Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, 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("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.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: | \(32.1238167332\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.365778 | 0.258644 | 0.129322 | − | 0.991603i | \(-0.458720\pi\) | ||||
0.129322 | + | 0.991603i | \(0.458720\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.86621 | −0.933103 | ||||||||
\(5\) | −3.76223 | −1.68252 | −0.841260 | − | 0.540631i | \(-0.818185\pi\) | ||||
−0.841260 | + | 0.540631i | \(0.818185\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.92149 | −1.10422 | −0.552109 | − | 0.833772i | \(-0.686177\pi\) | ||||
−0.552109 | + | 0.833772i | \(0.686177\pi\) | |||||||
\(8\) | −1.41417 | −0.499986 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.37614 | −0.435173 | ||||||||
\(11\) | 3.39144 | 1.02256 | 0.511279 | − | 0.859415i | \(-0.329172\pi\) | ||||
0.511279 | + | 0.859415i | \(0.329172\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.65902 | 0.460130 | 0.230065 | − | 0.973175i | \(-0.426106\pi\) | ||||
0.230065 | + | 0.973175i | \(0.426106\pi\) | |||||||
\(14\) | −1.06862 | −0.285600 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.21514 | 0.803785 | ||||||||
\(17\) | 1.97443 | 0.478869 | 0.239435 | − | 0.970912i | \(-0.423038\pi\) | ||||
0.239435 | + | 0.970912i | \(0.423038\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.94578 | −1.36406 | −0.682028 | − | 0.731326i | \(-0.738902\pi\) | ||||
−0.682028 | + | 0.731326i | \(0.738902\pi\) | |||||||
\(20\) | 7.02109 | 1.56996 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.24051 | 0.264478 | ||||||||
\(23\) | 5.19965 | 1.08420 | 0.542100 | − | 0.840314i | \(-0.317629\pi\) | ||||
0.542100 | + | 0.840314i | \(0.317629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.15436 | 1.83087 | ||||||||
\(26\) | 0.606833 | 0.119010 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.45210 | 1.03035 | ||||||||
\(29\) | −3.06884 | −0.569869 | −0.284935 | − | 0.958547i | \(-0.591972\pi\) | ||||
−0.284935 | + | 0.958547i | \(0.591972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.78939 | 1.21941 | 0.609705 | − | 0.792628i | \(-0.291288\pi\) | ||||
0.609705 | + | 0.792628i | \(0.291288\pi\) | |||||||
\(32\) | 4.00437 | 0.707880 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.722202 | 0.123857 | ||||||||
\(35\) | 10.9913 | 1.85787 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.04212 | 0.171324 | 0.0856621 | − | 0.996324i | \(-0.472699\pi\) | ||||
0.0856621 | + | 0.996324i | \(0.472699\pi\) | |||||||
\(38\) | −2.17484 | −0.352805 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.32044 | 0.841235 | ||||||||
\(41\) | 4.30891 | 0.672939 | 0.336470 | − | 0.941694i | \(-0.390767\pi\) | ||||
0.336470 | + | 0.941694i | \(0.390767\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.88453 | 1.04988 | 0.524940 | − | 0.851139i | \(-0.324088\pi\) | ||||
0.524940 | + | 0.851139i | \(0.324088\pi\) | |||||||
\(44\) | −6.32913 | −0.954152 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.90191 | 0.280422 | ||||||||
\(47\) | −7.18405 | −1.04790 | −0.523951 | − | 0.851749i | \(-0.675542\pi\) | ||||
−0.523951 | + | 0.851749i | \(0.675542\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.53509 | 0.219299 | ||||||||
\(50\) | 3.34846 | 0.473544 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.09608 | −0.429348 | ||||||||
\(53\) | −6.75951 | −0.928490 | −0.464245 | − | 0.885707i | \(-0.653674\pi\) | ||||
−0.464245 | + | 0.885707i | \(0.653674\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.7594 | −1.72047 | ||||||||
\(56\) | 4.13149 | 0.552093 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.12251 | −0.147393 | ||||||||
\(59\) | −8.13193 | −1.05869 | −0.529344 | − | 0.848408i | \(-0.677562\pi\) | ||||
−0.529344 | + | 0.848408i | \(0.677562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8085 | 1.38389 | 0.691944 | − | 0.721951i | \(-0.256754\pi\) | ||||
0.691944 | + | 0.721951i | \(0.256754\pi\) | |||||||
\(62\) | 2.48341 | 0.315393 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.96557 | −0.620696 | ||||||||
\(65\) | −6.24161 | −0.774177 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.26803 | −0.765761 | −0.382881 | − | 0.923798i | \(-0.625068\pi\) | ||||
−0.382881 | + | 0.923798i | \(0.625068\pi\) | |||||||
\(68\) | −3.68469 | −0.446835 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.02038 | 0.480527 | ||||||||
\(71\) | 3.91921 | 0.465125 | 0.232563 | − | 0.972581i | \(-0.425289\pi\) | ||||
0.232563 | + | 0.972581i | \(0.425289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.32230 | −1.09109 | −0.545546 | − | 0.838081i | \(-0.683678\pi\) | ||||
−0.545546 | + | 0.838081i | \(0.683678\pi\) | |||||||
\(74\) | 0.381186 | 0.0443120 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.0961 | 1.27281 | ||||||||
\(77\) | −9.90805 | −1.12913 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.65869 | 0.411635 | 0.205817 | − | 0.978590i | \(-0.434015\pi\) | ||||
0.205817 | + | 0.978590i | \(0.434015\pi\) | |||||||
\(80\) | −12.0961 | −1.35238 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.57611 | 0.174052 | ||||||||
\(83\) | −11.6033 | −1.27363 | −0.636813 | − | 0.771018i | \(-0.719748\pi\) | ||||
−0.636813 | + | 0.771018i | \(0.719748\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.42825 | −0.805707 | ||||||||
\(86\) | 2.51821 | 0.271545 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.79608 | −0.511264 | ||||||||
\(89\) | −11.9433 | −1.26598 | −0.632992 | − | 0.774159i | \(-0.718173\pi\) | ||||
−0.632992 | + | 0.774159i | \(0.718173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.84681 | −0.508084 | ||||||||
\(92\) | −9.70361 | −1.01167 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.62777 | −0.271033 | ||||||||
\(95\) | 22.3694 | 2.29505 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1415 | 1.02971 | 0.514856 | − | 0.857277i | \(-0.327845\pi\) | ||||
0.514856 | + | 0.857277i | \(0.327845\pi\) | |||||||
\(98\) | 0.561503 | 0.0567204 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −17.0839 | −1.70839 | ||||||||
\(101\) | 7.46540 | 0.742835 | 0.371417 | − | 0.928466i | \(-0.378872\pi\) | ||||
0.371417 | + | 0.928466i | \(0.378872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.9000 | 1.17254 | 0.586272 | − | 0.810114i | \(-0.300595\pi\) | ||||
0.586272 | + | 0.810114i | \(0.300595\pi\) | |||||||
\(104\) | −2.34614 | −0.230058 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.47248 | −0.240148 | ||||||||
\(107\) | −0.644073 | −0.0622649 | −0.0311324 | − | 0.999515i | \(-0.509911\pi\) | ||||
−0.0311324 | + | 0.999515i | \(0.509911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.21657 | 0.116526 | 0.0582632 | − | 0.998301i | \(-0.481444\pi\) | ||||
0.0582632 | + | 0.998301i | \(0.481444\pi\) | |||||||
\(110\) | −4.66709 | −0.444990 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.39299 | −0.887555 | ||||||||
\(113\) | 4.77472 | 0.449168 | 0.224584 | − | 0.974455i | \(-0.427898\pi\) | ||||
0.224584 | + | 0.974455i | \(0.427898\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.5622 | −1.82419 | ||||||||
\(116\) | 5.72709 | 0.531747 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.97448 | −0.273823 | ||||||||
\(119\) | −5.76827 | −0.528777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.501865 | 0.0456241 | ||||||||
\(122\) | 3.95352 | 0.357934 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.6704 | −1.13784 | ||||||||
\(125\) | −15.6296 | −1.39796 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.7828 | −1.13429 | −0.567143 | − | 0.823619i | \(-0.691952\pi\) | ||||
−0.567143 | + | 0.823619i | \(0.691952\pi\) | |||||||
\(128\) | −9.82504 | −0.868419 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.28304 | −0.200236 | ||||||||
\(131\) | 7.46513 | 0.652231 | 0.326116 | − | 0.945330i | \(-0.394260\pi\) | ||||
0.326116 | + | 0.945330i | \(0.394260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.3705 | 1.50622 | ||||||||
\(134\) | −2.29270 | −0.198060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.79218 | −0.239428 | ||||||||
\(137\) | −16.3681 | −1.39842 | −0.699211 | − | 0.714916i | \(-0.746465\pi\) | ||||
−0.699211 | + | 0.714916i | \(0.746465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4897 | 1.65310 | 0.826549 | − | 0.562865i | \(-0.190301\pi\) | ||||
0.826549 | + | 0.562865i | \(0.190301\pi\) | |||||||
\(140\) | −20.5120 | −1.73358 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.43356 | 0.120302 | ||||||||
\(143\) | 5.62647 | 0.470509 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.5457 | 0.958816 | ||||||||
\(146\) | −3.40989 | −0.282205 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.94482 | −0.159863 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.39072 | −0.764206 | −0.382103 | − | 0.924120i | \(-0.624800\pi\) | ||||
−0.382103 | + | 0.924120i | \(0.624800\pi\) | |||||||
\(152\) | 8.40836 | 0.682008 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.62415 | −0.292042 | ||||||||
\(155\) | −25.5432 | −2.05168 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.42584 | −0.113794 | −0.0568972 | − | 0.998380i | \(-0.518121\pi\) | ||||
−0.0568972 | + | 0.998380i | \(0.518121\pi\) | |||||||
\(158\) | 1.33827 | 0.106467 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.0654 | −1.19102 | ||||||||
\(161\) | −15.1907 | −1.19720 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.32087 | 0.573415 | 0.286708 | − | 0.958018i | \(-0.407439\pi\) | ||||
0.286708 | + | 0.958018i | \(0.407439\pi\) | |||||||
\(164\) | −8.04132 | −0.627922 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.24423 | −0.329416 | ||||||||
\(167\) | 6.85319 | 0.530316 | 0.265158 | − | 0.964205i | \(-0.414576\pi\) | ||||
0.265158 | + | 0.964205i | \(0.414576\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.2476 | −0.788281 | ||||||||
\(170\) | −2.71709 | −0.208391 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.8479 | −0.979647 | ||||||||
\(173\) | 7.35922 | 0.559511 | 0.279756 | − | 0.960071i | \(-0.409747\pi\) | ||||
0.279756 | + | 0.960071i | \(0.409747\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.7443 | −2.02168 | ||||||||
\(176\) | 10.9040 | 0.821917 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.36858 | −0.327439 | ||||||||
\(179\) | −15.9140 | −1.18947 | −0.594733 | − | 0.803923i | \(-0.702742\pi\) | ||||
−0.594733 | + | 0.803923i | \(0.702742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.0936 | 1.71654 | 0.858268 | − | 0.513202i | \(-0.171541\pi\) | ||||
0.858268 | + | 0.513202i | \(0.171541\pi\) | |||||||
\(182\) | −1.77286 | −0.131413 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.35320 | −0.542085 | ||||||||
\(185\) | −3.92071 | −0.288256 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.69616 | 0.489671 | ||||||||
\(188\) | 13.4069 | 0.977800 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.18223 | 0.593601 | ||||||||
\(191\) | −20.3176 | −1.47013 | −0.735065 | − | 0.677997i | \(-0.762848\pi\) | ||||
−0.735065 | + | 0.677997i | \(0.762848\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9436 | −0.787735 | −0.393867 | − | 0.919167i | \(-0.628863\pi\) | ||||
−0.393867 | + | 0.919167i | \(0.628863\pi\) | |||||||
\(194\) | 3.70953 | 0.266329 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.86480 | −0.204629 | ||||||||
\(197\) | −25.2674 | −1.80023 | −0.900115 | − | 0.435653i | \(-0.856518\pi\) | ||||
−0.900115 | + | 0.435653i | \(0.856518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4016 | −0.808240 | −0.404120 | − | 0.914706i | \(-0.632422\pi\) | ||||
−0.404120 | + | 0.914706i | \(0.632422\pi\) | |||||||
\(200\) | −12.9458 | −0.915409 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.73068 | 0.192130 | ||||||||
\(203\) | 8.96558 | 0.629261 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.2111 | −1.13223 | ||||||||
\(206\) | 4.35276 | 0.303271 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.33399 | 0.369845 | ||||||||
\(209\) | −20.1648 | −1.39483 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.25513 | −0.155249 | −0.0776246 | − | 0.996983i | \(-0.524734\pi\) | ||||
−0.0776246 | + | 0.996983i | \(0.524734\pi\) | |||||||
\(212\) | 12.6146 | 0.866377 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.235588 | −0.0161044 | ||||||||
\(215\) | −25.9012 | −1.76644 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.8351 | −1.34650 | ||||||||
\(218\) | 0.444995 | 0.0301389 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 23.8116 | 1.60538 | ||||||||
\(221\) | 3.27562 | 0.220342 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.77520 | 0.386736 | 0.193368 | − | 0.981126i | \(-0.438059\pi\) | ||||
0.193368 | + | 0.981126i | \(0.438059\pi\) | |||||||
\(224\) | −11.6987 | −0.781654 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.74649 | 0.116175 | ||||||||
\(227\) | 26.2629 | 1.74313 | 0.871564 | − | 0.490282i | \(-0.163106\pi\) | ||||
0.871564 | + | 0.490282i | \(0.163106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.9359 | 1.91214 | 0.956069 | − | 0.293141i | \(-0.0947005\pi\) | ||||
0.956069 | + | 0.293141i | \(0.0947005\pi\) | |||||||
\(230\) | −7.15544 | −0.471816 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.33987 | 0.284926 | ||||||||
\(233\) | −12.4194 | −0.813622 | −0.406811 | − | 0.913512i | \(-0.633359\pi\) | ||||
−0.406811 | + | 0.913512i | \(0.633359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.0280 | 1.76311 | ||||||||
\(236\) | 15.1759 | 0.987865 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.10991 | −0.136765 | ||||||||
\(239\) | −1.20431 | −0.0779004 | −0.0389502 | − | 0.999241i | \(-0.512401\pi\) | ||||
−0.0389502 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3214 | −0.858107 | −0.429054 | − | 0.903279i | \(-0.641153\pi\) | ||||
−0.429054 | + | 0.903279i | \(0.641153\pi\) | |||||||
\(242\) | 0.183571 | 0.0118004 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.1709 | −1.29131 | ||||||||
\(245\) | −5.77537 | −0.368975 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.86418 | −0.627643 | ||||||||
\(248\) | −9.60137 | −0.609688 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.71697 | −0.361573 | ||||||||
\(251\) | 19.8611 | 1.25362 | 0.626812 | − | 0.779171i | \(-0.284360\pi\) | ||||
0.626812 | + | 0.779171i | \(0.284360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.6343 | 1.10866 | ||||||||
\(254\) | −4.67565 | −0.293376 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.33736 | 0.396085 | ||||||||
\(257\) | −6.34398 | −0.395727 | −0.197863 | − | 0.980230i | \(-0.563400\pi\) | ||||
−0.197863 | + | 0.980230i | \(0.563400\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.04455 | −0.189179 | ||||||||
\(260\) | 11.6481 | 0.722387 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.73058 | 0.168696 | ||||||||
\(263\) | −11.6343 | −0.717405 | −0.358702 | − | 0.933452i | \(-0.616781\pi\) | ||||
−0.358702 | + | 0.933452i | \(0.616781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.4308 | 1.56220 | ||||||||
\(266\) | 6.35376 | 0.389574 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.6974 | 0.714534 | ||||||||
\(269\) | −15.4781 | −0.943715 | −0.471858 | − | 0.881675i | \(-0.656416\pi\) | ||||
−0.471858 | + | 0.881675i | \(0.656416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.3243 | −1.29536 | −0.647678 | − | 0.761914i | \(-0.724260\pi\) | ||||
−0.647678 | + | 0.761914i | \(0.724260\pi\) | |||||||
\(272\) | 6.34807 | 0.384908 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.98709 | −0.361693 | ||||||||
\(275\) | 31.0465 | 1.87217 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0313 | 0.843058 | 0.421529 | − | 0.906815i | \(-0.361494\pi\) | ||||
0.421529 | + | 0.906815i | \(0.361494\pi\) | |||||||
\(278\) | 7.12891 | 0.427564 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.5436 | −0.928908 | ||||||||
\(281\) | −2.32437 | −0.138660 | −0.0693302 | − | 0.997594i | \(-0.522086\pi\) | ||||
−0.0693302 | + | 0.997594i | \(0.522086\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.7990 | −1.35526 | −0.677631 | − | 0.735402i | \(-0.736993\pi\) | ||||
−0.677631 | + | 0.735402i | \(0.736993\pi\) | |||||||
\(284\) | −7.31406 | −0.434010 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.05804 | 0.121694 | ||||||||
\(287\) | −12.5884 | −0.743072 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.1016 | −0.770684 | ||||||||
\(290\) | 4.22315 | 0.247992 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.3973 | 1.01810 | ||||||||
\(293\) | −23.1108 | −1.35015 | −0.675073 | − | 0.737751i | \(-0.735888\pi\) | ||||
−0.675073 | + | 0.737751i | \(0.735888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.5942 | 1.78126 | ||||||||
\(296\) | −1.47374 | −0.0856596 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.365778 | −0.0211889 | ||||||||
\(299\) | 8.62632 | 0.498873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.1131 | −1.15930 | ||||||||
\(302\) | −3.43492 | −0.197657 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −19.1165 | −1.09641 | ||||||||
\(305\) | −40.6641 | −2.32842 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.95861 | 0.454222 | 0.227111 | − | 0.973869i | \(-0.427072\pi\) | ||||
0.227111 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(308\) | 18.4905 | 1.05359 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.34315 | −0.530655 | ||||||||
\(311\) | −2.11477 | −0.119918 | −0.0599588 | − | 0.998201i | \(-0.519097\pi\) | ||||
−0.0599588 | + | 0.998201i | \(0.519097\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.12070 | 0.402486 | 0.201243 | − | 0.979541i | \(-0.435502\pi\) | ||||
0.201243 | + | 0.979541i | \(0.435502\pi\) | |||||||
\(314\) | −0.521541 | −0.0294323 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.82787 | −0.384098 | ||||||||
\(317\) | 23.2371 | 1.30512 | 0.652562 | − | 0.757735i | \(-0.273694\pi\) | ||||
0.652562 | + | 0.757735i | \(0.273694\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.4078 | −0.582724 | ||||||||
\(320\) | 18.6816 | 1.04433 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.55642 | −0.309647 | ||||||||
\(323\) | −11.7395 | −0.653205 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.1873 | 0.842438 | ||||||||
\(326\) | 2.67781 | 0.148310 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.09355 | −0.336460 | ||||||||
\(329\) | 20.9881 | 1.15711 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.5567 | −1.78948 | −0.894739 | − | 0.446589i | \(-0.852639\pi\) | ||||
−0.894739 | + | 0.446589i | \(0.852639\pi\) | |||||||
\(332\) | 21.6541 | 1.18843 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.50675 | 0.137163 | ||||||||
\(335\) | 23.5817 | 1.28841 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.4417 | 1.16800 | 0.584002 | − | 0.811752i | \(-0.301486\pi\) | ||||
0.584002 | + | 0.811752i | \(0.301486\pi\) | |||||||
\(338\) | −3.74836 | −0.203884 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.8627 | 0.751808 | ||||||||
\(341\) | 23.0258 | 1.24692 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.9657 | 0.862065 | ||||||||
\(344\) | −9.73591 | −0.524925 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.69184 | 0.144714 | ||||||||
\(347\) | −6.86807 | −0.368698 | −0.184349 | − | 0.982861i | \(-0.559018\pi\) | ||||
−0.184349 | + | 0.982861i | \(0.559018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.6046 | 1.79881 | 0.899405 | − | 0.437115i | \(-0.144000\pi\) | ||||
0.899405 | + | 0.437115i | \(0.144000\pi\) | |||||||
\(350\) | −9.78249 | −0.522896 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.5806 | 0.723848 | ||||||||
\(353\) | −5.40572 | −0.287717 | −0.143859 | − | 0.989598i | \(-0.545951\pi\) | ||||
−0.143859 | + | 0.989598i | \(0.545951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.7450 | −0.782582 | ||||||||
\(356\) | 22.2886 | 1.18129 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.82098 | −0.307648 | ||||||||
\(359\) | 7.21437 | 0.380760 | 0.190380 | − | 0.981711i | \(-0.439028\pi\) | ||||
0.190380 | + | 0.981711i | \(0.439028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.3523 | 0.860650 | ||||||||
\(362\) | 8.44714 | 0.443972 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.04515 | 0.474095 | ||||||||
\(365\) | 35.0726 | 1.83578 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.5758 | 1.17845 | 0.589224 | − | 0.807969i | \(-0.299433\pi\) | ||||
0.589224 | + | 0.807969i | \(0.299433\pi\) | |||||||
\(368\) | 16.7176 | 0.871465 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.43411 | −0.0745557 | ||||||||
\(371\) | 19.7478 | 1.02526 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.49410 | −0.388030 | −0.194015 | − | 0.980999i | \(-0.562151\pi\) | ||||
−0.194015 | + | 0.980999i | \(0.562151\pi\) | |||||||
\(374\) | 2.44931 | 0.126651 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.1595 | 0.523935 | ||||||||
\(377\) | −5.09127 | −0.262214 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.22719 | −0.165770 | −0.0828848 | − | 0.996559i | \(-0.526413\pi\) | ||||
−0.0828848 | + | 0.996559i | \(0.526413\pi\) | |||||||
\(380\) | −41.7459 | −2.14152 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.43173 | −0.380240 | ||||||||
\(383\) | −33.2748 | −1.70026 | −0.850131 | − | 0.526571i | \(-0.823477\pi\) | ||||
−0.850131 | + | 0.526571i | \(0.823477\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37.2763 | 1.89978 | ||||||||
\(386\) | −4.00291 | −0.203743 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.9261 | −0.960827 | ||||||||
\(389\) | −34.5478 | −1.75164 | −0.875820 | − | 0.482637i | \(-0.839679\pi\) | ||||
−0.875820 | + | 0.482637i | \(0.839679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2663 | 0.519191 | ||||||||
\(392\) | −2.17089 | −0.109646 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.24227 | −0.465619 | ||||||||
\(395\) | −13.7648 | −0.692583 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9049 | 1.09938 | 0.549688 | − | 0.835370i | \(-0.314746\pi\) | ||||
0.549688 | + | 0.835370i | \(0.314746\pi\) | |||||||
\(398\) | −4.17046 | −0.209046 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 29.4325 | 1.47163 | ||||||||
\(401\) | −31.2502 | −1.56056 | −0.780280 | − | 0.625430i | \(-0.784924\pi\) | ||||
−0.780280 | + | 0.625430i | \(0.784924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.2637 | 0.561087 | ||||||||
\(404\) | −13.9320 | −0.693142 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.27941 | 0.162754 | ||||||||
\(407\) | 3.53430 | 0.175189 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3295 | −1.05468 | −0.527338 | − | 0.849655i | \(-0.676810\pi\) | ||||
−0.527338 | + | 0.849655i | \(0.676810\pi\) | |||||||
\(410\) | −5.92967 | −0.292845 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.2079 | −1.09410 | ||||||||
\(413\) | 23.7573 | 1.16902 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 43.6542 | 2.14290 | ||||||||
\(416\) | 6.64334 | 0.325716 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.37582 | −0.360763 | ||||||||
\(419\) | 7.40525 | 0.361770 | 0.180885 | − | 0.983504i | \(-0.442104\pi\) | ||||
0.180885 | + | 0.983504i | \(0.442104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.5504 | 0.855353 | 0.427676 | − | 0.903932i | \(-0.359332\pi\) | ||||
0.427676 | + | 0.903932i | \(0.359332\pi\) | |||||||
\(422\) | −0.824875 | −0.0401543 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.55911 | 0.464232 | ||||||||
\(425\) | 18.0746 | 0.876748 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.5770 | −1.52812 | ||||||||
\(428\) | 1.20197 | 0.0580996 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.47407 | −0.456880 | ||||||||
\(431\) | −29.9688 | −1.44355 | −0.721773 | − | 0.692130i | \(-0.756673\pi\) | ||||
−0.721773 | + | 0.692130i | \(0.756673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.64094 | −0.319143 | −0.159571 | − | 0.987186i | \(-0.551011\pi\) | ||||
−0.159571 | + | 0.987186i | \(0.551011\pi\) | |||||||
\(434\) | −7.25525 | −0.348263 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.27037 | −0.108731 | ||||||||
\(437\) | −30.9160 | −1.47891 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0857 | 1.34046 | 0.670228 | − | 0.742155i | \(-0.266196\pi\) | ||||
0.670228 | + | 0.742155i | \(0.266196\pi\) | |||||||
\(440\) | 18.0440 | 0.860212 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.19815 | 0.0569901 | ||||||||
\(443\) | 11.4861 | 0.545722 | 0.272861 | − | 0.962054i | \(-0.412030\pi\) | ||||
0.272861 | + | 0.962054i | \(0.412030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.9333 | 2.13004 | ||||||||
\(446\) | 2.11244 | 0.100027 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.5069 | 0.685384 | ||||||||
\(449\) | −11.7104 | −0.552649 | −0.276325 | − | 0.961064i | \(-0.589116\pi\) | ||||
−0.276325 | + | 0.961064i | \(0.589116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6134 | 0.688119 | ||||||||
\(452\) | −8.91062 | −0.419120 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.60638 | 0.450850 | ||||||||
\(455\) | 18.2348 | 0.854861 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6519 | −1.10639 | −0.553194 | − | 0.833052i | \(-0.686591\pi\) | ||||
−0.553194 | + | 0.833052i | \(0.686591\pi\) | |||||||
\(458\) | 10.5841 | 0.494563 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 36.5072 | 1.70216 | ||||||||
\(461\) | −30.8073 | −1.43484 | −0.717420 | − | 0.696641i | \(-0.754677\pi\) | ||||
−0.717420 | + | 0.696641i | \(0.754677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6345 | 0.587173 | 0.293587 | − | 0.955932i | \(-0.405151\pi\) | ||||
0.293587 | + | 0.955932i | \(0.405151\pi\) | |||||||
\(464\) | −9.86675 | −0.458053 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.54274 | −0.210438 | ||||||||
\(467\) | 17.4707 | 0.808447 | 0.404223 | − | 0.914660i | \(-0.367542\pi\) | ||||
0.404223 | + | 0.914660i | \(0.367542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.3120 | 0.845568 | ||||||||
\(470\) | 9.88625 | 0.456019 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.5000 | 0.529328 | ||||||||
\(473\) | 23.3485 | 1.07356 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −54.4298 | −2.49741 | ||||||||
\(476\) | 10.7648 | 0.493403 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.440510 | −0.0201485 | ||||||||
\(479\) | −14.4042 | −0.658144 | −0.329072 | − | 0.944305i | \(-0.606736\pi\) | ||||
−0.329072 | + | 0.944305i | \(0.606736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.72891 | 0.0788313 | ||||||||
\(482\) | −4.87268 | −0.221944 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.936585 | −0.0425720 | ||||||||
\(485\) | −38.1546 | −1.73251 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.3687 | −1.46676 | −0.733382 | − | 0.679817i | \(-0.762059\pi\) | ||||
−0.733382 | + | 0.679817i | \(0.762059\pi\) | |||||||
\(488\) | −15.2851 | −0.691924 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.11250 | −0.0954332 | ||||||||
\(491\) | −21.7705 | −0.982490 | −0.491245 | − | 0.871022i | \(-0.663458\pi\) | ||||
−0.491245 | + | 0.871022i | \(0.663458\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.05921 | −0.272893 | ||||||||
\(494\) | −3.60810 | −0.162336 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.8288 | 0.980144 | ||||||||
\(497\) | −11.4499 | −0.513600 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.04209 | 0.0914167 | 0.0457083 | − | 0.998955i | \(-0.485446\pi\) | ||||
0.0457083 | + | 0.998955i | \(0.485446\pi\) | |||||||
\(500\) | 29.1681 | 1.30444 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.26476 | 0.324242 | ||||||||
\(503\) | −1.40290 | −0.0625522 | −0.0312761 | − | 0.999511i | \(-0.509957\pi\) | ||||
−0.0312761 | + | 0.999511i | \(0.509957\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.0865 | −1.24983 | ||||||||
\(506\) | 6.45023 | 0.286748 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 23.8553 | 1.05841 | ||||||||
\(509\) | 38.1088 | 1.68914 | 0.844571 | − | 0.535443i | \(-0.179855\pi\) | ||||
0.844571 | + | 0.535443i | \(0.179855\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.2350 | 1.20480 | ||||||||
\(512\) | 21.9681 | 0.970864 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.32049 | −0.102352 | ||||||||
\(515\) | −44.7706 | −1.97283 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.3643 | −1.07154 | ||||||||
\(518\) | −1.11363 | −0.0489301 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.82672 | 0.387077 | ||||||||
\(521\) | 1.83967 | 0.0805974 | 0.0402987 | − | 0.999188i | \(-0.487169\pi\) | ||||
0.0402987 | + | 0.999188i | \(0.487169\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.1344 | −0.661780 | −0.330890 | − | 0.943669i | \(-0.607349\pi\) | ||||
−0.330890 | + | 0.943669i | \(0.607349\pi\) | |||||||
\(524\) | −13.9315 | −0.608599 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.25559 | −0.185552 | ||||||||
\(527\) | 13.4052 | 0.583938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.03631 | 0.175492 | ||||||||
\(530\) | 9.30203 | 0.404054 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −32.4170 | −1.40546 | ||||||||
\(533\) | 7.14858 | 0.309639 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.42315 | 0.104762 | ||||||||
\(536\) | 8.86407 | 0.382870 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.66154 | −0.244086 | ||||||||
\(539\) | 5.20618 | 0.224246 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2234 | −0.525526 | −0.262763 | − | 0.964860i | \(-0.584634\pi\) | ||||
−0.262763 | + | 0.964860i | \(0.584634\pi\) | |||||||
\(542\) | −7.79994 | −0.335036 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.90635 | 0.338982 | ||||||||
\(545\) | −4.57702 | −0.196058 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.66498 | 0.156703 | 0.0783516 | − | 0.996926i | \(-0.475034\pi\) | ||||
0.0783516 | + | 0.996926i | \(0.475034\pi\) | |||||||
\(548\) | 30.5463 | 1.30487 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.3561 | 0.484226 | ||||||||
\(551\) | 18.2467 | 0.777334 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.6888 | −0.454535 | ||||||||
\(554\) | 5.13233 | 0.218052 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36.3719 | −1.54251 | ||||||||
\(557\) | 27.6348 | 1.17092 | 0.585461 | − | 0.810700i | \(-0.300913\pi\) | ||||
0.585461 | + | 0.810700i | \(0.300913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.4216 | 0.483081 | ||||||||
\(560\) | 35.3386 | 1.49333 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.850204 | −0.0358637 | ||||||||
\(563\) | −4.02658 | −0.169700 | −0.0848500 | − | 0.996394i | \(-0.527041\pi\) | ||||
−0.0848500 | + | 0.996394i | \(0.527041\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.9636 | −0.755734 | ||||||||
\(566\) | −8.33938 | −0.350530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.54244 | −0.232556 | ||||||||
\(569\) | 7.02698 | 0.294586 | 0.147293 | − | 0.989093i | \(-0.452944\pi\) | ||||
0.147293 | + | 0.989093i | \(0.452944\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.5714 | −1.27938 | −0.639688 | − | 0.768635i | \(-0.720936\pi\) | ||||
−0.639688 | + | 0.768635i | \(0.720936\pi\) | |||||||
\(572\) | −10.5002 | −0.439034 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.60457 | −0.192191 | ||||||||
\(575\) | 47.5994 | 1.98503 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.1510 | −1.75477 | −0.877385 | − | 0.479786i | \(-0.840714\pi\) | ||||
−0.877385 | + | 0.479786i | \(0.840714\pi\) | |||||||
\(578\) | −4.79229 | −0.199333 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.5466 | −0.894675 | ||||||||
\(581\) | 33.8989 | 1.40636 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.9245 | −0.949434 | ||||||||
\(584\) | 13.1833 | 0.545530 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.45341 | −0.349207 | ||||||||
\(587\) | 12.2011 | 0.503595 | 0.251797 | − | 0.967780i | \(-0.418978\pi\) | ||||
0.251797 | + | 0.967780i | \(0.418978\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.3682 | −1.66334 | ||||||||
\(590\) | 11.1907 | 0.460713 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.35058 | 0.137708 | ||||||||
\(593\) | −12.3294 | −0.506306 | −0.253153 | − | 0.967426i | \(-0.581468\pi\) | ||||
−0.253153 | + | 0.967426i | \(0.581468\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.7015 | 0.889677 | ||||||||
\(596\) | 1.86621 | 0.0764428 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.15532 | 0.129030 | ||||||||
\(599\) | 14.7447 | 0.602452 | 0.301226 | − | 0.953553i | \(-0.402604\pi\) | ||||
0.301226 | + | 0.953553i | \(0.402604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.7113 | −0.559295 | −0.279647 | − | 0.960103i | \(-0.590218\pi\) | ||||
−0.279647 | + | 0.960103i | \(0.590218\pi\) | |||||||
\(602\) | −7.35691 | −0.299845 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.5250 | 0.713083 | ||||||||
\(605\) | −1.88813 | −0.0767635 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.1891 | 0.413563 | 0.206782 | − | 0.978387i | \(-0.433701\pi\) | ||||
0.206782 | + | 0.978387i | \(0.433701\pi\) | |||||||
\(608\) | −23.8091 | −0.965588 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.8740 | −0.602232 | ||||||||
\(611\) | −11.9185 | −0.482170 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.3390 | −0.417586 | −0.208793 | − | 0.977960i | \(-0.566954\pi\) | ||||
−0.208793 | + | 0.977960i | \(0.566954\pi\) | |||||||
\(614\) | 2.91108 | 0.117482 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.0117 | 0.564547 | ||||||||
\(617\) | −6.33913 | −0.255204 | −0.127602 | − | 0.991825i | \(-0.540728\pi\) | ||||
−0.127602 | + | 0.991825i | \(0.540728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.5154 | −0.583423 | −0.291712 | − | 0.956506i | \(-0.594225\pi\) | ||||
−0.291712 | + | 0.956506i | \(0.594225\pi\) | |||||||
\(620\) | 47.6689 | 1.91443 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.773536 | −0.0310160 | ||||||||
\(623\) | 34.8921 | 1.39792 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.0305 | 0.521218 | ||||||||
\(626\) | 2.60460 | 0.104101 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.66091 | 0.106182 | ||||||||
\(629\) | 2.05760 | 0.0820419 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8501 | 1.42717 | 0.713584 | − | 0.700570i | \(-0.247071\pi\) | ||||
0.713584 | + | 0.700570i | \(0.247071\pi\) | |||||||
\(632\) | −5.17402 | −0.205811 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.49961 | 0.337563 | ||||||||
\(635\) | 48.0917 | 1.90846 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.54675 | 0.100906 | ||||||||
\(638\) | −3.80694 | −0.150718 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 36.9640 | 1.46113 | ||||||||
\(641\) | 46.9030 | 1.85256 | 0.926279 | − | 0.376839i | \(-0.122989\pi\) | ||||
0.926279 | + | 0.376839i | \(0.122989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.0632 | −1.85599 | −0.927995 | − | 0.372593i | \(-0.878469\pi\) | ||||
−0.927995 | + | 0.372593i | \(0.878469\pi\) | |||||||
\(644\) | 28.3490 | 1.11711 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.29406 | −0.168947 | ||||||||
\(647\) | 50.7955 | 1.99698 | 0.998488 | − | 0.0549708i | \(-0.0175066\pi\) | ||||
0.998488 | + | 0.0549708i | \(0.0175066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.5790 | −1.08257 | ||||||||
\(650\) | 5.55517 | 0.217892 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.6623 | −0.535056 | ||||||||
\(653\) | −19.3835 | −0.758534 | −0.379267 | − | 0.925287i | \(-0.623824\pi\) | ||||
−0.379267 | + | 0.925287i | \(0.623824\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.0855 | −1.09739 | ||||||||
\(656\) | 13.8538 | 0.540899 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.67699 | 0.299280 | ||||||||
\(659\) | −39.6111 | −1.54303 | −0.771514 | − | 0.636212i | \(-0.780500\pi\) | ||||
−0.771514 | + | 0.636212i | \(0.780500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.53392 | −0.254140 | −0.127070 | − | 0.991894i | \(-0.540557\pi\) | ||||
−0.127070 | + | 0.991894i | \(0.540557\pi\) | |||||||
\(662\) | −11.9085 | −0.462838 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.4091 | 0.636795 | ||||||||
\(665\) | −65.3519 | −2.53424 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.9569 | −0.617853 | ||||||||
\(668\) | −12.7895 | −0.494840 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.62568 | 0.333239 | ||||||||
\(671\) | 36.6564 | 1.41511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.1581 | 1.12396 | 0.561981 | − | 0.827150i | \(-0.310040\pi\) | ||||
0.561981 | + | 0.827150i | \(0.310040\pi\) | |||||||
\(674\) | 7.84290 | 0.302097 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.1242 | 0.735547 | ||||||||
\(677\) | −47.3893 | −1.82132 | −0.910659 | − | 0.413159i | \(-0.864426\pi\) | ||||
−0.910659 | + | 0.413159i | \(0.864426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.6282 | −1.13703 | ||||||||
\(680\) | 10.5048 | 0.402842 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.42233 | 0.322508 | ||||||||
\(683\) | −44.2885 | −1.69465 | −0.847326 | − | 0.531073i | \(-0.821789\pi\) | ||||
−0.847326 | + | 0.531073i | \(0.821789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 61.5805 | 2.35287 | ||||||||
\(686\) | 5.83988 | 0.222968 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 22.1347 | 0.843878 | ||||||||
\(689\) | −11.2142 | −0.427226 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.5417 | 1.58032 | 0.790161 | − | 0.612900i | \(-0.209997\pi\) | ||||
0.790161 | + | 0.612900i | \(0.209997\pi\) | |||||||
\(692\) | −13.7338 | −0.522082 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.51219 | −0.0953614 | ||||||||
\(695\) | −73.3248 | −2.78137 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.50765 | 0.322250 | ||||||||
\(698\) | 12.2918 | 0.465252 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 49.9105 | 1.88644 | ||||||||
\(701\) | 38.4336 | 1.45162 | 0.725809 | − | 0.687896i | \(-0.241466\pi\) | ||||
0.725809 | + | 0.687896i | \(0.241466\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.19625 | −0.233696 | ||||||||
\(704\) | −16.8404 | −0.634698 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.97729 | −0.0744164 | ||||||||
\(707\) | −21.8101 | −0.820252 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.9347 | 0.861329 | 0.430664 | − | 0.902512i | \(-0.358279\pi\) | ||||
0.430664 | + | 0.902512i | \(0.358279\pi\) | |||||||
\(710\) | −5.39338 | −0.202410 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.8898 | 0.632973 | ||||||||
\(713\) | 35.3024 | 1.32209 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.1681 | −0.791641 | ||||||||
\(716\) | 29.6988 | 1.10990 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.63886 | 0.0984812 | ||||||||
\(719\) | 21.6943 | 0.809060 | 0.404530 | − | 0.914525i | \(-0.367435\pi\) | ||||
0.404530 | + | 0.914525i | \(0.367435\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.7658 | −1.29474 | ||||||||
\(722\) | 5.98132 | 0.222602 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −43.0975 | −1.60171 | ||||||||
\(725\) | −28.0933 | −1.04336 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.5274 | −1.35473 | −0.677363 | − | 0.735649i | \(-0.736877\pi\) | ||||
−0.677363 | + | 0.735649i | \(0.736877\pi\) | |||||||
\(728\) | 6.85423 | 0.254035 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.8288 | 0.474815 | ||||||||
\(731\) | 13.5930 | 0.502756 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.5790 | −1.12946 | −0.564731 | − | 0.825275i | \(-0.691020\pi\) | ||||
−0.564731 | + | 0.825275i | \(0.691020\pi\) | |||||||
\(734\) | 8.25774 | 0.304799 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8213 | 0.767484 | ||||||||
\(737\) | −21.2576 | −0.783035 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.19635 | 0.117580 | 0.0587899 | − | 0.998270i | \(-0.481276\pi\) | ||||
0.0587899 | + | 0.998270i | \(0.481276\pi\) | |||||||
\(740\) | 7.31685 | 0.268973 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.22332 | 0.265176 | ||||||||
\(743\) | 36.4235 | 1.33625 | 0.668124 | − | 0.744050i | \(-0.267098\pi\) | ||||
0.668124 | + | 0.744050i | \(0.267098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.76223 | 0.137837 | ||||||||
\(746\) | −2.74118 | −0.100362 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.4964 | −0.456914 | ||||||||
\(749\) | 1.88165 | 0.0687541 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.0659 | −1.71746 | −0.858730 | − | 0.512428i | \(-0.828746\pi\) | ||||
−0.858730 | + | 0.512428i | \(0.828746\pi\) | |||||||
\(752\) | −23.0977 | −0.842287 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.86227 | −0.0678200 | ||||||||
\(755\) | 35.3300 | 1.28579 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.6332 | −0.786272 | −0.393136 | − | 0.919480i | \(-0.628610\pi\) | ||||
−0.393136 | + | 0.919480i | \(0.628610\pi\) | |||||||
\(758\) | −1.18043 | −0.0428753 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −31.6342 | −1.14749 | ||||||||
\(761\) | 11.6574 | 0.422581 | 0.211290 | − | 0.977423i | \(-0.432233\pi\) | ||||
0.211290 | + | 0.977423i | \(0.432233\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.55420 | −0.128671 | ||||||||
\(764\) | 37.9168 | 1.37178 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.1712 | −0.439763 | ||||||||
\(767\) | −13.4910 | −0.487133 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.41304 | 0.123077 | 0.0615387 | − | 0.998105i | \(-0.480399\pi\) | ||||
0.0615387 | + | 0.998105i | \(0.480399\pi\) | |||||||
\(770\) | 13.6349 | 0.491366 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.4229 | 0.735038 | ||||||||
\(773\) | −27.8909 | −1.00317 | −0.501583 | − | 0.865109i | \(-0.667249\pi\) | ||||
−0.501583 | + | 0.865109i | \(0.667249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 62.1525 | 2.23258 | ||||||||
\(776\) | −14.3418 | −0.514841 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.6368 | −0.453051 | ||||||||
\(779\) | −25.6199 | −0.917927 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.2918 | 0.475617 | ||||||||
\(782\) | 3.75520 | 0.134286 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.93554 | 0.176269 | ||||||||
\(785\) | 5.36434 | 0.191461 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5283 | −0.803047 | −0.401523 | − | 0.915849i | \(-0.631519\pi\) | ||||
−0.401523 | + | 0.915849i | \(0.631519\pi\) | |||||||
\(788\) | 47.1542 | 1.67980 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.03486 | −0.179132 | ||||||||
\(791\) | −13.9493 | −0.495980 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.9316 | 0.636768 | ||||||||
\(794\) | 8.01234 | 0.284347 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.2778 | 0.754171 | ||||||||
\(797\) | −10.8184 | −0.383207 | −0.191604 | − | 0.981472i | \(-0.561369\pi\) | ||||
−0.191604 | + | 0.981472i | \(0.561369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.1844 | −0.501808 | ||||||||
\(800\) | 36.6574 | 1.29604 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.4306 | −0.403630 | ||||||||
\(803\) | −31.6160 | −1.11571 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 57.1509 | 2.01430 | ||||||||
\(806\) | 4.12003 | 0.145122 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.5574 | −0.371407 | ||||||||
\(809\) | 26.5554 | 0.933638 | 0.466819 | − | 0.884353i | \(-0.345400\pi\) | ||||
0.466819 | + | 0.884353i | \(0.345400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.3496 | −1.24129 | −0.620645 | − | 0.784091i | \(-0.713129\pi\) | ||||
−0.620645 | + | 0.784091i | \(0.713129\pi\) | |||||||
\(812\) | −16.7316 | −0.587165 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.29277 | 0.0453115 | ||||||||
\(815\) | −27.5428 | −0.964782 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.9339 | −1.43210 | ||||||||
\(818\) | −7.80186 | −0.272786 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.2533 | 1.05649 | ||||||||
\(821\) | −1.64779 | −0.0575084 | −0.0287542 | − | 0.999587i | \(-0.509154\pi\) | ||||
−0.0287542 | + | 0.999587i | \(0.509154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.92753 | −0.171763 | −0.0858815 | − | 0.996305i | \(-0.527371\pi\) | ||||
−0.0858815 | + | 0.996305i | \(0.527371\pi\) | |||||||
\(824\) | −16.8287 | −0.586255 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.68991 | 0.302361 | ||||||||
\(827\) | −8.78117 | −0.305351 | −0.152676 | − | 0.988276i | \(-0.548789\pi\) | ||||
−0.152676 | + | 0.988276i | \(0.548789\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.12166 | −0.282077 | −0.141039 | − | 0.990004i | \(-0.545044\pi\) | ||||
−0.141039 | + | 0.990004i | \(0.545044\pi\) | |||||||
\(830\) | 15.9677 | 0.554248 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.23798 | −0.285601 | ||||||||
\(833\) | 3.03093 | 0.105016 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.7833 | −0.892267 | ||||||||
\(836\) | 37.6316 | 1.30152 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.70868 | 0.0935697 | ||||||||
\(839\) | −17.5061 | −0.604378 | −0.302189 | − | 0.953248i | \(-0.597717\pi\) | ||||
−0.302189 | + | 0.953248i | \(0.597717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.5822 | −0.675249 | ||||||||
\(842\) | 6.41954 | 0.221232 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.20853 | 0.144864 | ||||||||
\(845\) | 38.5540 | 1.32630 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.46619 | −0.0503790 | ||||||||
\(848\) | −21.7328 | −0.746306 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.61130 | 0.226766 | ||||||||
\(851\) | 5.41868 | 0.185750 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.8387 | 0.645024 | 0.322512 | − | 0.946565i | \(-0.395473\pi\) | ||||
0.322512 | + | 0.946565i | \(0.395473\pi\) | |||||||
\(854\) | −11.5501 | −0.395238 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.910831 | 0.0311315 | ||||||||
\(857\) | −9.49372 | −0.324299 | −0.162150 | − | 0.986766i | \(-0.551843\pi\) | ||||
−0.162150 | + | 0.986766i | \(0.551843\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.7825 | 1.49384 | 0.746919 | − | 0.664915i | \(-0.231532\pi\) | ||||
0.746919 | + | 0.664915i | \(0.231532\pi\) | |||||||
\(860\) | 48.3369 | 1.64827 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.9619 | −0.373364 | ||||||||
\(863\) | −9.65541 | −0.328674 | −0.164337 | − | 0.986404i | \(-0.552548\pi\) | ||||
−0.164337 | + | 0.986404i | \(0.552548\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.6871 | −0.941388 | ||||||||
\(866\) | −2.42911 | −0.0825444 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 37.0164 | 1.25642 | ||||||||
\(869\) | 12.4082 | 0.420920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3988 | −0.352349 | ||||||||
\(872\) | −1.72044 | −0.0582615 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.3084 | −0.382511 | ||||||||
\(875\) | 45.6618 | 1.54365 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.00570362 | 0.000192598 0 | 9.62988e−5 | − | 1.00000i | \(-0.499969\pi\) | ||||
9.62988e−5 | 1.00000i | \(0.499969\pi\) | ||||||||
\(878\) | 10.2731 | 0.346701 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −41.0232 | −1.38289 | ||||||||
\(881\) | −20.2925 | −0.683671 | −0.341835 | − | 0.939760i | \(-0.611049\pi\) | ||||
−0.341835 | + | 0.939760i | \(0.611049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.3237 | −1.42431 | −0.712153 | − | 0.702024i | \(-0.752280\pi\) | ||||
−0.712153 | + | 0.702024i | \(0.752280\pi\) | |||||||
\(884\) | −6.11298 | −0.205602 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.20136 | 0.141148 | ||||||||
\(887\) | −23.4444 | −0.787187 | −0.393594 | − | 0.919285i | \(-0.628768\pi\) | ||||
−0.393594 | + | 0.919285i | \(0.628768\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.3447 | 1.25250 | ||||||||
\(890\) | 16.4356 | 0.550922 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.7777 | −0.360865 | ||||||||
\(893\) | 42.7148 | 1.42940 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 59.8720 | 2.00130 | ||||||||
\(896\) | 28.7037 | 0.958925 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.28341 | −0.142939 | ||||||||
\(899\) | −20.8356 | −0.694905 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.3462 | −0.444625 | ||||||||
\(902\) | 5.34527 | 0.177978 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.75228 | −0.224578 | ||||||||
\(905\) | −86.8835 | −2.88811 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3453 | 1.10721 | 0.553607 | − | 0.832778i | \(-0.313251\pi\) | ||||
0.553607 | + | 0.832778i | \(0.313251\pi\) | |||||||
\(908\) | −49.0120 | −1.62652 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.66989 | 0.221105 | ||||||||
\(911\) | −6.41847 | −0.212653 | −0.106327 | − | 0.994331i | \(-0.533909\pi\) | ||||
−0.106327 | + | 0.994331i | \(0.533909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.3519 | −1.30236 | ||||||||
\(914\) | −8.65133 | −0.286161 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −54.0004 | −1.78422 | ||||||||
\(917\) | −21.8093 | −0.720206 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.9016 | −0.854416 | −0.427208 | − | 0.904153i | \(-0.640503\pi\) | ||||
−0.427208 | + | 0.904153i | \(0.640503\pi\) | |||||||
\(920\) | 27.6644 | 0.912068 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.2686 | −0.371113 | ||||||||
\(923\) | 6.50206 | 0.214018 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.53998 | 0.313673 | ||||||||
\(926\) | 4.62141 | 0.151869 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.2888 | −0.403399 | ||||||||
\(929\) | 37.1415 | 1.21857 | 0.609287 | − | 0.792950i | \(-0.291456\pi\) | ||||
0.609287 | + | 0.792950i | \(0.291456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.12733 | −0.299136 | ||||||||
\(932\) | 23.1772 | 0.759193 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.39039 | 0.209100 | ||||||||
\(935\) | −25.1925 | −0.823882 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.5304 | −1.03005 | −0.515026 | − | 0.857175i | \(-0.672218\pi\) | ||||
−0.515026 | + | 0.857175i | \(0.672218\pi\) | |||||||
\(938\) | 6.69811 | 0.218701 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −50.4399 | −1.64517 | ||||||||
\(941\) | −49.7790 | −1.62275 | −0.811375 | − | 0.584526i | \(-0.801281\pi\) | ||||
−0.811375 | + | 0.584526i | \(0.801281\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.4048 | 0.729602 | ||||||||
\(944\) | −26.1453 | −0.850957 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.54035 | 0.277671 | ||||||||
\(947\) | −37.6660 | −1.22398 | −0.611990 | − | 0.790865i | \(-0.709631\pi\) | ||||
−0.611990 | + | 0.790865i | \(0.709631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.4659 | −0.502044 | ||||||||
\(950\) | −19.9092 | −0.645940 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.15733 | 0.264381 | ||||||||
\(953\) | 15.5730 | 0.504461 | 0.252230 | − | 0.967667i | \(-0.418836\pi\) | ||||
0.252230 | + | 0.967667i | \(0.418836\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 76.4394 | 2.47352 | ||||||||
\(956\) | 2.24749 | 0.0726891 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.26873 | −0.170225 | ||||||||
\(959\) | 47.8192 | 1.54416 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0958 | 0.486962 | ||||||||
\(962\) | 0.632396 | 0.0203893 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.8605 | 0.800703 | ||||||||
\(965\) | 41.1722 | 1.32538 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.33607 | 0.0429651 | 0.0214825 | − | 0.999769i | \(-0.493161\pi\) | ||||
0.0214825 | + | 0.999769i | \(0.493161\pi\) | |||||||
\(968\) | −0.709724 | −0.0228114 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.9561 | −0.448103 | ||||||||
\(971\) | 34.7058 | 1.11376 | 0.556881 | − | 0.830592i | \(-0.311998\pi\) | ||||
0.556881 | + | 0.830592i | \(0.311998\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −56.9390 | −1.82538 | ||||||||
\(974\) | −11.8397 | −0.379370 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 34.7509 | 1.11235 | ||||||||
\(977\) | 47.6195 | 1.52348 | 0.761742 | − | 0.647881i | \(-0.224344\pi\) | ||||
0.761742 | + | 0.647881i | \(0.224344\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.5049 | −1.29454 | ||||||||
\(980\) | 10.7780 | 0.344292 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.96317 | −0.254115 | ||||||||
\(983\) | −39.0836 | −1.24657 | −0.623286 | − | 0.781994i | \(-0.714203\pi\) | ||||
−0.623286 | + | 0.781994i | \(0.714203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 95.0618 | 3.02892 | ||||||||
\(986\) | −2.21632 | −0.0705821 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.4086 | 0.585656 | ||||||||
\(989\) | 35.7971 | 1.13828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5424 | −1.31964 | −0.659819 | − | 0.751424i | \(-0.729367\pi\) | ||||
−0.659819 | + | 0.751424i | \(0.729367\pi\) | |||||||
\(992\) | 27.1872 | 0.863196 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.18813 | −0.132840 | ||||||||
\(995\) | 42.8955 | 1.35988 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0081 | 0.601993 | 0.300996 | − | 0.953625i | \(-0.402681\pi\) | ||||
0.300996 | + | 0.953625i | \(0.402681\pi\) | |||||||
\(998\) | 0.746952 | 0.0236444 | ||||||||
\(999\) | 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 | 4023.2.a.e.1.15 | ✓ | 25 | |
3.2 | odd | 2 | 4023.2.a.f.1.11 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4023.2.a.e.1.15 | ✓ | 25 | 1.1 | even | 1 | trivial | |
4023.2.a.f.1.11 | yes | 25 | 3.2 | odd | 2 |