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.51626 | 0.198406 | 0.0992031 | − | 0.995067i | \(-0.468371\pi\) | ||||
0.0992031 | + | 0.995067i | \(0.468371\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.75270 | −0.0629589 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.64918 | −0.238231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.04421 | 0.323627 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.203967 | 0.00728919 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.4160 | −0.692986 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.7979 | 1.88204 | 0.941022 | − | 0.338347i | \(-0.109868\pi\) | ||||
0.941022 | + | 0.338347i | \(0.109868\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 43.0547 | 1.53279 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.07802 | 0.322370 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −40.0194 | −1.41934 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.4437 | −1.36174 | −0.680872 | − | 0.732402i | \(-0.738399\pi\) | ||||
−0.680872 | + | 0.732402i | \(0.738399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.4942 | −1.46796 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.11953 | 0.110223 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 49.5072 | 1.74707 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −59.9039 | −2.10872 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.92193 | 0.313678 | 0.156839 | − | 0.987624i | \(-0.449870\pi\) | ||||
0.156839 | + | 0.987624i | \(0.449870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.1790 | 0.533006 | 0.266503 | − | 0.963834i | \(-0.414132\pi\) | ||||
0.266503 | + | 0.963834i | \(0.414132\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.2921 | −0.536318 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.7292 | −0.866225 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.8979 | 1.78069 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.8558 | 1.14668 | 0.573338 | − | 0.819319i | \(-0.305648\pi\) | ||||
0.573338 | + | 0.819319i | \(0.305648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.8271 | −0.865418 | −0.432709 | − | 0.901534i | \(-0.642442\pi\) | ||||
−0.432709 | + | 0.901534i | \(0.642442\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.30116 | −0.149747 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.9638 | 1.63309 | 0.816546 | − | 0.577281i | \(-0.195886\pi\) | ||||
0.816546 | + | 0.577281i | \(0.195886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.7377 | 0.754982 | 0.377491 | − | 0.926013i | \(-0.376787\pi\) | ||||
0.377491 | + | 0.926013i | \(0.376787\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.83605 | 0.237140 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.91973 | 0.308680 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.373220 | −0.0129004 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.7400 | −1.71722 | −0.858608 | − | 0.512632i | \(-0.828670\pi\) | ||||
−0.858608 | + | 0.512632i | \(0.828670\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3074 | −0.907150 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −52.3448 | −1.80285 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.5303 | 0.878269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.7912 | 1.39995 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −57.3660 | −1.96648 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.1076 | 0.585753 | 0.292876 | − | 0.956150i | \(-0.405388\pi\) | ||||
0.292876 | + | 0.956150i | \(0.405388\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −42.6257 | −1.45777 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.6162 | −0.840873 | −0.420437 | − | 0.907322i | \(-0.638123\pi\) | ||||
−0.420437 | + | 0.907322i | \(0.638123\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.5001 | −1.10889 | −0.554445 | − | 0.832220i | \(-0.687069\pi\) | ||||
−0.554445 | + | 0.832220i | \(0.687069\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.6514 | −0.839143 | −0.419572 | − | 0.907722i | \(-0.637820\pi\) | ||||
−0.419572 | + | 0.907722i | \(0.637820\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.5465 | 1.68463 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −53.4709 | −1.81597 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.579548 | −0.0196598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.62263 | −0.258283 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 53.4063 | 1.80753 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.9313 | 1.88867 | 0.944333 | − | 0.328991i | \(-0.106709\pi\) | ||||
0.944333 | + | 0.328991i | \(0.106709\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.3212 | 0.617960 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.22704 | −0.142413 | −0.0712064 | − | 0.997462i | \(-0.522685\pi\) | ||||
−0.0712064 | + | 0.997462i | \(0.522685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.46057 | −0.318374 | −0.159187 | − | 0.987248i | \(-0.550887\pi\) | ||||
−0.159187 | + | 0.987248i | \(0.550887\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −68.8659 | −2.31490 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.4890 | −0.620800 | −0.310400 | − | 0.950606i | \(-0.600463\pi\) | ||||
−0.310400 | + | 0.950606i | \(0.600463\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.4980 | 0.887717 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −44.3288 | −1.48341 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.30029 | 0.277448 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.3917 | 0.480527 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.92700 | −0.164325 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.1854 | −1.60529 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.6016 | −0.851025 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −56.4241 | −1.87353 | −0.936766 | − | 0.349955i | \(-0.886197\pi\) | ||||
−0.936766 | + | 0.349955i | \(0.886197\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.8241 | 1.25455 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.9011 | 0.394300 | 0.197150 | − | 0.980373i | \(-0.436831\pi\) | ||||
0.197150 | + | 0.980373i | \(0.436831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.55684 | −0.183905 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 50.8585 | 1.68133 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.13243 | 0.301251 | 0.150626 | − | 0.988591i | \(-0.451871\pi\) | ||||
0.150626 | + | 0.988591i | \(0.451871\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −40.0261 | −1.31890 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.78579 | −0.0916955 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.28086 | −0.173634 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.8234 | 1.27513 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.42592 | 0.112401 | 0.0562003 | − | 0.998420i | \(-0.482101\pi\) | ||||
0.0562003 | + | 0.998420i | \(0.482101\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.2892 | −1.38449 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.1805 | 1.28134 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.9422 | 1.33752 | 0.668761 | − | 0.743477i | \(-0.266825\pi\) | ||||
0.668761 | + | 0.743477i | \(0.266825\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −62.7238 | −2.04691 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.97770 | −0.0644712 | −0.0322356 | − | 0.999480i | \(-0.510263\pi\) | ||||
−0.0322356 | + | 0.999480i | \(0.510263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.34110 | 0.206495 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.4560 | 0.827207 | 0.413604 | − | 0.910457i | \(-0.364270\pi\) | ||||
0.413604 | + | 0.910457i | \(0.364270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.2492 | −0.495009 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.9690 | −0.842102 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.4963 | −1.31180 | −0.655902 | − | 0.754846i | \(-0.727711\pi\) | ||||
−0.655902 | + | 0.754846i | \(0.727711\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.6485 | 0.732889 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0909 | −0.390844 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.9846 | −0.709179 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.0085 | −0.483641 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 49.9589 | 1.60823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.0567 | 0.741454 | 0.370727 | − | 0.928742i | \(-0.379109\pi\) | ||||
0.370727 | + | 0.928742i | \(0.379109\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −101.797 | −3.27018 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.38223 | 0.108541 | 0.0542705 | − | 0.998526i | \(-0.482717\pi\) | ||||
0.0542705 | + | 0.998526i | \(0.482717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.32484 | 0.0424288 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.6374 | 0.596263 | 0.298132 | − | 0.954525i | \(-0.403637\pi\) | ||||
0.298132 | + | 0.954525i | \(0.403637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.06328 | −0.0979028 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.5129 | −0.878421 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.6211 | 1.71025 | 0.855123 | − | 0.518425i | \(-0.173481\pi\) | ||||
0.855123 | + | 0.518425i | \(0.173481\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.7719 | −0.757435 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.5396 | −1.54347 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.1420 | 1.46575 | 0.732875 | − | 0.680363i | \(-0.238178\pi\) | ||||
0.732875 | + | 0.680363i | \(0.238178\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.6746 | −0.656089 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.26454 | 0.166897 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.7038 | −0.338993 | −0.169496 | − | 0.985531i | \(-0.554214\pi\) | ||||
−0.169496 | + | 0.985531i | \(0.554214\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.12450 | −0.0355777 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8036.2.a.t.1.2 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.19 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.19 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.2 | yes | 20 | 1.1 | even | 1 | trivial |