Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(689,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.n (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 689.19 | ||
Character | \(\chi\) | \(=\) | 1380.689 |
Dual form | 1380.2.n.a.689.17 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.779801 | + | 1.54658i | −0.450219 | + | 0.892918i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.268100 | + | 2.21994i | −0.119898 | + | 0.992786i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.49920 | 0.944610 | 0.472305 | − | 0.881435i | \(-0.343422\pi\) | ||||
0.472305 | + | 0.881435i | \(0.343422\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.78382 | − | 2.41205i | −0.594607 | − | 0.804017i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.17850 | −0.958353 | −0.479177 | − | 0.877718i | \(-0.659065\pi\) | ||||
−0.479177 | + | 0.877718i | \(0.659065\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.31475i | − | 1.47405i | −0.675868 | − | 0.737023i | \(-0.736231\pi\) | ||
0.675868 | − | 0.737023i | \(-0.263769\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.22425 | − | 2.14575i | −0.832497 | − | 0.554030i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.70251i | − | 0.655456i | −0.944772 | − | 0.327728i | \(-0.893717\pi\) | ||
0.944772 | − | 0.327728i | \(-0.106283\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.13115i | − | 1.86541i | −0.360634 | − | 0.932707i | \(-0.617440\pi\) | ||
0.360634 | − | 0.932707i | \(-0.382560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.94888 | + | 3.86522i | −0.425281 | + | 0.843460i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.12360 | − | 2.44865i | −0.859830 | − | 0.510580i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.85624 | − | 1.19033i | −0.971249 | − | 0.238066i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.12145 | − | 0.877900i | 0.985624 | − | 0.168952i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82516i | 0.524619i | 0.964984 | + | 0.262310i | \(0.0844842\pi\) | ||||
−0.964984 | + | 0.262310i | \(0.915516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.28802 | −1.12936 | −0.564680 | − | 0.825310i | \(-0.691001\pi\) | ||||
−0.564680 | + | 0.825310i | \(0.691001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.47860 | − | 4.91580i | 0.431468 | − | 0.855731i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.670036 | + | 5.54808i | −0.113257 | + | 0.937796i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.82520 | 0.628860 | 0.314430 | − | 0.949281i | \(-0.398187\pi\) | ||||
0.314430 | + | 0.949281i | \(0.398187\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.21968 | + | 4.14445i | 1.31620 | + | 0.663643i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.17048i | − | 0.495146i | −0.968869 | − | 0.247573i | \(-0.920367\pi\) | ||
0.968869 | − | 0.247573i | \(-0.0796330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.93673 | 1.05784 | 0.528920 | − | 0.848671i | \(-0.322597\pi\) | ||||
0.528920 | + | 0.848671i | \(0.322597\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.83284 | − | 3.31330i | 0.869509 | − | 0.493917i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.10788 | −1.18266 | −0.591328 | − | 0.806431i | \(-0.701396\pi\) | ||||
−0.591328 | + | 0.806431i | \(0.701396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.753980 | −0.107711 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.17965 | + | 2.10742i | 0.585268 | + | 0.295098i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.79254i | − | 0.520946i | −0.965481 | − | 0.260473i | \(-0.916122\pi\) | ||
0.965481 | − | 0.260473i | \(-0.0838784\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.852155 | − | 7.05607i | 0.114905 | − | 0.951440i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.5755 | + | 6.34069i | 1.66566 | + | 0.839844i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.2202i | 1.46075i | 0.683049 | + | 0.730373i | \(0.260654\pi\) | ||||
−0.683049 | + | 0.730373i | \(0.739346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.443335i | 0.0567632i | 0.999597 | + | 0.0283816i | \(0.00903536\pi\) | ||||
−0.999597 | + | 0.0283816i | \(0.990965\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.45813 | − | 6.02821i | −0.561671 | − | 0.759483i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.7984 | + | 1.42488i | 1.46341 | + | 0.176735i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.68981 | −0.817290 | −0.408645 | − | 0.912693i | \(-0.633999\pi\) | ||||
−0.408645 | + | 0.912693i | \(0.633999\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.00263 | − | 4.46802i | 0.843018 | − | 0.537886i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.4086i | − | 1.70998i | −0.518641 | − | 0.854992i | \(-0.673562\pi\) | ||
0.518641 | − | 0.854992i | \(-0.326438\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.80940i | 0.328816i | 0.986392 | + | 0.164408i | \(0.0525713\pi\) | ||||
−0.986392 | + | 0.164408i | \(0.947429\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.62785 | − | 6.58235i | 0.649848 | − | 0.760064i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.94372 | −0.905271 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.08039i | 0.684097i | 0.939682 | + | 0.342049i | \(0.111121\pi\) | ||||
−0.939682 | + | 0.342049i | \(0.888879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.63597 | + | 8.60533i | −0.292886 | + | 0.956147i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.29322i | 0.910299i | 0.890415 | + | 0.455150i | \(0.150414\pi\) | ||||
−0.890415 | + | 0.455150i | \(0.849586\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.99941 | + | 0.724543i | 0.650727 | + | 0.0785877i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.36934 | − | 2.20306i | −0.468442 | − | 0.236193i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.80790 | −1.03964 | −0.519818 | − | 0.854277i | \(-0.674000\pi\) | ||||
−0.519818 | + | 0.854277i | \(0.674000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.2826i | − | 1.39240i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.90340 | − | 9.72492i | 0.508459 | − | 1.00843i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.0507 | + | 2.17996i | 1.85196 | + | 0.223659i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.6155 | 1.68705 | 0.843523 | − | 0.537093i | \(-0.180477\pi\) | ||||
0.843523 | + | 0.537093i | \(0.180477\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.66987 | + | 7.66670i | 0.569843 | + | 0.770532i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 11.4594i | − | 1.14025i | −0.821558 | − | 0.570125i | \(-0.806895\pi\) | ||
0.821558 | − | 0.570125i | \(-0.193105\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.97953 | 0.195049 | 0.0975245 | − | 0.995233i | \(-0.468908\pi\) | ||||
0.0975245 | + | 0.995233i | \(0.468908\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.05805 | − | 5.36266i | −0.786385 | − | 0.523342i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.29812i | − | 0.318841i | −0.987211 | − | 0.159421i | \(-0.949037\pi\) | ||
0.987211 | − | 0.159421i | \(-0.0509626\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.6960i | − | 1.02449i | −0.858840 | − | 0.512243i | \(-0.828815\pi\) | ||
0.858840 | − | 0.512243i | \(-0.171185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.98290 | + | 5.91598i | −0.283124 | + | 0.561520i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 18.1325i | − | 1.70576i | −0.522108 | − | 0.852879i | \(-0.674854\pi\) | ||
0.522108 | − | 0.852879i | \(-0.325146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.54140 | − | 8.49765i | 0.609988 | − | 0.792410i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.8194 | + | 9.48055i | −1.18516 | + | 0.876477i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.75413i | − | 0.619150i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.897145 | −0.0815586 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.90340 | + | 2.47235i | 0.442125 | + | 0.222924i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.94442 | − | 10.4614i | 0.352799 | − | 0.935699i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.3592i | 1.62911i | 0.580083 | + | 0.814557i | \(0.303020\pi\) | ||||
−0.580083 | + | 0.814557i | \(0.696980\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.40927 | + | 10.7282i | −0.476260 | + | 0.944566i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.358033i | 0.0312815i | 0.999878 | + | 0.0156408i | \(0.00497881\pi\) | ||||
−0.999878 | + | 0.0156408i | \(0.995021\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 20.3214i | − | 1.76209i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.575822 | + | 11.6047i | 0.0495588 | + | 0.998771i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.52990i | 0.472452i | 0.971698 | + | 0.236226i | \(0.0759105\pi\) | ||||
−0.971698 | + | 0.236226i | \(0.924090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.68656 | −0.227871 | −0.113936 | − | 0.993488i | \(-0.536346\pi\) | ||||
−0.113936 | + | 0.993488i | \(0.536346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.32254 | − | 12.5395i | 0.532454 | − | 1.05602i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.8929i | 1.41266i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.27168 | − | 0.757425i | −0.520835 | − | 0.0629007i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.587955 | − | 1.16609i | 0.0484937 | − | 0.0961775i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.8994 | 1.22060 | 0.610302 | − | 0.792169i | \(-0.291048\pi\) | ||||
0.610302 | + | 0.792169i | \(0.291048\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8285 | −1.20673 | −0.603365 | − | 0.797465i | \(-0.706174\pi\) | ||||
−0.603365 | + | 0.797465i | \(0.706174\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.51860 | + | 4.82080i | −0.526997 | + | 0.389738i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.68582 | − | 13.9590i | 0.135408 | − | 1.12121i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1780 | 0.971907 | 0.485953 | − | 0.873985i | \(-0.338472\pi\) | ||||
0.485953 | + | 0.873985i | \(0.338472\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.86547 | + | 2.95743i | 0.465162 | + | 0.234539i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3057 | − | 6.11969i | −0.812205 | − | 0.482299i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.09350i | 0.555606i | 0.960638 | + | 0.277803i | \(0.0896062\pi\) | ||||
−0.960638 | + | 0.277803i | \(0.910394\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.2483 | + | 6.82026i | 0.797826 | + | 0.530956i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.35456 | −0.182201 | −0.0911006 | − | 0.995842i | \(-0.529038\pi\) | ||||
−0.0911006 | + | 0.995842i | \(0.529038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.2465 | −1.17281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.6128 | + | 14.5045i | −1.49982 | + | 1.10919i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.58728 | −0.728907 | −0.364454 | − | 0.931222i | \(-0.618744\pi\) | ||||
−0.364454 | + | 0.931222i | \(0.618744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.1367 | − | 2.97488i | −0.917452 | − | 0.224880i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.3529 | − | 8.74953i | −1.30433 | − | 0.657655i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.33683i | − | 0.324150i | −0.986778 | − | 0.162075i | \(-0.948181\pi\) | ||
0.986778 | − | 0.162075i | \(-0.0518187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0682i | 0.897022i | 0.893777 | + | 0.448511i | \(0.148046\pi\) | ||||
−0.893777 | + | 0.448511i | \(0.851954\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.685653 | − | 0.345713i | −0.0506849 | − | 0.0255559i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.02554 | + | 8.49171i | −0.0753989 | + | 0.624323i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.58993i | 0.628158i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.7996 | − | 2.19405i | 0.931031 | − | 0.159594i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.4312 | −1.18892 | −0.594460 | − | 0.804125i | \(-0.702634\pi\) | ||||
−0.594460 | + | 0.804125i | \(0.702634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 7.22962i | − | 0.520399i | −0.965555 | − | 0.260200i | \(-0.916212\pi\) | ||
0.965555 | − | 0.260200i | \(-0.0837884\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.4041 | + | 17.1361i | −0.816665 | + | 1.22714i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3898 | 1.52396 | 0.761980 | − | 0.647601i | \(-0.224228\pi\) | ||||
0.761980 | + | 0.647601i | \(0.224228\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 13.5953i | − | 0.963748i | −0.876241 | − | 0.481874i | \(-0.839956\pi\) | ||
0.876241 | − | 0.481874i | \(-0.160044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.21672 | − | 10.3463i | 0.367959 | − | 0.729773i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.06065i | 0.495561i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.03827 | + | 0.850005i | 0.491574 | + | 0.0593670i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.44948 | + | 14.3143i | 0.100746 | + | 0.994912i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.8449i | 1.78773i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.6245 | −1.69522 | −0.847611 | − | 0.530618i | \(-0.821960\pi\) | ||||
−0.847611 | + | 0.530618i | \(0.821960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.2840 | + | 11.2358i | 1.52688 | + | 0.769866i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.85974 | + | 15.3991i | −0.126833 | + | 1.05021i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.7150 | −1.06681 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.34496 | − | 2.19078i | −0.293606 | − | 0.148039i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.3632 | −0.966171 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.3111i | 1.36013i | 0.733151 | + | 0.680066i | \(0.238049\pi\) | ||||
−0.733151 | + | 0.680066i | \(0.761951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.79153 | + | 13.8368i | 0.386102 | + | 0.922456i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5641i | 0.833910i | 0.908927 | + | 0.416955i | \(0.136903\pi\) | ||||
−0.908927 | + | 0.416955i | \(0.863097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.51559i | − | 0.232317i | −0.993231 | − | 0.116158i | \(-0.962942\pi\) | ||
0.993231 | − | 0.116158i | \(-0.0370580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.19452 | − | 12.2856i | 0.407570 | − | 0.808333i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9281 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.17372 | − | 17.9990i | 0.141798 | − | 1.17412i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.40381 | − | 4.74150i | −0.610843 | − | 0.307993i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.02203i | 0.130794i | 0.997859 | + | 0.0653971i | \(0.0208314\pi\) | ||||
−0.997859 | + | 0.0653971i | \(0.979169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.7982i | − | 1.08207i | −0.841000 | − | 0.541034i | \(-0.818033\pi\) | ||
0.841000 | − | 0.541034i | \(-0.181967\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2533 | − | 10.7872i | −0.721899 | − | 0.691999i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.202142 | − | 1.67379i | 0.0129144 | − | 0.106934i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −43.2150 | −2.74971 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.8261 | − | 6.46707i | −0.812823 | − | 0.409834i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.1796 | 1.27372 | 0.636862 | − | 0.770978i | \(-0.280232\pi\) | ||||
0.636862 | + | 0.770978i | \(0.280232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.1069 | + | 7.78305i | 0.824021 | + | 0.489316i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.79891 | + | 8.71357i | −0.363142 | + | 0.545665i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.5299 | 1.59251 | 0.796254 | − | 0.604962i | \(-0.206812\pi\) | ||||
0.796254 | + | 0.604962i | \(0.206812\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.55996 | 0.594027 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.81443 | − | 5.03958i | 0.421803 | − | 0.311942i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.9949i | 1.47959i | 0.672832 | + | 0.739795i | \(0.265078\pi\) | ||||
−0.672832 | + | 0.739795i | \(0.734922\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.41920 | + | 1.01678i | 0.517188 | + | 0.0624603i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.64822 | − | 15.1687i | 0.468063 | − | 0.928310i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 15.9382i | − | 0.971766i | −0.874024 | − | 0.485883i | \(-0.838498\pi\) | ||
0.874024 | − | 0.485883i | \(-0.161502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9813 | −0.849302 | −0.424651 | − | 0.905357i | \(-0.639603\pi\) | ||||
−0.424651 | + | 0.905357i | \(0.639603\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.5427 | + | 10.3578i | 1.24330 | + | 0.626884i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.4356 | + | 3.78346i | 0.930800 | + | 0.228151i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.5924i | − | 0.636439i | −0.948017 | − | 0.318219i | \(-0.896915\pi\) | ||
0.948017 | − | 0.318219i | \(-0.103085\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.2167 | + | 15.1670i | 0.671525 | + | 0.908025i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.21896 | −0.311337 | −0.155668 | − | 0.987809i | \(-0.549753\pi\) | ||||
−0.155668 | + | 0.987809i | \(0.549753\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.8748 | −1.71643 | −0.858214 | − | 0.513291i | \(-0.828426\pi\) | ||||
−0.858214 | + | 0.513291i | \(0.828426\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.4474 | + | 26.2168i | −1.03350 | + | 1.55295i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7.92368i | − | 0.467720i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.69642 | 0.570378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.9568 | + | 25.6972i | −0.759540 | + | 1.50639i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.16268i | − | 0.0679248i | −0.999423 | − | 0.0339624i | \(-0.989187\pi\) | ||
0.999423 | − | 0.0339624i | \(-0.0108126\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.9081 | − | 3.00813i | −1.45021 | − | 0.175140i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.2785 | + | 2.79040i | −0.944576 | + | 0.161916i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.0140 | + | 21.9159i | −0.752618 | + | 1.26743i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.3363 | 0.999247 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.7228 | + | 8.93603i | 1.01815 | + | 0.513362i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.984176 | − | 0.118858i | −0.0563538 | − | 0.00680579i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.6278i | − | 0.948998i | −0.880256 | − | 0.474499i | \(-0.842629\pi\) | ||
0.880256 | − | 0.474499i | \(-0.157371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.54364 | + | 3.06150i | −0.0878147 | + | 0.174163i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 23.5661i | − | 1.33631i | −0.744021 | − | 0.668156i | \(-0.767084\pi\) | ||
0.744021 | − | 0.668156i | \(-0.232916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.4502 | −1.09939 | −0.549694 | − | 0.835366i | \(-0.685256\pi\) | ||||
−0.549694 | + | 0.835366i | \(0.685256\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.5775 | − | 8.28061i | 0.821347 | − | 0.466559i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.7869 | −1.05518 | −0.527588 | − | 0.849500i | \(-0.676904\pi\) | ||||
−0.527588 | + | 0.849500i | \(0.676904\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.97977i | − | 0.502771i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.10081 | + | 2.57188i | 0.284699 | + | 0.143548i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.9746 | −1.22270 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.32630 | + | 25.8097i | −0.350920 | + | 1.43167i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.5421 | + | 8.34072i | 0.914783 | + | 0.461243i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.2632 | −1.11715 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.1440 | 1.93169 | 0.965843 | − | 0.259126i | \(-0.0834345\pi\) | ||||
0.965843 | + | 0.259126i | \(0.0834345\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.82347 | − | 9.22659i | −0.373924 | − | 0.505614i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.79354 | − | 14.8510i | 0.0979914 | − | 0.811394i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.06020 | 0.0577527 | 0.0288763 | − | 0.999583i | \(-0.490807\pi\) | ||||
0.0288763 | + | 0.999583i | \(0.490807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.0433 | + | 14.1397i | 1.52310 | + | 0.767964i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.9864 | 1.08233 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.3788 | −1.04636 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.04131 | + | 16.7433i | 0.432930 | + | 0.901428i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.8541 | 1.49529 | 0.747643 | − | 0.664100i | \(-0.231185\pi\) | ||||
0.747643 | + | 0.664100i | \(0.231185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.55010 | 0.297090 | 0.148545 | − | 0.988906i | \(-0.452541\pi\) | ||||
0.148545 | + | 0.988906i | \(0.452541\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.66581 | − | 27.2192i | −0.249043 | − | 1.45285i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.4788 | −1.24965 | −0.624825 | − | 0.780765i | \(-0.714830\pi\) | ||||
−0.624825 | + | 0.780765i | \(0.714830\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.9861 | + | 3.86294i | 1.69765 | + | 0.205023i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.4458 | + | 5.26688i | 0.552851 | + | 0.278753i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0484 | −0.635892 | −0.317946 | − | 0.948109i | \(-0.602993\pi\) | ||||
−0.317946 | + | 0.948109i | \(0.602993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −47.1157 | −2.47977 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.699595 | − | 1.38751i | 0.0367192 | − | 0.0728252i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.23670 | − | 0.753200i | −0.326444 | − | 0.0394243i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.87742 | −0.150200 | −0.0750999 | − | 0.997176i | \(-0.523928\pi\) | ||||
−0.0750999 | + | 0.997176i | \(0.523928\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.64736 | + | 5.65557i | −0.398106 | + | 0.294417i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.47833i | − | 0.492091i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.78585 | −0.299580 | −0.149790 | − | 0.988718i | \(-0.547860\pi\) | ||||
−0.149790 | + | 0.988718i | \(0.547860\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.1036 | + | 14.2582i | 0.676666 | + | 0.736290i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.0150 | 0.773312 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.59598i | 0.492912i | 0.969154 | + | 0.246456i | \(0.0792661\pi\) | ||||
−0.969154 | + | 0.246456i | \(0.920734\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.3940 | − | 14.3165i | −1.45467 | − | 0.733458i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 13.8929i | − | 0.709892i | −0.934887 | − | 0.354946i | \(-0.884499\pi\) | ||
0.934887 | − | 0.354946i | \(-0.115501\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.12971 | − | 17.6346i | 0.108540 | − | 0.898740i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.3739 | − | 16.7317i | −0.628999 | − | 0.850522i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.2864 | 0.673646 | 0.336823 | − | 0.941568i | \(-0.390648\pi\) | ||||
0.336823 | + | 0.941568i | \(0.390648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.61752 | + | 11.1441i | −0.334662 | + | 0.563581i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.553727 | − | 0.279195i | −0.0279318 | − | 0.0140835i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.4981 | − | 1.63015i | −0.679162 | − | 0.0820218i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.894529i | 0.0448951i | 0.999748 | + | 0.0224476i | \(0.00714588\pi\) | ||||
−0.999748 | + | 0.0224476i | \(0.992854\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 31.4287 | + | 15.8467i | 1.57340 | + | 0.793326i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.536200 | 0.0267765 | 0.0133883 | − | 0.999910i | \(-0.495738\pi\) | ||||
0.0133883 | + | 0.999910i | \(0.495738\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.4192i | 1.66473i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.3966 | − | 8.15879i | −0.914133 | − | 0.405413i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.1584 | −0.602670 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0581 | 0.645680 | 0.322840 | − | 0.946454i | \(-0.395362\pi\) | ||||
0.322840 | + | 0.946454i | \(0.395362\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.55244 | − | 4.31223i | −0.421861 | − | 0.212706i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.0416i | 1.37984i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.4104 | − | 2.22341i | −0.903733 | − | 0.109143i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.09498 | − | 4.15498i | 0.102592 | − | 0.203470i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.4686 | 1.58620 | 0.793098 | − | 0.609094i | \(-0.208467\pi\) | ||||
0.793098 | + | 0.609094i | \(0.208467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.5546i | 1.73283i | 0.499327 | + | 0.866413i | \(0.333581\pi\) | ||||
−0.499327 | + | 0.866413i | \(0.666419\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.4630 | + | 19.5566i | 0.703215 | + | 0.950875i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.21688 | + | 13.1241i | −0.156042 | + | 0.636611i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.10798i | 0.0536191i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −26.1262 | − | 13.1731i | −1.26139 | − | 0.636004i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.7467 | −0.806660 | −0.403330 | − | 0.915055i | \(-0.632147\pi\) | ||||
−0.403330 | + | 0.915055i | \(0.632147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.98017 | 0.239332 | 0.119666 | − | 0.992814i | \(-0.461818\pi\) | ||||
0.119666 | + | 0.992814i | \(0.461818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.06208 | − | 9.10901i | 0.290655 | − | 0.436744i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.9104 | + | 33.5296i | −0.952443 | + | 1.60394i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.39758 | 0.257612 | 0.128806 | − | 0.991670i | \(-0.458886\pi\) | ||||
0.128806 | + | 0.991670i | \(0.458886\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.34496 | + | 1.81864i | 0.0640459 | + | 0.0866018i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.46631 | 0.0696664 | 0.0348332 | − | 0.999393i | \(-0.488910\pi\) | ||||
0.0348332 | + | 0.999393i | \(0.488910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.62950 | − | 21.7729i | 0.124650 | − | 1.03214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.6185 | + | 23.0431i | −0.549538 | + | 1.08990i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.7265i | − | 0.978142i | −0.872244 | − | 0.489071i | \(-0.837336\pi\) | ||
0.872244 | − | 0.489071i | \(-0.162664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0774i | 0.474525i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5633 | − | 22.9335i | 0.543292 | − | 1.07751i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.4866 | + | 3.56107i | 1.38235 | + | 0.166946i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.31011 | 0.435509 | 0.217754 | − | 0.976004i | \(-0.430127\pi\) | ||||
0.217754 | + | 0.976004i | \(0.430127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.37254 | − | 13.8408i | −0.110740 | − | 0.646033i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.79612i | − | 0.130228i | −0.997878 | − | 0.0651142i | \(-0.979259\pi\) | ||
0.997878 | − | 0.0651142i | \(-0.0207412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.8431i | − | 1.06161i | −0.847495 | − | 0.530803i | \(-0.821890\pi\) | ||
0.847495 | − | 0.530803i | \(-0.178110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.2741 | + | 13.4925i | 0.940189 | + | 0.625700i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 20.0898i | − | 0.929647i | −0.885403 | − | 0.464824i | \(-0.846118\pi\) | ||
0.885403 | − | 0.464824i | \(-0.153882\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.7192 | −0.772021 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.49639 | + | 18.8342i | −0.437570 | + | 0.867834i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.0484 | −1.01379 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.67875 | + | 39.4869i | −0.444092 | + | 1.81178i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.14780 | + | 6.76521i | −0.418849 | + | 0.309758i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.0548 | 1.87584 | 0.937921 | − | 0.346848i | \(-0.112748\pi\) | ||||
0.937921 | + | 0.346848i | \(0.112748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 20.3300i | − | 0.926968i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.5010 | − | 11.1665i | 0.796323 | − | 0.508093i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.45461 | + | 36.8853i | −0.202273 | + | 1.67488i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9628i | 0.587401i | 0.955898 | + | 0.293700i | \(0.0948868\pi\) | ||||
−0.955898 | + | 0.293700i | \(0.905113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.9707 | − | 5.53152i | −0.496111 | − | 0.250144i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.0378i | − | 1.17507i | −0.809199 | − | 0.587535i | \(-0.800098\pi\) | ||
0.809199 | − | 0.587535i | \(-0.199902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.63503 | 0.343865 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.5397 | + | 10.5313i | −0.833297 | + | 0.473347i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 36.0100i | − | 1.61527i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0017 | −0.447737 | −0.223868 | − | 0.974619i | \(-0.571869\pi\) | ||||
−0.223868 | + | 0.974619i | \(0.571869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.83609 | − | 3.64152i | 0.0820304 | − | 0.162691i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.1067i | 1.11945i | 0.828678 | + | 0.559726i | \(0.189093\pi\) | ||||
−0.828678 | + | 0.559726i | \(0.810907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.4391 | + | 3.07226i | 1.13202 | + | 0.136714i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.8893 | − | 23.5800i | 0.528021 | − | 1.04722i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 8.88230i | − | 0.393701i | −0.980433 | − | 0.196851i | \(-0.936929\pi\) | ||
0.980433 | − | 0.196851i | \(-0.0630714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.02127i | 0.310603i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.13834 | − | 41.6433i | −0.315165 | − | 1.83860i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.530712 | + | 4.39444i | −0.0233860 | + | 0.193642i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.7709 | 1.13340 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.47617 | − | 14.8275i | 0.328167 | − | 0.650855i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.6427 | −1.56154 | −0.780768 | − | 0.624821i | \(-0.785172\pi\) | ||||
−0.780768 | + | 0.624821i | \(0.785172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.4731 | 1.07013 | 0.535066 | − | 0.844810i | \(-0.320287\pi\) | ||||
0.535066 | + | 0.844810i | \(0.320287\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.0651 | − | 16.4506i | 0.613853 | − | 0.717965i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9934i | 0.740246i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0082 | + | 20.1946i | 0.478617 | + | 0.878024i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.0637 | − | 20.0148i | 1.17446 | − | 0.868569i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.8503 | −0.729868 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.32162 | + | 0.884225i | 0.316541 | + | 0.0382284i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.70726 | + | 3.38187i | 0.289440 | + | 0.145938i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.39653 | 0.103226 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.6885 | 0.502526 | 0.251263 | − | 0.967919i | \(-0.419154\pi\) | ||||
0.251263 | + | 0.967919i | \(0.419154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.6644 | − | 9.41080i | −0.800968 | − | 0.403856i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.7443 | + | 2.86758i | 1.01710 | + | 0.122834i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.1601i | − | 1.07577i | −0.843019 | − | 0.537883i | \(-0.819224\pi\) | ||
0.843019 | − | 0.537883i | \(-0.180776\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.06935 | − | 0.790830i | 0.0456386 | − | 0.0337518i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.9718 | 0.978632 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.1961i | 0.646205i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.3334 | − | 8.20792i | −0.523524 | − | 0.348407i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 35.0941i | − | 1.48699i | −0.668744 | − | 0.743493i | \(-0.733168\pi\) | ||
0.668744 | − | 0.743493i | \(-0.266832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 36.8669i | − | 1.55931i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.2850 | − | 6.69844i | −0.560894 | − | 0.282808i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 31.2531i | − | 1.31716i | −0.752510 | − | 0.658581i | \(-0.771157\pi\) | ||
0.752510 | − | 0.658581i | \(-0.228843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.2529 | + | 4.86131i | 1.69345 | + | 0.204517i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.58784 | + | 21.5065i | −0.276663 | + | 0.903187i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.3858 | 1.14807 | 0.574035 | − | 0.818830i | \(-0.305377\pi\) | ||||
0.574035 | + | 0.818830i | \(0.305377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 30.5119i | − | 1.27688i | −0.769670 | − | 0.638442i | \(-0.779579\pi\) | ||
0.769670 | − | 0.638442i | \(-0.220421\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8131 | − | 25.4122i | 0.535274 | − | 1.06161i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.1105 | + | 16.7997i | 0.713558 | + | 0.700596i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11.6438i | − | 0.484739i | −0.970184 | − | 0.242370i | \(-0.922075\pi\) | ||
0.970184 | − | 0.242370i | \(-0.0779247\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.1812 | + | 5.63767i | 0.464674 | + | 0.234293i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.7265i | 0.859878i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0546i | 0.499250i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.6093 | − | 31.0001i | −0.728056 | − | 1.28170i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.2461 | 0.670547 | 0.335274 | − | 0.942121i | \(-0.391171\pi\) | ||||
0.335274 | + | 0.942121i | \(0.391171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 51.1288i | 2.10673i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.6798 | + | 33.0810i | −0.686115 | + | 1.36077i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.6545 | −0.766048 | −0.383024 | − | 0.923738i | \(-0.625117\pi\) | ||||
−0.383024 | + | 0.923738i | \(0.625117\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9937 | + | 1.81078i | 0.614684 | + | 0.0742348i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.0263 | + | 10.6017i | 0.860548 | + | 0.433897i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.4728i | 0.999933i | 0.866045 | + | 0.499967i | \(0.166654\pi\) | ||||
−0.866045 | + | 0.499967i | \(0.833346\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.74294 | 0.234259 | 0.117130 | − | 0.993117i | \(-0.462631\pi\) | ||||
0.117130 | + | 0.993117i | \(0.462631\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.9334 | + | 16.1362i | 0.485966 | + | 0.657115i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.240524 | − | 1.99161i | 0.00977871 | − | 0.0809703i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.1013i | − | 0.897064i | −0.893767 | − | 0.448532i | \(-0.851947\pi\) | ||
0.893767 | − | 0.448532i | \(-0.148053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.9199 | − | 5.50591i | −0.442495 | − | 0.223111i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 43.0913i | 1.74329i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.2545 | −0.939241 | −0.469620 | − | 0.882868i | \(-0.655609\pi\) | ||||
−0.469620 | + | 0.882868i | \(0.655609\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.80305 | + | 10.2224i | −0.274326 | + | 0.412207i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.6444i | − | 0.509045i | −0.967067 | − | 0.254522i | \(-0.918082\pi\) | ||
0.967067 | − | 0.254522i | \(-0.0819183\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 25.8745i | − | 1.03998i | −0.854172 | − | 0.519991i | \(-0.825935\pi\) | ||
0.854172 | − | 0.519991i | \(-0.174065\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.2685 | − | 8.92056i | −0.933733 | − | 0.357970i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.5120 | −0.982051 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.1662 | + | 11.5611i | 0.886649 | + | 0.462443i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −39.9712 | − | 20.1539i | −1.59629 | − | 0.804868i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 10.3377i | − | 0.412190i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 34.6299i | − | 1.37859i | −0.724478 | − | 0.689297i | \(-0.757919\pi\) | ||
0.724478 | − | 0.689297i | \(-0.242081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.2022 | − | 38.0838i | 0.763220 | − | 1.51369i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.7563 | − | 4.92210i | −1.61736 | − | 0.195327i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00721i | 0.158772i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.7542 | + | 25.7023i | −1.37486 | + | 1.01677i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.0695 | −1.78014 | −0.890069 | − | 0.455826i | \(-0.849344\pi\) | ||||
−0.890069 | + | 0.455826i | \(0.849344\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.0417 | 1.73684 | 0.868418 | − | 0.495833i | \(-0.165137\pi\) | ||||
0.868418 | + | 0.495833i | \(0.165137\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22.3657 | − | 14.8845i | −0.880649 | − | 0.586075i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.98438 | −0.274584 | −0.137292 | − | 0.990531i | \(-0.543840\pi\) | ||||
−0.137292 | + | 0.990531i | \(0.543840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 35.6634i | − | 1.39991i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.2546 | − | 24.3046i | 0.480296 | − | 0.952571i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.2824 | −1.06764 | −0.533822 | − | 0.845597i | \(-0.679245\pi\) | ||||
−0.533822 | + | 0.845597i | \(0.679245\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.794812 | − | 0.0959887i | −0.0310559 | − | 0.00375059i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.77642 | − | 5.01147i | 0.264373 | − | 0.195516i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.6987 | −1.07899 | −0.539495 | − | 0.841989i | \(-0.681385\pi\) | ||||
−0.539495 | + | 0.841989i | \(0.681385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4773i | 0.990951i | 0.868622 | + | 0.495475i | \(0.165006\pi\) | ||||
−0.868622 | + | 0.495475i | \(0.834994\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.2004 | − | 22.2138i | 0.434988 | − | 0.862712i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 45.1123 | + | 5.44817i | 1.74938 | + | 0.211271i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.91784 | − | 11.6498i | 0.267860 | − | 0.451083i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31.4128 | − | 15.8386i | −1.21449 | − | 0.612357i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.40914i | − | 0.0543993i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9655i | 0.461238i | 0.973044 | + | 0.230619i | \(0.0740751\pi\) | ||||
−0.973044 | + | 0.230619i | \(0.925925\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9160 | − | 1.83292i | −0.997508 | − | 0.0705492i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 0.225684i | − | 0.00867374i | −0.999991 | − | 0.00433687i | \(-0.998620\pi\) | ||
0.999991 | − | 0.00433687i | \(-0.00138047\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.5255 | 1.59360 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.4314 | − | 9.79752i | −0.744614 | − | 0.375442i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.6950 | −0.447495 | −0.223747 | − | 0.974647i | \(-0.571829\pi\) | ||||
−0.223747 | + | 0.974647i | \(0.571829\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.2760 | − | 1.48257i | −0.469043 | − | 0.0566459i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.43714 | + | 2.74146i | 0.207440 | + | 0.104593i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.1564 | −0.767897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.71396 | −0.103244 | −0.0516220 | − | 0.998667i | \(-0.516439\pi\) | ||||
−0.0516220 | + | 0.998667i | \(0.516439\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.1702 | + | 19.1606i | 0.538280 | + | 0.727853i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.720266 | − | 5.96400i | 0.0273213 | − | 0.226227i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.56827 | −0.324546 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.6409 | + | 23.0875i | −0.440301 | + | 0.873249i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.06128 | 0.0400838 | 0.0200419 | − | 0.999799i | \(-0.493620\pi\) | ||||
0.0200419 | + | 0.999799i | \(0.493620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 31.1033i | − | 1.17308i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.1418 | + | 17.3975i | 0.984557 | + | 0.655226i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 28.6393i | − | 1.07709i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.4258i | 0.804661i | 0.915494 | + | 0.402331i | \(0.131800\pi\) | ||||
−0.915494 | + | 0.402331i | \(0.868200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6662 | − | 10.8463i | 0.550026 | − | 0.406769i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.9293 | + | 15.3972i | 0.971059 | + | 0.576629i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.5012 | − | 4.52899i | −1.40247 | − | 0.169375i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.12723 | − | 1.57678i | −0.116788 | − | 0.0588859i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.8860i | 0.928092i | 0.885811 | + | 0.464046i | \(0.153603\pi\) | ||||
−0.885811 | + | 0.464046i | \(0.846397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.94725 | 0.184245 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.9798 | + | 13.0993i | 0.966199 | + | 0.487167i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.36287 | − | 13.7197i | 0.124894 | − | 0.509536i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.2531 | −0.417354 | −0.208677 | − | 0.977985i | \(-0.566916\pi\) | ||||
−0.208677 | + | 0.977985i | \(0.566916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.4586 | − | 8.99225i | 0.942911 | − | 0.333046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 18.7466i | − | 0.693368i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.2939 | 1.52522 | 0.762612 | − | 0.646856i | \(-0.223917\pi\) | ||||
0.762612 | + | 0.646856i | \(0.223917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.43102 | + | 1.61785i | 0.0896695 | + | 0.0596754i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.2635 | 0.783253 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.5017 | −1.78417 | −0.892083 | − | 0.451872i | \(-0.850756\pi\) | ||||
−0.892083 | + | 0.451872i | \(0.850756\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.6991 | − | 66.8355i | 1.23797 | − | 2.45526i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.34205i | 0.0859214i | 0.999077 | + | 0.0429607i | \(0.0136790\pi\) | ||||
−0.999077 | + | 0.0429607i | \(0.986321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.99452 | + | 33.0757i | −0.146348 | + | 1.21180i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.0037 | − | 14.7936i | 0.731896 | − | 0.541270i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 8.24267i | − | 0.301181i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.1689i | 0.553521i | 0.960939 | + | 0.276761i | \(0.0892609\pi\) | ||||
−0.960939 | + | 0.276761i | \(0.910739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.7361 | + | 31.2093i | −0.573454 | + | 1.13733i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.97553 | − | 32.9184i | 0.144684 | − | 1.19802i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.9066 | −1.12332 | −0.561660 | − | 0.827368i | \(-0.689837\pi\) | ||||
−0.561660 | + | 0.827368i | \(0.689837\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.2579 | + | 14.2016i | −0.807909 | + | 0.515485i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 44.8828i | − | 1.62700i | −0.581566 | − | 0.813499i | \(-0.697560\pi\) | ||
0.581566 | − | 0.813499i | \(-0.302440\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 26.7314i | − | 0.967740i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.95423 | − | 15.7633i | −0.323741 | − | 0.569925i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 59.6325 | 2.15320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.9985i | 1.58663i | 0.608814 | + | 0.793313i | \(0.291646\pi\) | ||||
−0.608814 | + | 0.793313i | \(0.708354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.9082 | + | 39.4840i | −0.716977 | + | 1.42198i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.2898i | 0.549936i | 0.961453 | + | 0.274968i | \(0.0886673\pi\) | ||||
−0.961453 | + | 0.274968i | \(0.911333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.5361 | + | 7.48481i | 1.09689 | + | 0.268862i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.45487 | + | 14.7853i | −0.267442 | + | 0.530418i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.7797 | −0.923653 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.7977i | 1.63877i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.48021 | + | 14.4689i | 0.0886354 | + | 0.517077i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.26491 | + | 27.0343i | −0.116530 | + | 0.964896i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.2054 | 1.54011 | 0.770054 | − | 0.637979i | \(-0.220229\pi\) | ||||
0.770054 | + | 0.637979i | \(0.220229\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.1101 | − | 18.7113i | −1.32115 | − | 0.666139i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 45.3167i | − | 1.61128i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.35621 | 0.0836716 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.13784 | + | 12.2281i | −0.288619 | + | 0.433686i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 38.4093i | − | 1.36053i | −0.732968 | − | 0.680263i | \(-0.761866\pi\) | ||
0.732968 | − | 0.680263i | \(-0.238134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.9116i | 0.775178i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.4955 | + | 23.6572i | 0.618174 | + | 0.835885i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 8.92968i | − | 0.315122i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.3483 | − | 21.2374i | 0.576201 | − | 0.748519i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.6496 | + | 12.4286i | 0.867708 | + | 0.437507i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.40234i | − | 0.154778i | −0.997001 | − | 0.0773891i | \(-0.975342\pi\) | ||
0.997001 | − | 0.0773891i | \(-0.0246584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.52615 | −0.264279 | −0.132139 | − | 0.991231i | \(-0.542185\pi\) | ||||
−0.132139 | + | 0.991231i | \(0.542185\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.9026 | − | 21.6232i | 0.382372 | − | 0.758358i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.7471 | − | 1.90177i | −0.551598 | − | 0.0666160i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 56.4036i | − | 1.97331i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −32.0384 | + | 23.6938i | −1.11951 | + | 0.827929i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.7227i | 1.45613i | 0.685508 | + | 0.728065i | \(0.259580\pi\) | ||||
−0.685508 | + | 0.728065i | \(0.740420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.8585i | 0.727083i | 0.931578 | + | 0.363541i | \(0.118432\pi\) | ||||
−0.931578 | + | 0.363541i | \(0.881568\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.8881 | + | 20.9220i | −0.622784 | + | 0.728410i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.2222i | 0.529329i | 0.964341 | + | 0.264665i | \(0.0852613\pi\) | ||||
−0.964341 | + | 0.264665i | \(0.914739\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.34887 | 0.0815798 | 0.0407899 | − | 0.999168i | \(-0.487013\pi\) | ||||
0.0407899 | + | 0.999168i | \(0.487013\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.3821 | + | 8.26001i | 0.568288 | + | 0.286536i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.03764i | 0.0706001i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.631257 | − | 5.22698i | 0.0218455 | − | 0.180887i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.2038 | + | 5.52025i | −1.11313 | + | 0.190808i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.6875 | 1.05945 | 0.529725 | − | 0.848169i | \(-0.322295\pi\) | ||||
0.529725 | + | 0.848169i | \(0.322295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0185 | 0.724775 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.06975 | − | 8.07153i | 0.140170 | − | 0.277998i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.08759 | − | 33.8463i | 0.140617 | − | 1.16435i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.24215 | −0.0770411 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.5166 | − | 44.6572i | 0.772768 | − | 1.53263i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.7736 | − | 9.36660i | −0.540713 | − | 0.321083i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 30.4110i | − | 1.04125i | −0.853784 | − | 0.520627i | \(-0.825698\pi\) | ||
0.853784 | − | 0.520627i | \(-0.174302\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26.9409 | − | 47.4277i | −0.921361 | − | 1.62199i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.89538 | −0.167223 | −0.0836115 | − | 0.996498i | \(-0.526645\pi\) | ||||
−0.0836115 | + | 0.996498i | \(0.526645\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.0860 | −0.992400 | −0.496200 | − | 0.868208i | \(-0.665272\pi\) | ||||
−0.496200 | + | 0.868208i | \(0.665272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.2546 | + | 6.17890i | 0.417636 | + | 0.210576i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.680690 | 0.0231709 | 0.0115855 | − | 0.999933i | \(-0.496312\pi\) | ||||
0.0115855 | + | 0.999933i | \(0.496312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.57035 | − | 21.2832i | 0.0873944 | − | 0.723649i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.56128 | + | 14.9963i | −0.256795 | + | 0.509301i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 19.3265i | − | 0.655607i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.5546i | 1.20472i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.6390 | − | 40.0774i | −1.00313 | − | 1.35641i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.85790 | − | 26.1453i | 0.333258 | − | 0.883871i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.8136i | 1.07427i | 0.843496 | + | 0.537135i | \(0.180493\pi\) | ||||
−0.843496 | + | 0.537135i | \(0.819507\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.79819 | + | 0.906663i | 0.0606513 | + | 0.0305810i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.6165 | 0.694586 | 0.347293 | − | 0.937757i | \(-0.387101\pi\) | ||||
0.347293 | + | 0.937757i | \(0.387101\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 32.9502i | − | 1.10886i | −0.832230 | − | 0.554431i | \(-0.812936\pi\) | ||
0.832230 | − | 0.554431i | \(-0.187064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.0757 | − | 36.1767i | 0.809296 | − | 1.21607i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.94098 | −0.300209 | −0.150104 | − | 0.988670i | \(-0.547961\pi\) | ||||
−0.150104 | + | 0.988670i | \(0.547961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.8834i | 1.53888i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.37844 | − | 27.3520i | 0.280688 | − | 0.916327i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 65.9264i | 2.20614i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.62750 | + | 1.16270i | 0.321812 | + | 0.0388649i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.7464 | − | 37.2172i | −0.792868 | − | 1.24265i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 17.7647i | − | 0.592484i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.2494 | −0.341457 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.5189 | + | 26.8120i | −0.449880 | + | 0.892246i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.7906 | − | 3.23548i | −0.890551 | − | 0.107551i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.9025 | 1.02610 | 0.513050 | − | 0.858359i | \(-0.328515\pi\) | ||||
0.513050 | + | 0.858359i | \(0.328515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.6406 | + | 20.4415i | −0.916780 | + | 0.678000i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.7517 | −1.88027 | −0.940133 | − | 0.340807i | \(-0.889300\pi\) | ||||
−0.940133 | + | 0.340807i | \(0.889300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 26.3600i | − | 0.872389i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.951286 | − | 1.42942i | 0.0314485 | − | 0.0472552i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.894798i | 0.0295488i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 25.8160i | − | 0.851593i | −0.904819 | − | 0.425796i | \(-0.859994\pi\) | ||
0.904819 | − | 0.425796i | \(-0.140006\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.7162 | + | 12.9664i | 0.847378 | + | 0.427256i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −76.5779 | −2.52059 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.5761 | − | 4.55325i | −0.610779 | − | 0.149710i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.53113 | − | 4.77473i | −0.115977 | − | 0.156823i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.60757i | − | 0.315214i | −0.987502 | − | 0.157607i | \(-0.949622\pi\) | ||
0.987502 | − | 0.157607i | \(-0.0503779\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.13073i | 0.200927i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.4469 | + | 18.3769i | 1.19322 | + | 0.601632i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.0691 | − | 2.30296i | −0.623627 | − | 0.0753148i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9430 | 0.488165 | 0.244083 | − | 0.969754i | \(-0.421513\pi\) | ||||
0.244083 | + | 0.969754i | \(0.421513\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.1673 | − | 30.0812i | 0.494965 | − | 0.981664i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.0066 | 1.10858 | 0.554291 | − | 0.832323i | \(-0.312989\pi\) | ||||
0.554291 | + | 0.832323i | \(0.312989\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.76341 | + | 13.0738i | −0.252812 | + | 0.425742i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.43910 | + | 29.0024i | 0.0468138 | + | 0.943450i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.50235 | 0.178802 | 0.0894012 | − | 0.995996i | \(-0.471505\pi\) | ||||
0.0894012 | + | 0.995996i | \(0.471505\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.9313 | 0.484689 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.6500 | − | 29.0554i | 0.475060 | − | 0.942187i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 19.3830i | − | 0.627878i | −0.949443 | − | 0.313939i | \(-0.898351\pi\) | ||
0.949443 | − | 0.313939i | \(-0.101649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.40520 | − | 36.4762i | 0.142549 | − | 1.18034i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.8879 | + | 7.00244i | 0.448933 | + | 0.226357i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.8204i | 0.446283i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.53914 | 0.275456 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.95523 | + | 5.88325i | −0.256354 | + | 0.189585i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.0493 | + | 1.93826i | 0.516645 | + | 0.0623948i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.6937i | 1.05136i | 0.850682 | + | 0.525680i | \(0.176189\pi\) | ||||
−0.850682 | + | 0.525680i | \(0.823811\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.1358 | − | 33.9854i | 0.550481 | − | 1.09177i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.7120 | 1.91625 | 0.958124 | − | 0.286353i | \(-0.0924430\pi\) | ||||
0.958124 | + | 0.286353i | \(0.0924430\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.71426 | −0.215249 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −34.9835 | − | 29.9106i | −1.12037 | − | 0.957905i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.3823i | 1.32394i | 0.749532 | + | 0.661968i | \(0.230278\pi\) | ||||
−0.749532 | + | 0.661968i | \(0.769722\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.1744 | 0.996338 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.7992 | + | 19.0797i | −0.823704 | + | 0.609166i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 31.2013i | − | 0.995166i | −0.867416 | − | 0.497583i | \(-0.834221\pi\) | ||
0.867416 | − | 0.497583i | \(-0.165779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.73460 | + | 47.4840i | −0.182719 | + | 1.51297i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.8013 | − | 31.3387i | 0.502961 | − | 0.997523i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.6043 | − | 16.9856i | −0.909564 | − | 0.540112i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.0687 | 1.05046 | 0.525230 | − | 0.850960i | \(-0.323979\pi\) | ||||
0.525230 | + | 0.850960i | \(0.323979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.4053 | + | 54.3530i | −0.869681 | + | 1.72484i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.1808 | + | 3.64491i | 0.956795 | + | 0.115551i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.4909i | 1.12401i | 0.827134 | + | 0.562005i | \(0.189970\pi\) | ||||
−0.827134 | + | 0.562005i | \(0.810030\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.5906 | − | 3.35815i | 0.619819 | − | 0.106247i |
(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 | 1380.2.n.a.689.19 | yes | 48 | |
3.2 | odd | 2 | inner | 1380.2.n.a.689.32 | yes | 48 | |
5.4 | even | 2 | inner | 1380.2.n.a.689.29 | yes | 48 | |
15.14 | odd | 2 | inner | 1380.2.n.a.689.18 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.n.a.689.20 | yes | 48 | |
69.68 | even | 2 | inner | 1380.2.n.a.689.31 | yes | 48 | |
115.114 | odd | 2 | inner | 1380.2.n.a.689.30 | yes | 48 | |
345.344 | even | 2 | inner | 1380.2.n.a.689.17 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.n.a.689.17 | ✓ | 48 | 345.344 | even | 2 | inner | |
1380.2.n.a.689.18 | yes | 48 | 15.14 | odd | 2 | inner | |
1380.2.n.a.689.19 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.n.a.689.20 | yes | 48 | 23.22 | odd | 2 | inner | |
1380.2.n.a.689.29 | yes | 48 | 5.4 | even | 2 | inner | |
1380.2.n.a.689.30 | yes | 48 | 115.114 | odd | 2 | inner | |
1380.2.n.a.689.31 | yes | 48 | 69.68 | even | 2 | inner | |
1380.2.n.a.689.32 | yes | 48 | 3.2 | odd | 2 | inner |