Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,2,Mod(101,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.y (of order \(8\), degree \(4\), 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: | \(6.38803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 101.8 | ||
Character | \(\chi\) | \(=\) | 800.101 |
Dual form | 800.2.y.e.301.8 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.349813 | − | 1.37027i | −0.247355 | − | 0.968925i | ||||
\(3\) | −1.06125 | − | 2.56208i | −0.612712 | − | 1.47922i | −0.860010 | − | 0.510277i | \(-0.829543\pi\) |
0.247298 | − | 0.968939i | \(-0.420457\pi\) | |||||||
\(4\) | −1.75526 | + | 0.958675i | −0.877631 | + | 0.479337i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.13949 | + | 2.35044i | −1.28169 | + | 0.959564i | ||||
\(7\) | 2.94098 | + | 2.94098i | 1.11159 | + | 1.11159i | 0.992936 | + | 0.118651i | \(0.0378568\pi\) |
0.118651 | + | 0.992936i | \(0.462143\pi\) | |||||||
\(8\) | 1.92765 | + | 2.06982i | 0.681528 | + | 0.731792i | ||||
\(9\) | −3.31668 | + | 3.31668i | −1.10556 | + | 1.10556i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.569137 | + | 1.37402i | −0.171601 | + | 0.414282i | −0.986159 | − | 0.165800i | \(-0.946979\pi\) |
0.814558 | + | 0.580082i | \(0.196979\pi\) | |||||||
\(12\) | 4.31897 | + | 3.47973i | 1.24678 | + | 1.00451i | ||||
\(13\) | 4.53377 | − | 1.87795i | 1.25744 | − | 0.520850i | 0.348319 | − | 0.937376i | \(-0.386753\pi\) |
0.909124 | + | 0.416526i | \(0.136753\pi\) | |||||||
\(14\) | 3.00114 | − | 5.05872i | 0.802087 | − | 1.35200i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.16189 | − | 3.36545i | 0.540471 | − | 0.841362i | ||||
\(17\) | 2.78896i | 0.676423i | 0.941070 | + | 0.338211i | \(0.109822\pi\) | ||||
−0.941070 | + | 0.338211i | \(0.890178\pi\) | |||||||
\(18\) | 5.70495 | + | 3.38452i | 1.34467 | + | 0.797738i | ||||
\(19\) | 2.08461 | − | 0.863472i | 0.478242 | − | 0.198094i | −0.130523 | − | 0.991445i | \(-0.541666\pi\) |
0.608764 | + | 0.793351i | \(0.291666\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.41392 | − | 10.6561i | 0.963195 | − | 2.32536i | ||||
\(22\) | 2.08186 | + | 0.299220i | 0.443855 | + | 0.0637939i | ||||
\(23\) | 3.26157 | − | 3.26157i | 0.680085 | − | 0.680085i | −0.279934 | − | 0.960019i | \(-0.590313\pi\) |
0.960019 | + | 0.279934i | \(0.0903127\pi\) | |||||||
\(24\) | 3.25732 | − | 7.13539i | 0.664898 | − | 1.45651i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.15927 | − | 5.55555i | −0.815699 | − | 1.08953i | ||||
\(27\) | 4.33117 | + | 1.79403i | 0.833535 | + | 0.345261i | ||||
\(28\) | −7.98164 | − | 2.34275i | −1.50839 | − | 0.442738i | ||||
\(29\) | 2.85519 | + | 6.89303i | 0.530195 | + | 1.28000i | 0.931394 | + | 0.364012i | \(0.118593\pi\) |
−0.401200 | + | 0.915991i | \(0.631407\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.800126 | −0.143707 | −0.0718535 | − | 0.997415i | \(-0.522891\pi\) | ||||
−0.0718535 | + | 0.997415i | \(0.522891\pi\) | |||||||
\(32\) | −5.36782 | − | 1.78508i | −0.948905 | − | 0.315561i | ||||
\(33\) | 4.12434 | 0.717955 | ||||||||
\(34\) | 3.82162 | − | 0.975616i | 0.655403 | − | 0.167317i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.64202 | − | 9.00125i | 0.440337 | − | 1.50021i | ||||
\(37\) | 8.52386 | + | 3.53070i | 1.40131 | + | 0.580443i | 0.950093 | − | 0.311968i | \(-0.100988\pi\) |
0.451222 | + | 0.892412i | \(0.350988\pi\) | |||||||
\(38\) | −1.91241 | − | 2.55441i | −0.310234 | − | 0.414380i | ||||
\(39\) | −9.62291 | − | 9.62291i | −1.54090 | − | 1.54090i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.87560 | + | 8.87560i | −1.38614 | + | 1.38614i | −0.552864 | + | 0.833271i | \(0.686465\pi\) |
−0.833271 | + | 0.552864i | \(0.813535\pi\) | |||||||
\(42\) | −16.1458 | − | 2.32059i | −2.49135 | − | 0.358074i | ||||
\(43\) | 1.93686 | − | 4.67600i | 0.295369 | − | 0.713083i | −0.704625 | − | 0.709580i | \(-0.748885\pi\) |
0.999994 | − | 0.00350351i | \(-0.00111520\pi\) | |||||||
\(44\) | −0.318252 | − | 2.95738i | −0.0479783 | − | 0.445842i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.61017 | − | 3.32828i | −0.827174 | − | 0.490729i | ||||
\(47\) | − | 2.86075i | − | 0.417284i | −0.977992 | − | 0.208642i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208642i | \(-0.0669043\pi\) | |||||||
\(48\) | −10.9168 | − | 1.96735i | −1.57571 | − | 0.283962i | ||||
\(49\) | 10.2987i | 1.47125i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.14554 | − | 2.95978i | 1.00058 | − | 0.414452i | ||||
\(52\) | −6.15762 | + | 7.64271i | −0.853908 | + | 1.05985i | ||||
\(53\) | −2.24891 | + | 5.42935i | −0.308912 | + | 0.745779i | 0.690829 | + | 0.723018i | \(0.257246\pi\) |
−0.999741 | + | 0.0227609i | \(0.992754\pi\) | |||||||
\(54\) | 0.943199 | − | 6.56244i | 0.128353 | − | 0.893035i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.418107 | + | 11.7565i | −0.0558719 | + | 1.57103i | ||||
\(57\) | −4.42457 | − | 4.42457i | −0.586048 | − | 0.586048i | ||||
\(58\) | 8.44650 | − | 6.32364i | 1.10908 | − | 0.830334i | ||||
\(59\) | 13.6375 | + | 5.64885i | 1.77545 | + | 0.735417i | 0.993732 | + | 0.111790i | \(0.0356583\pi\) |
0.781722 | + | 0.623627i | \(0.214342\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.72380 | − | 11.4043i | −0.604820 | − | 1.46016i | −0.868567 | − | 0.495573i | \(-0.834958\pi\) |
0.263747 | − | 0.964592i | \(-0.415042\pi\) | |||||||
\(62\) | 0.279895 | + | 1.09639i | 0.0355467 | + | 0.139241i | ||||
\(63\) | −19.5086 | −2.45785 | ||||||||
\(64\) | −0.568304 | + | 7.97979i | −0.0710380 | + | 0.997474i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.44275 | − | 5.65144i | −0.177590 | − | 0.695645i | ||||
\(67\) | −5.23321 | − | 12.6341i | −0.639338 | − | 1.54350i | −0.827563 | − | 0.561373i | \(-0.810273\pi\) |
0.188225 | − | 0.982126i | \(-0.439727\pi\) | |||||||
\(68\) | −2.67371 | − | 4.89536i | −0.324235 | − | 0.593649i | ||||
\(69\) | −11.8177 | − | 4.89507i | −1.42269 | − | 0.589297i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.90308 | + | 2.90308i | 0.344532 | + | 0.344532i | 0.858068 | − | 0.513536i | \(-0.171665\pi\) |
−0.513536 | + | 0.858068i | \(0.671665\pi\) | |||||||
\(72\) | −13.2583 | − | 0.471518i | −1.56251 | − | 0.0555690i | ||||
\(73\) | 1.13529 | − | 1.13529i | 0.132876 | − | 0.132876i | −0.637541 | − | 0.770417i | \(-0.720048\pi\) |
0.770417 | + | 0.637541i | \(0.220048\pi\) | |||||||
\(74\) | 1.85624 | − | 12.9151i | 0.215784 | − | 1.50134i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.83124 | + | 3.51408i | −0.324766 | + | 0.403093i | ||||
\(77\) | −5.71478 | + | 2.36714i | −0.651260 | + | 0.269761i | ||||
\(78\) | −9.81974 | + | 16.5522i | −1.11187 | + | 1.87417i | ||||
\(79\) | − | 6.06396i | − | 0.682249i | −0.940018 | − | 0.341124i | \(-0.889192\pi\) | ||
0.940018 | − | 0.341124i | \(-0.110808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.07076i | 0.118973i | ||||||||
\(82\) | 15.2667 | + | 9.05714i | 1.68593 | + | 1.00019i | ||||
\(83\) | 0.292304 | − | 0.121076i | 0.0320846 | − | 0.0132899i | −0.366583 | − | 0.930385i | \(-0.619473\pi\) |
0.398668 | + | 0.917095i | \(0.369473\pi\) | |||||||
\(84\) | 2.46819 | + | 22.9358i | 0.269302 | + | 2.50250i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.08491 | − | 1.01829i | −0.763985 | − | 0.109805i | ||||
\(87\) | 14.6304 | − | 14.6304i | 1.56855 | − | 1.56855i | ||||
\(88\) | −3.94107 | + | 1.47062i | −0.420119 | + | 0.156769i | ||||
\(89\) | −8.97315 | − | 8.97315i | −0.951152 | − | 0.951152i | 0.0477088 | − | 0.998861i | \(-0.484808\pi\) |
−0.998861 | + | 0.0477088i | \(0.984808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.8568 | + | 7.81073i | 1.97673 | + | 0.818787i | ||||
\(92\) | −2.59813 | + | 8.85170i | −0.270873 | + | 0.922854i | ||||
\(93\) | 0.849132 | + | 2.04999i | 0.0880509 | + | 0.212574i | ||||
\(94\) | −3.91999 | + | 1.00073i | −0.404316 | + | 0.103217i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.12307 | + | 15.6472i | 0.114622 | + | 1.59698i | ||||
\(97\) | 13.5255 | 1.37330 | 0.686651 | − | 0.726987i | \(-0.259080\pi\) | ||||
0.686651 | + | 0.726987i | \(0.259080\pi\) | |||||||
\(98\) | 14.1120 | − | 3.60264i | 1.42553 | − | 0.363921i | ||||
\(99\) | −2.66953 | − | 6.44482i | −0.268298 | − | 0.647729i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.14849 | + | 3.37522i | 0.810805 | + | 0.335846i | 0.749275 | − | 0.662259i | \(-0.230402\pi\) |
0.0615299 | + | 0.998105i | \(0.480402\pi\) | |||||||
\(102\) | −6.55529 | − | 8.75592i | −0.649070 | − | 0.866966i | ||||
\(103\) | −6.88114 | − | 6.88114i | −0.678019 | − | 0.678019i | 0.281532 | − | 0.959552i | \(-0.409157\pi\) |
−0.959552 | + | 0.281532i | \(0.909157\pi\) | |||||||
\(104\) | 12.6266 | + | 5.76406i | 1.23814 | + | 0.565212i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.22636 | + | 1.18235i | 0.799015 | + | 0.114840i | ||||
\(107\) | −0.936975 | + | 2.26206i | −0.0905807 | + | 0.218681i | −0.962677 | − | 0.270653i | \(-0.912760\pi\) |
0.872096 | + | 0.489335i | \(0.162760\pi\) | |||||||
\(108\) | −9.32223 | + | 1.00319i | −0.897032 | + | 0.0965323i | ||||
\(109\) | −4.31645 | + | 1.78793i | −0.413441 | + | 0.171253i | −0.579702 | − | 0.814829i | \(-0.696831\pi\) |
0.166260 | + | 0.986082i | \(0.446831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 25.5858i | − | 2.42849i | ||||||
\(112\) | 16.2558 | − | 3.53966i | 1.53603 | − | 0.334466i | ||||
\(113\) | 0.592560i | 0.0557433i | 0.999612 | + | 0.0278717i | \(0.00887297\pi\) | ||||
−0.999612 | + | 0.0278717i | \(0.991127\pi\) | |||||||
\(114\) | −4.51507 | + | 7.61061i | −0.422875 | + | 0.712799i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.6198 | − | 9.36187i | −1.07887 | − | 0.869228i | ||||
\(117\) | −8.80851 | + | 21.2656i | −0.814347 | + | 1.96601i | ||||
\(118\) | 2.96984 | − | 20.6631i | 0.273396 | − | 1.90219i | ||||
\(119\) | −8.20229 | + | 8.20229i | −0.751902 | + | 0.751902i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.21416 | + | 6.21416i | 0.564924 | + | 0.564924i | ||||
\(122\) | −13.9744 | + | 10.4622i | −1.26518 | + | 0.947205i | ||||
\(123\) | 32.1592 | + | 13.3208i | 2.89970 | + | 1.20109i | ||||
\(124\) | 1.40443 | − | 0.767061i | 0.126122 | − | 0.0688841i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.82436 | + | 26.7320i | 0.607962 | + | 2.38147i | ||||
\(127\) | −3.21186 | −0.285006 | −0.142503 | − | 0.989794i | \(-0.545515\pi\) | ||||
−0.142503 | + | 0.989794i | \(0.545515\pi\) | |||||||
\(128\) | 11.1332 | − | 2.01271i | 0.984049 | − | 0.177900i | ||||
\(129\) | −14.0358 | −1.23578 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.16454 | − | 7.63987i | −0.276487 | − | 0.667499i | 0.723246 | − | 0.690590i | \(-0.242649\pi\) |
−0.999733 | + | 0.0230915i | \(0.992649\pi\) | |||||||
\(132\) | −7.23929 | + | 3.95390i | −0.630100 | + | 0.344143i | ||||
\(133\) | 8.67025 | + | 3.59133i | 0.751806 | + | 0.311408i | ||||
\(134\) | −15.4814 | + | 11.5905i | −1.33739 | + | 1.00126i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.77265 | + | 5.37615i | −0.495000 | + | 0.461001i | ||||
\(137\) | −3.47339 | + | 3.47339i | −0.296751 | + | 0.296751i | −0.839740 | − | 0.542989i | \(-0.817293\pi\) |
0.542989 | + | 0.839740i | \(0.317293\pi\) | |||||||
\(138\) | −2.57355 | + | 17.9058i | −0.219075 | + | 1.52424i | ||||
\(139\) | 7.36134 | − | 17.7718i | 0.624380 | − | 1.50739i | −0.222131 | − | 0.975017i | \(-0.571301\pi\) |
0.846511 | − | 0.532371i | \(-0.178699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.32947 | + | 3.03597i | −0.617253 | + | 0.255674i | ||||
\(142\) | 2.96245 | − | 4.99352i | 0.248604 | − | 0.419047i | ||||
\(143\) | 7.29830i | 0.610315i | ||||||||
\(144\) | 3.99183 | + | 18.3324i | 0.332653 | + | 1.52770i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.95279 | − | 1.15851i | −0.161614 | − | 0.0958791i | ||||
\(147\) | 26.3862 | − | 10.9295i | 2.17630 | − | 0.901452i | ||||
\(148\) | −18.3464 | + | 1.97431i | −1.50806 | + | 0.162287i | ||||
\(149\) | −0.649458 | + | 1.56793i | −0.0532056 | + | 0.128450i | −0.948247 | − | 0.317533i | \(-0.897146\pi\) |
0.895042 | + | 0.445983i | \(0.147146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.11339 | + | 6.11339i | −0.497501 | + | 0.497501i | −0.910659 | − | 0.413158i | \(-0.864426\pi\) |
0.413158 | + | 0.910659i | \(0.364426\pi\) | |||||||
\(152\) | 5.80563 | + | 2.65028i | 0.470899 | + | 0.214966i | ||||
\(153\) | −9.25009 | − | 9.25009i | −0.747826 | − | 0.747826i | ||||
\(154\) | 5.24272 | + | 7.00272i | 0.422471 | + | 0.564295i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 26.1160 | + | 7.66549i | 2.09095 | + | 0.613730i | ||||
\(157\) | −4.78009 | − | 11.5402i | −0.381493 | − | 0.921005i | −0.991678 | − | 0.128746i | \(-0.958905\pi\) |
0.610185 | − | 0.792259i | \(-0.291095\pi\) | |||||||
\(158\) | −8.30924 | + | 2.12125i | −0.661048 | + | 0.168758i | ||||
\(159\) | 16.2971 | 1.29244 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.1845 | 1.51195 | ||||||||
\(162\) | 1.46723 | − | 0.374566i | 0.115276 | − | 0.0294287i | ||||
\(163\) | −0.459523 | − | 1.10939i | −0.0359926 | − | 0.0868938i | 0.904861 | − | 0.425707i | \(-0.139975\pi\) |
−0.940854 | + | 0.338813i | \(0.889975\pi\) | |||||||
\(164\) | 7.07019 | − | 24.0878i | 0.552089 | − | 1.88094i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.268159 | − | 0.358181i | −0.0208132 | − | 0.0278002i | ||||
\(167\) | 3.35519 | + | 3.35519i | 0.259632 | + | 0.259632i | 0.824904 | − | 0.565272i | \(-0.191229\pi\) |
−0.565272 | + | 0.824904i | \(0.691229\pi\) | |||||||
\(168\) | 30.5648 | − | 11.4053i | 2.35812 | − | 0.879940i | ||||
\(169\) | 7.83602 | − | 7.83602i | 0.602771 | − | 0.602771i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.05011 | + | 9.77783i | −0.309720 | + | 0.747729i | ||||
\(172\) | 1.08306 | + | 10.0644i | 0.0825827 | + | 0.767405i | ||||
\(173\) | 10.3559 | − | 4.28956i | 0.787345 | − | 0.326129i | 0.0474697 | − | 0.998873i | \(-0.484884\pi\) |
0.739876 | + | 0.672744i | \(0.234884\pi\) | |||||||
\(174\) | −25.1655 | − | 14.9297i | −1.90779 | − | 1.13181i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.39378 | + | 4.88587i | 0.255816 | + | 0.368287i | ||||
\(177\) | − | 40.9352i | − | 3.07688i | ||||||
\(178\) | −9.15669 | + | 15.4345i | −0.686323 | + | 1.15687i | ||||
\(179\) | 4.10991 | − | 1.70238i | 0.307189 | − | 0.127242i | −0.223763 | − | 0.974643i | \(-0.571834\pi\) |
0.530952 | + | 0.847402i | \(0.321834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0541726 | + | 0.130784i | −0.00402662 | + | 0.00972112i | −0.925880 | − | 0.377818i | \(-0.876675\pi\) |
0.921853 | + | 0.387539i | \(0.126675\pi\) | |||||||
\(182\) | 4.10644 | − | 28.5711i | 0.304389 | − | 2.11783i | ||||
\(183\) | −24.2055 | + | 24.2055i | −1.78932 | + | 1.78932i | ||||
\(184\) | 13.0380 | + | 0.463684i | 0.961178 | + | 0.0341833i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.51199 | − | 1.88065i | 0.184188 | − | 0.137896i | ||||
\(187\) | −3.83209 | − | 1.58730i | −0.280230 | − | 0.116075i | ||||
\(188\) | 2.74253 | + | 5.02137i | 0.200020 | + | 0.366221i | ||||
\(189\) | 7.46169 | + | 18.0141i | 0.542758 | + | 1.31033i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.866006 | −0.0626620 | −0.0313310 | − | 0.999509i | \(-0.509975\pi\) | ||||
−0.0313310 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(192\) | 21.0480 | − | 7.01249i | 1.51901 | − | 0.506083i | ||||
\(193\) | 16.6416 | 1.19789 | 0.598946 | − | 0.800790i | \(-0.295586\pi\) | ||||
0.598946 | + | 0.800790i | \(0.295586\pi\) | |||||||
\(194\) | −4.73138 | − | 18.5335i | −0.339694 | − | 1.33063i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.87315 | − | 18.0770i | −0.705225 | − | 1.29121i | ||||
\(197\) | 5.18658 | + | 2.14835i | 0.369529 | + | 0.153064i | 0.559717 | − | 0.828684i | \(-0.310910\pi\) |
−0.190188 | + | 0.981748i | \(0.560910\pi\) | |||||||
\(198\) | −7.89729 | + | 5.91246i | −0.561236 | + | 0.420180i | ||||
\(199\) | 10.7219 | + | 10.7219i | 0.760055 | + | 0.760055i | 0.976332 | − | 0.216277i | \(-0.0693916\pi\) |
−0.216277 | + | 0.976332i | \(0.569392\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.8158 | + | 26.8158i | −1.89144 | + | 1.89144i | ||||
\(202\) | 1.77450 | − | 12.3463i | 0.124853 | − | 0.868683i | ||||
\(203\) | −11.8752 | + | 28.6693i | −0.833477 | + | 2.01219i | ||||
\(204\) | −9.70482 | + | 12.0454i | −0.679474 | + | 0.843349i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.02189 | + | 11.8361i | −0.489238 | + | 0.824661i | ||||
\(207\) | 21.6352i | 1.50375i | ||||||||
\(208\) | 3.48135 | − | 19.3181i | 0.241388 | − | 1.33947i | ||||
\(209\) | 3.35572i | 0.232120i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5357 | + | 5.60666i | −0.931835 | + | 0.385979i | −0.796374 | − | 0.604804i | \(-0.793251\pi\) |
−0.135461 | + | 0.990783i | \(0.543251\pi\) | |||||||
\(212\) | −1.25755 | − | 11.6859i | −0.0863692 | − | 0.802591i | ||||
\(213\) | 4.35702 | − | 10.5188i | 0.298538 | − | 0.720736i | ||||
\(214\) | 3.42739 | + | 0.492608i | 0.234291 | + | 0.0336740i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.63568 | + | 12.4230i | 0.315418 | + | 0.845279i | ||||
\(217\) | −2.35316 | − | 2.35316i | −0.159743 | − | 0.159743i | ||||
\(218\) | 3.95990 | + | 5.28925i | 0.268198 | + | 0.358233i | ||||
\(219\) | −4.11353 | − | 1.70388i | −0.277967 | − | 0.115138i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.23753 | + | 12.6445i | 0.352315 | + | 0.850563i | ||||
\(222\) | −35.0593 | + | 8.95023i | −2.35303 | + | 0.600700i | ||||
\(223\) | −10.8919 | −0.729378 | −0.364689 | − | 0.931129i | \(-0.618825\pi\) | ||||
−0.364689 | + | 0.931129i | \(0.618825\pi\) | |||||||
\(224\) | −10.5368 | − | 21.0366i | −0.704017 | − | 1.40556i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.811965 | − | 0.207285i | 0.0540111 | − | 0.0137884i | ||||
\(227\) | −0.469337 | − | 1.13308i | −0.0311510 | − | 0.0752051i | 0.907539 | − | 0.419969i | \(-0.137959\pi\) |
−0.938689 | + | 0.344764i | \(0.887959\pi\) | |||||||
\(228\) | 12.0080 | + | 3.52455i | 0.795249 | + | 0.233419i | ||||
\(229\) | −2.28178 | − | 0.945143i | −0.150784 | − | 0.0624568i | 0.306015 | − | 0.952027i | \(-0.401004\pi\) |
−0.456799 | + | 0.889570i | \(0.651004\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.1296 | + | 12.1296i | 0.798069 | + | 0.798069i | ||||
\(232\) | −8.76351 | + | 19.1971i | −0.575353 | + | 1.26035i | ||||
\(233\) | −3.16863 | + | 3.16863i | −0.207584 | + | 0.207584i | −0.803240 | − | 0.595656i | \(-0.796892\pi\) |
0.595656 | + | 0.803240i | \(0.296892\pi\) | |||||||
\(234\) | 32.2209 | + | 4.63101i | 2.10635 | + | 0.302739i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −29.3528 | + | 3.15874i | −1.91071 | + | 0.205617i | ||||
\(237\) | −15.5363 | + | 6.43536i | −1.00919 | + | 0.418022i | ||||
\(238\) | 14.1086 | + | 8.37005i | 0.914524 | + | 0.542550i | ||||
\(239\) | 8.68507i | 0.561790i | 0.959738 | + | 0.280895i | \(0.0906313\pi\) | ||||
−0.959738 | + | 0.280895i | \(0.909369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.76968i | 0.500489i | 0.968183 | + | 0.250244i | \(0.0805110\pi\) | ||||
−0.968183 | + | 0.250244i | \(0.919489\pi\) | |||||||
\(242\) | 6.34127 | − | 10.6889i | 0.407632 | − | 0.687106i | ||||
\(243\) | 15.7369 | − | 6.51843i | 1.00952 | − | 0.418158i | ||||
\(244\) | 19.2245 | + | 15.4889i | 1.23072 | + | 0.991573i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.00330 | − | 48.7264i | 0.446514 | − | 3.10668i | ||||
\(247\) | 7.82958 | − | 7.82958i | 0.498184 | − | 0.498184i | ||||
\(248\) | −1.54237 | − | 1.65612i | −0.0979404 | − | 0.105164i | ||||
\(249\) | −0.620414 | − | 0.620414i | −0.0393172 | − | 0.0393172i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3540 | − | 7.18827i | −1.09538 | − | 0.453720i | −0.239498 | − | 0.970897i | \(-0.576983\pi\) |
−0.855878 | + | 0.517177i | \(0.826983\pi\) | |||||||
\(252\) | 34.2427 | − | 18.7024i | 2.15709 | − | 1.17814i | ||||
\(253\) | 2.62518 | + | 6.33774i | 0.165044 | + | 0.398451i | ||||
\(254\) | 1.12355 | + | 4.40110i | 0.0704978 | + | 0.276150i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.65250 | − | 14.5514i | −0.415781 | − | 0.909465i | ||||
\(257\) | −15.7332 | −0.981413 | −0.490707 | − | 0.871325i | \(-0.663261\pi\) | ||||
−0.490707 | + | 0.871325i | \(0.663261\pi\) | |||||||
\(258\) | 4.90990 | + | 19.2327i | 0.305677 | + | 1.19738i | ||||
\(259\) | 14.6848 | + | 35.4523i | 0.912469 | + | 2.20290i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −32.3317 | − | 13.3922i | −2.00128 | − | 0.828958i | ||||
\(262\) | −9.36166 | + | 7.00879i | −0.578365 | + | 0.433004i | ||||
\(263\) | 5.45192 | + | 5.45192i | 0.336180 | + | 0.336180i | 0.854927 | − | 0.518748i | \(-0.173602\pi\) |
−0.518748 | + | 0.854927i | \(0.673602\pi\) | |||||||
\(264\) | 7.95030 | + | 8.53664i | 0.489307 | + | 0.525394i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.88812 | − | 13.1368i | 0.115768 | − | 0.805472i | ||||
\(267\) | −13.4672 | + | 32.5127i | −0.824178 | + | 1.98974i | ||||
\(268\) | 21.2976 | + | 17.1592i | 1.30096 | + | 1.04816i | ||||
\(269\) | −7.58007 | + | 3.13977i | −0.462165 | + | 0.191435i | −0.601602 | − | 0.798796i | \(-0.705471\pi\) |
0.139437 | + | 0.990231i | \(0.455471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.7286i | 1.25918i | 0.776929 | + | 0.629588i | \(0.216776\pi\) | ||||
−0.776929 | + | 0.629588i | \(0.783224\pi\) | |||||||
\(272\) | 9.38611 | + | 6.02942i | 0.569117 | + | 0.365587i | ||||
\(273\) | − | 56.6016i | − | 3.42569i | ||||||
\(274\) | 5.97450 | + | 3.54443i | 0.360933 | + | 0.214127i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 25.4360 | − | 2.73724i | 1.53107 | − | 0.164763i | ||||
\(277\) | −9.02027 | + | 21.7769i | −0.541975 | + | 1.30844i | 0.381352 | + | 0.924430i | \(0.375459\pi\) |
−0.923327 | + | 0.384014i | \(0.874541\pi\) | |||||||
\(278\) | −26.9273 | − | 3.87017i | −1.61499 | − | 0.232117i | ||||
\(279\) | 2.65376 | − | 2.65376i | 0.158877 | − | 0.158877i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.41047 | + | 1.41047i | 0.0841416 | + | 0.0841416i | 0.747925 | − | 0.663783i | \(-0.231050\pi\) |
−0.663783 | + | 0.747925i | \(0.731050\pi\) | |||||||
\(282\) | 6.72403 | + | 8.98131i | 0.400410 | + | 0.534829i | ||||
\(283\) | −1.84276 | − | 0.763298i | −0.109541 | − | 0.0453733i | 0.327240 | − | 0.944941i | \(-0.393881\pi\) |
−0.436781 | + | 0.899568i | \(0.643881\pi\) | |||||||
\(284\) | −7.87876 | − | 2.31255i | −0.467518 | − | 0.137225i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.0006 | − | 2.55304i | 0.591349 | − | 0.150965i | ||||
\(287\) | −52.2059 | −3.08162 | ||||||||
\(288\) | 23.7239 | − | 11.8828i | 1.39794 | − | 0.700200i | ||||
\(289\) | 9.22169 | 0.542452 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.3539 | − | 34.6533i | −0.841438 | − | 2.03141i | ||||
\(292\) | −0.904358 | + | 3.08111i | −0.0529236 | + | 0.180308i | ||||
\(293\) | −9.76088 | − | 4.04309i | −0.570236 | − | 0.236200i | 0.0788860 | − | 0.996884i | \(-0.474864\pi\) |
−0.649122 | + | 0.760684i | \(0.724864\pi\) | |||||||
\(294\) | −24.2066 | − | 32.3328i | −1.41176 | − | 1.88569i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.12314 | + | 24.4488i | 0.530272 | + | 1.42106i | ||||
\(297\) | −4.93006 | + | 4.93006i | −0.286071 | + | 0.286071i | ||||
\(298\) | 2.37567 | + | 0.341448i | 0.137619 | + | 0.0197795i | ||||
\(299\) | 8.66216 | − | 20.9123i | 0.500946 | − | 1.20939i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.4483 | − | 8.05575i | 1.12098 | − | 0.464326i | ||||
\(302\) | 10.5155 | + | 6.23843i | 0.605100 | + | 0.358981i | ||||
\(303\) | − | 24.4590i | − | 1.40513i | ||||||
\(304\) | 1.60071 | − | 8.88237i | 0.0918070 | − | 0.509439i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.43929 | + | 15.9109i | −0.539608 | + | 0.909565i | ||||
\(307\) | −4.19762 | + | 1.73871i | −0.239571 | + | 0.0992336i | −0.499239 | − | 0.866464i | \(-0.666387\pi\) |
0.259668 | + | 0.965698i | \(0.416387\pi\) | |||||||
\(308\) | 7.76162 | − | 9.63357i | 0.442260 | − | 0.548924i | ||||
\(309\) | −10.3274 | + | 24.9326i | −0.587507 | + | 1.41837i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.5777 | − | 22.5777i | 1.28026 | − | 1.28026i | 0.339745 | − | 0.940518i | \(-0.389659\pi\) |
0.940518 | − | 0.339745i | \(-0.110341\pi\) | |||||||
\(312\) | 1.36805 | − | 38.4673i | 0.0774506 | − | 2.17778i | ||||
\(313\) | −18.6877 | − | 18.6877i | −1.05629 | − | 1.05629i | −0.998318 | − | 0.0579726i | \(-0.981536\pi\) |
−0.0579726 | − | 0.998318i | \(-0.518464\pi\) | |||||||
\(314\) | −14.1410 | + | 10.5869i | −0.798020 | + | 0.597453i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.81336 | + | 10.6438i | 0.327027 | + | 0.598763i | ||||
\(317\) | −10.2773 | − | 24.8116i | −0.577231 | − | 1.39356i | −0.895288 | − | 0.445488i | \(-0.853030\pi\) |
0.318057 | − | 0.948072i | \(-0.396970\pi\) | |||||||
\(318\) | −5.70093 | − | 22.3313i | −0.319692 | − | 1.25228i | ||||
\(319\) | −11.0961 | −0.621264 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.78993 | 0.378977 | ||||||||
\(322\) | −6.71097 | − | 26.2878i | −0.373988 | − | 1.46496i | ||||
\(323\) | 2.40819 | + | 5.81389i | 0.133995 | + | 0.323493i | ||||
\(324\) | −1.02651 | − | 1.87946i | −0.0570283 | − | 0.104415i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.35941 | + | 1.01775i | −0.0752906 | + | 0.0563678i | ||||
\(327\) | 9.16165 | + | 9.16165i | 0.506641 | + | 0.506641i | ||||
\(328\) | −35.4800 | − | 1.26181i | −1.95905 | − | 0.0696716i | ||||
\(329\) | 8.41342 | − | 8.41342i | 0.463847 | − | 0.463847i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.97531 | + | 12.0115i | −0.273468 | + | 0.660210i | −0.999627 | − | 0.0273171i | \(-0.991304\pi\) |
0.726159 | + | 0.687527i | \(0.241304\pi\) | |||||||
\(332\) | −0.396997 | + | 0.492745i | −0.0217881 | + | 0.0270429i | ||||
\(333\) | −39.9811 | + | 16.5607i | −2.19095 | + | 0.907522i | ||||
\(334\) | 3.42381 | − | 5.77119i | 0.187343 | − | 0.315786i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −26.3203 | − | 37.8922i | −1.43589 | − | 2.06719i | ||||
\(337\) | 30.1871i | 1.64440i | 0.569200 | + | 0.822199i | \(0.307253\pi\) | ||||
−0.569200 | + | 0.822199i | \(0.692747\pi\) | |||||||
\(338\) | −13.4786 | − | 7.99630i | −0.733138 | − | 0.434941i | ||||
\(339\) | 1.51818 | − | 0.628852i | 0.0824564 | − | 0.0341546i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.455382 | − | 1.09939i | 0.0246603 | − | 0.0595352i | ||||
\(342\) | 14.8150 | + | 2.12932i | 0.801104 | + | 0.115140i | ||||
\(343\) | −9.70156 | + | 9.70156i | −0.523835 | + | 0.523835i | ||||
\(344\) | 13.4121 | − | 5.00475i | 0.723131 | − | 0.269838i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.50047 | − | 12.6898i | −0.510749 | − | 0.682209i | ||||
\(347\) | −2.36957 | − | 0.981507i | −0.127205 | − | 0.0526900i | 0.318173 | − | 0.948033i | \(-0.396931\pi\) |
−0.445378 | + | 0.895343i | \(0.646931\pi\) | |||||||
\(348\) | −11.6544 | + | 39.7060i | −0.624741 | + | 2.12847i | ||||
\(349\) | 5.45739 | + | 13.1753i | 0.292127 | + | 0.705258i | 0.999999 | − | 0.00108291i | \(-0.000344701\pi\) |
−0.707872 | + | 0.706341i | \(0.750345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.0057 | 1.22795 | ||||||||
\(352\) | 5.50776 | − | 6.35953i | 0.293565 | − | 0.338964i | ||||
\(353\) | 3.26004 | 0.173514 | 0.0867571 | − | 0.996229i | \(-0.472350\pi\) | ||||
0.0867571 | + | 0.996229i | \(0.472350\pi\) | |||||||
\(354\) | −56.0922 | + | 14.3197i | −2.98126 | + | 0.761082i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 24.3526 | + | 7.14790i | 1.29068 | + | 0.378838i | ||||
\(357\) | 29.7196 | + | 12.3102i | 1.57293 | + | 0.651527i | ||||
\(358\) | −3.77041 | − | 5.03616i | −0.199273 | − | 0.266169i | ||||
\(359\) | −5.76463 | − | 5.76463i | −0.304245 | − | 0.304245i | 0.538427 | − | 0.842672i | \(-0.319019\pi\) |
−0.842672 | + | 0.538427i | \(0.819019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.83503 | + | 9.83503i | −0.517633 | + | 0.517633i | ||||
\(362\) | 0.198160 | + | 0.0284809i | 0.0104150 | + | 0.00149692i | ||||
\(363\) | 9.32641 | − | 22.5159i | 0.489510 | − | 1.18178i | ||||
\(364\) | −40.5865 | + | 4.36763i | −2.12731 | + | 0.228926i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 41.6353 | + | 24.7006i | 2.17631 | + | 1.29112i | ||||
\(367\) | − | 3.11540i | − | 0.162622i | −0.996689 | − | 0.0813112i | \(-0.974089\pi\) | ||
0.996689 | − | 0.0813112i | \(-0.0259108\pi\) | |||||||
\(368\) | −3.92551 | − | 18.0278i | −0.204631 | − | 0.939764i | ||||
\(369\) | − | 58.8750i | − | 3.06491i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.5816 | + | 9.35362i | −1.17238 | + | 0.485616i | ||||
\(372\) | −3.45572 | − | 2.78422i | −0.179171 | − | 0.144355i | ||||
\(373\) | 3.19002 | − | 7.70139i | 0.165173 | − | 0.398763i | −0.819522 | − | 0.573047i | \(-0.805761\pi\) |
0.984695 | + | 0.174284i | \(0.0557612\pi\) | |||||||
\(374\) | −0.834513 | + | 5.80624i | −0.0431516 | + | 0.300233i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.92124 | − | 5.51454i | 0.305365 | − | 0.284391i | ||||
\(377\) | 25.8895 | + | 25.8895i | 1.33338 | + | 1.33338i | ||||
\(378\) | 22.0739 | − | 16.5261i | 1.13536 | − | 0.850010i | ||||
\(379\) | 13.1426 | + | 5.44383i | 0.675089 | + | 0.279631i | 0.693772 | − | 0.720194i | \(-0.255947\pi\) |
−0.0186833 | + | 0.999825i | \(0.505947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.40858 | + | 8.22903i | 0.174627 | + | 0.421586i | ||||
\(382\) | 0.302940 | + | 1.18666i | 0.0154998 | + | 0.0607148i | ||||
\(383\) | 23.2837 | 1.18974 | 0.594870 | − | 0.803822i | \(-0.297203\pi\) | ||||
0.594870 | + | 0.803822i | \(0.297203\pi\) | |||||||
\(384\) | −16.9718 | − | 26.3883i | −0.866090 | − | 1.34662i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.82147 | − | 22.8035i | −0.296305 | − | 1.16067i | ||||
\(387\) | 9.08484 | + | 21.9327i | 0.461808 | + | 1.11490i | ||||
\(388\) | −23.7407 | + | 12.9665i | −1.20525 | + | 0.658275i | ||||
\(389\) | −10.0350 | − | 4.15664i | −0.508796 | − | 0.210750i | 0.113492 | − | 0.993539i | \(-0.463796\pi\) |
−0.622287 | + | 0.782789i | \(0.713796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.09640 | + | 9.09640i | 0.460025 | + | 0.460025i | ||||
\(392\) | −21.3165 | + | 19.8524i | −1.07665 | + | 1.00270i | ||||
\(393\) | −16.2156 | + | 16.2156i | −0.817968 | + | 0.817968i | ||||
\(394\) | 1.12948 | − | 7.85852i | 0.0569025 | − | 0.395907i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.8642 | + | 8.75314i | 0.545947 | + | 0.439862i | ||||
\(397\) | 15.3292 | − | 6.34955i | 0.769349 | − | 0.318675i | 0.0367406 | − | 0.999325i | \(-0.488302\pi\) |
0.732609 | + | 0.680650i | \(0.238302\pi\) | |||||||
\(398\) | 10.9412 | − | 18.4425i | 0.548432 | − | 0.924439i | ||||
\(399\) | − | 26.0251i | − | 1.30289i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.7249i | − | 1.23470i | −0.786687 | − | 0.617352i | \(-0.788206\pi\) | ||
0.786687 | − | 0.617352i | \(-0.211794\pi\) | |||||||
\(402\) | 46.1253 | + | 27.3643i | 2.30052 | + | 1.36481i | ||||
\(403\) | −3.62759 | + | 1.50260i | −0.180703 | + | 0.0748497i | ||||
\(404\) | −17.5385 | + | 1.88737i | −0.872571 | + | 0.0939000i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 43.4387 | + | 6.24331i | 2.15583 | + | 0.309850i | ||||
\(407\) | −9.70249 | + | 9.70249i | −0.480935 | + | 0.480935i | ||||
\(408\) | 19.9003 | + | 9.08455i | 0.985213 | + | 0.449752i | ||||
\(409\) | 13.2241 | + | 13.2241i | 0.653888 | + | 0.653888i | 0.953927 | − | 0.300039i | \(-0.0969996\pi\) |
−0.300039 | + | 0.953927i | \(0.597000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.5852 | + | 5.21296i | 0.620782 | + | 0.257137i | ||||
\(412\) | 18.6750 | + | 5.48143i | 0.920051 | + | 0.270051i | ||||
\(413\) | 23.4945 | + | 56.7208i | 1.15609 | + | 2.79105i | ||||
\(414\) | 29.6460 | − | 7.56827i | 1.45702 | − | 0.371960i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −27.6888 | + | 1.98734i | −1.35755 | + | 0.0974375i | ||||
\(417\) | −53.3451 | −2.61232 | ||||||||
\(418\) | 4.59823 | − | 1.17388i | 0.224907 | − | 0.0574161i | ||||
\(419\) | −1.44829 | − | 3.49648i | −0.0707536 | − | 0.170814i | 0.884547 | − | 0.466452i | \(-0.154468\pi\) |
−0.955300 | + | 0.295638i | \(0.904468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.95627 | − | 1.22453i | −0.144080 | − | 0.0596797i | 0.309478 | − | 0.950906i | \(-0.399846\pi\) |
−0.453558 | + | 0.891227i | \(0.649846\pi\) | |||||||
\(422\) | 12.4176 | + | 16.5862i | 0.604479 | + | 0.807404i | ||||
\(423\) | 9.48819 | + | 9.48819i | 0.461332 | + | 0.461332i | ||||
\(424\) | −15.5729 | + | 5.81107i | −0.756287 | + | 0.282211i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15.9377 | − | 2.29068i | −0.772184 | − | 0.110984i | ||||
\(427\) | 19.6471 | − | 47.4323i | 0.950790 | − | 2.29541i | ||||
\(428\) | −0.523941 | − | 4.86875i | −0.0253256 | − | 0.235340i | ||||
\(429\) | 18.6988 | − | 7.74530i | 0.902788 | − | 0.373947i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.8098i | − | 1.58039i | −0.612855 | − | 0.790195i | \(-0.709979\pi\) | ||
0.612855 | − | 0.790195i | \(-0.290021\pi\) | |||||||
\(432\) | 15.4012 | − | 10.6979i | 0.740992 | − | 0.514701i | ||||
\(433\) | − | 2.17672i | − | 0.104606i | −0.998631 | − | 0.0523032i | \(-0.983344\pi\) | ||
0.998631 | − | 0.0523032i | \(-0.0166562\pi\) | |||||||
\(434\) | −2.40129 | + | 4.04762i | −0.115265 | + | 0.194292i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.86246 | − | 7.27637i | 0.280761 | − | 0.348475i | ||||
\(437\) | 3.98282 | − | 9.61537i | 0.190524 | − | 0.459966i | ||||
\(438\) | −0.895803 | + | 6.23267i | −0.0428031 | + | 0.297809i | ||||
\(439\) | −17.7331 | + | 17.7331i | −0.846357 | + | 0.846357i | −0.989676 | − | 0.143319i | \(-0.954222\pi\) |
0.143319 | + | 0.989676i | \(0.454222\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −34.1576 | − | 34.1576i | −1.62655 | − | 1.62655i | ||||
\(442\) | 15.4942 | − | 11.6000i | 0.736985 | − | 0.551758i | ||||
\(443\) | −27.4536 | − | 11.3716i | −1.30436 | − | 0.540283i | −0.381126 | − | 0.924523i | \(-0.624464\pi\) |
−0.923233 | + | 0.384240i | \(0.874464\pi\) | |||||||
\(444\) | 24.5284 | + | 44.9097i | 1.16407 | + | 2.13132i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.81014 | + | 14.9249i | 0.180415 | + | 0.706712i | ||||
\(447\) | 4.70639 | 0.222605 | ||||||||
\(448\) | −25.1398 | + | 21.7970i | −1.18774 | + | 1.02981i | ||||
\(449\) | −27.1341 | −1.28054 | −0.640268 | − | 0.768152i | \(-0.721177\pi\) | ||||
−0.640268 | + | 0.768152i | \(0.721177\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.14380 | − | 17.2467i | −0.336389 | − | 0.812114i | ||||
\(452\) | −0.568072 | − | 1.04010i | −0.0267199 | − | 0.0489220i | ||||
\(453\) | 22.1508 | + | 9.17516i | 1.04074 | + | 0.431087i | ||||
\(454\) | −1.38844 | + | 1.03948i | −0.0651627 | + | 0.0487853i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.629022 | − | 17.6871i | 0.0294567 | − | 0.828274i | ||||
\(457\) | −11.5359 | + | 11.5359i | −0.539627 | + | 0.539627i | −0.923419 | − | 0.383793i | \(-0.874618\pi\) |
0.383793 | + | 0.923419i | \(0.374618\pi\) | |||||||
\(458\) | −0.496902 | + | 3.45727i | −0.0232187 | + | 0.161547i | ||||
\(459\) | −5.00348 | + | 12.0795i | −0.233543 | + | 0.563822i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.7669 | + | 13.1583i | −1.47953 | + | 0.612843i | −0.969010 | − | 0.247022i | \(-0.920548\pi\) |
−0.510523 | + | 0.859864i | \(0.670548\pi\) | |||||||
\(462\) | 12.3777 | − | 20.8639i | 0.575863 | − | 0.970676i | ||||
\(463\) | − | 9.22961i | − | 0.428937i | −0.976731 | − | 0.214468i | \(-0.931198\pi\) | ||
0.976731 | − | 0.214468i | \(-0.0688019\pi\) | |||||||
\(464\) | 29.3707 | + | 5.29296i | 1.36350 | + | 0.245719i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.45029 | + | 3.23344i | 0.252480 | + | 0.149786i | ||||
\(467\) | 13.7067 | − | 5.67749i | 0.634270 | − | 0.262723i | −0.0422963 | − | 0.999105i | \(-0.513467\pi\) |
0.676566 | + | 0.736382i | \(0.263467\pi\) | |||||||
\(468\) | −4.92558 | − | 45.7712i | −0.227685 | − | 2.11578i | ||||
\(469\) | 21.7658 | − | 52.5474i | 1.00505 | − | 2.42641i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.4939 | + | 24.4939i | −1.12862 | + | 1.12862i | ||||
\(472\) | 14.5963 | + | 39.1162i | 0.671850 | + | 1.80047i | ||||
\(473\) | 5.32257 | + | 5.32257i | 0.244732 | + | 0.244732i | ||||
\(474\) | 14.2530 | + | 19.0378i | 0.654661 | + | 0.874433i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.53383 | − | 22.2605i | 0.299478 | − | 1.02031i | ||||
\(477\) | −10.5485 | − | 25.4663i | −0.482983 | − | 1.16602i | ||||
\(478\) | 11.9009 | − | 3.03815i | 0.544333 | − | 0.138962i | ||||
\(479\) | 1.86348 | 0.0851446 | 0.0425723 | − | 0.999093i | \(-0.486445\pi\) | ||||
0.0425723 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.2758 | 2.06440 | ||||||||
\(482\) | 10.6465 | − | 2.71793i | 0.484936 | − | 0.123799i | ||||
\(483\) | −20.3595 | − | 49.1521i | −0.926387 | − | 2.23650i | ||||
\(484\) | −16.8648 | − | 4.95012i | −0.766584 | − | 0.225006i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.4370 | − | 19.2835i | −0.654874 | − | 0.874717i | ||||
\(487\) | −25.1963 | − | 25.1963i | −1.14175 | − | 1.14175i | −0.988129 | − | 0.153624i | \(-0.950905\pi\) |
−0.153624 | − | 0.988129i | \(-0.549095\pi\) | |||||||
\(488\) | 14.4989 | − | 31.7608i | 0.656334 | − | 1.43775i | ||||
\(489\) | −2.35467 | + | 2.35467i | −0.106482 | + | 0.106482i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.62967 | − | 8.76279i | 0.163805 | − | 0.395459i | −0.820570 | − | 0.571546i | \(-0.806344\pi\) |
0.984375 | + | 0.176087i | \(0.0563439\pi\) | |||||||
\(492\) | −69.2181 | + | 7.44876i | −3.12059 | + | 0.335816i | ||||
\(493\) | −19.2244 | + | 7.96300i | −0.865823 | + | 0.358636i | ||||
\(494\) | −13.4675 | − | 7.98972i | −0.605931 | − | 0.359474i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.72978 | + | 2.69279i | −0.0776695 | + | 0.120910i | ||||
\(497\) | 17.0758i | 0.765954i | ||||||||
\(498\) | −0.633104 | + | 1.06716i | −0.0283701 | + | 0.0478207i | ||||
\(499\) | 6.90859 | − | 2.86163i | 0.309271 | − | 0.128104i | −0.222649 | − | 0.974899i | \(-0.571471\pi\) |
0.531921 | + | 0.846794i | \(0.321471\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.03557 | − | 12.1569i | 0.224973 | − | 0.543132i | ||||
\(502\) | −3.77918 | + | 26.2942i | −0.168673 | + | 1.17357i | ||||
\(503\) | −22.1549 | + | 22.1549i | −0.987836 | + | 0.987836i | −0.999927 | − | 0.0120907i | \(-0.996151\pi\) |
0.0120907 | + | 0.999927i | \(0.496151\pi\) | |||||||
\(504\) | −37.6058 | − | 40.3792i | −1.67510 | − | 1.79863i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.76608 | − | 5.81422i | 0.345244 | − | 0.258474i | ||||
\(507\) | −28.3925 | − | 11.7605i | −1.26095 | − | 0.522304i | ||||
\(508\) | 5.63765 | − | 3.07913i | 0.250130 | − | 0.136614i | ||||
\(509\) | −2.19097 | − | 5.28948i | −0.0971132 | − | 0.234452i | 0.867856 | − | 0.496816i | \(-0.165498\pi\) |
−0.964969 | + | 0.262364i | \(0.915498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.67774 | 0.295406 | ||||||||
\(512\) | −17.6122 | + | 14.2060i | −0.778357 | + | 0.627822i | ||||
\(513\) | 10.5779 | 0.467025 | ||||||||
\(514\) | 5.50370 | + | 21.5587i | 0.242758 | + | 0.950916i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 24.6364 | − | 13.4557i | 1.08456 | − | 0.592356i | ||||
\(517\) | 3.93073 | + | 1.62816i | 0.172873 | + | 0.0716064i | ||||
\(518\) | 43.4421 | − | 32.5238i | 1.90874 | − | 1.42901i | ||||
\(519\) | −21.9804 | − | 21.9804i | −0.964831 | − | 0.964831i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8673 | − | 28.8673i | 1.26470 | − | 1.26470i | 0.315912 | − | 0.948789i | \(-0.397690\pi\) |
0.948789 | − | 0.315912i | \(-0.102310\pi\) | |||||||
\(522\) | −7.04087 | + | 48.9878i | −0.308170 | + | 2.14414i | ||||
\(523\) | 9.98767 | − | 24.1124i | 0.436731 | − | 1.05436i | −0.540340 | − | 0.841447i | \(-0.681705\pi\) |
0.977071 | − | 0.212914i | \(-0.0682955\pi\) | |||||||
\(524\) | 12.8787 | + | 10.3762i | 0.562610 | + | 0.453287i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.56343 | − | 9.37774i | 0.242577 | − | 0.408889i | ||||
\(527\) | − | 2.23152i | − | 0.0972066i | ||||||
\(528\) | 8.91635 | − | 13.8803i | 0.388034 | − | 0.604060i | ||||
\(529\) | 1.72428i | 0.0749688i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −63.9667 | + | 26.4959i | −2.77592 | + | 1.14982i | ||||
\(532\) | −18.6615 | + | 2.00822i | −0.809077 | + | 0.0870672i | ||||
\(533\) | −23.5720 | + | 56.9079i | −1.02102 | + | 2.46495i | ||||
\(534\) | 49.2620 | + | 7.08028i | 2.13178 | + | 0.306394i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16.0625 | − | 35.1859i | 0.693793 | − | 1.51980i | ||||
\(537\) | −8.72326 | − | 8.72326i | −0.376437 | − | 0.376437i | ||||
\(538\) | 6.95393 | + | 9.28839i | 0.299805 | + | 0.400451i | ||||
\(539\) | −14.1507 | − | 5.86140i | −0.609512 | − | 0.252468i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.97446 | + | 19.2520i | 0.342849 | + | 0.827710i | 0.997425 | + | 0.0717144i | \(0.0228470\pi\) |
−0.654576 | + | 0.755996i | \(0.727153\pi\) | |||||||
\(542\) | 28.4038 | − | 7.25115i | 1.22005 | − | 0.311464i | ||||
\(543\) | 0.392570 | 0.0168468 | ||||||||
\(544\) | 4.97852 | − | 14.9706i | 0.213452 | − | 0.641861i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −77.5593 | + | 19.8000i | −3.31923 | + | 0.847362i | ||||
\(547\) | 10.9909 | + | 26.5343i | 0.469935 | + | 1.13452i | 0.964191 | + | 0.265207i | \(0.0854404\pi\) |
−0.494256 | + | 0.869316i | \(0.664560\pi\) | |||||||
\(548\) | 2.76685 | − | 9.42655i | 0.118194 | − | 0.402682i | ||||
\(549\) | 53.4915 | + | 22.1569i | 2.28296 | + | 0.945634i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.9039 | + | 11.9039i | 0.507122 | + | 0.507122i | ||||
\(552\) | −12.6486 | − | 33.8966i | −0.538360 | − | 1.44273i | ||||
\(553\) | 17.8340 | − | 17.8340i | 0.758379 | − | 0.758379i | ||||
\(554\) | 32.9955 | + | 4.74234i | 1.40184 | + | 0.201483i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.11634 | + | 38.2514i | 0.174572 | + | 1.62222i | ||||
\(557\) | −3.56948 | + | 1.47853i | −0.151244 | + | 0.0626472i | −0.457021 | − | 0.889456i | \(-0.651084\pi\) |
0.305777 | + | 0.952103i | \(0.401084\pi\) | |||||||
\(558\) | −4.56468 | − | 2.70804i | −0.193238 | − | 0.114641i | ||||
\(559\) | − | 24.8373i | − | 1.05050i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.5026i | 0.485641i | ||||||||
\(562\) | 1.43932 | − | 2.42612i | 0.0607140 | − | 0.102340i | ||||
\(563\) | −20.8899 | + | 8.65287i | −0.880404 | + | 0.364675i | −0.776653 | − | 0.629928i | \(-0.783084\pi\) |
−0.103750 | + | 0.994603i | \(0.533084\pi\) | |||||||
\(564\) | 9.95463 | − | 12.3555i | 0.419166 | − | 0.520260i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.401298 | + | 2.79209i | −0.0168678 | + | 0.117360i | ||||
\(567\) | −3.14908 | + | 3.14908i | −0.132249 | + | 0.132249i | ||||
\(568\) | −0.412718 | + | 11.6050i | −0.0173173 | + | 0.486934i | ||||
\(569\) | −3.66437 | − | 3.66437i | −0.153618 | − | 0.153618i | 0.626114 | − | 0.779732i | \(-0.284645\pi\) |
−0.779732 | + | 0.626114i | \(0.784645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.9785 | + | 12.0033i | 1.21271 | + | 0.502321i | 0.895085 | − | 0.445895i | \(-0.147114\pi\) |
0.317626 | + | 0.948216i | \(0.397114\pi\) | |||||||
\(572\) | −6.99670 | − | 12.8104i | −0.292547 | − | 0.535631i | ||||
\(573\) | 0.919047 | + | 2.21878i | 0.0383937 | + | 0.0926907i | ||||
\(574\) | 18.2623 | + | 71.5361i | 0.762255 | + | 2.98586i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.5815 | − | 28.3513i | −1.02423 | − | 1.18130i | ||||
\(577\) | 39.1035 | 1.62790 | 0.813950 | − | 0.580935i | \(-0.197313\pi\) | ||||
0.813950 | + | 0.580935i | \(0.197313\pi\) | |||||||
\(578\) | −3.22587 | − | 12.6362i | −0.134178 | − | 0.525596i | ||||
\(579\) | −17.6609 | − | 42.6372i | −0.733962 | − | 1.77194i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.21574 | + | 0.503578i | 0.0504376 | + | 0.0208919i | ||||
\(582\) | −42.4631 | + | 31.7908i | −1.76015 | + | 1.31777i | ||||
\(583\) | −6.18009 | − | 6.18009i | −0.255953 | − | 0.255953i | ||||
\(584\) | 4.53830 | + | 0.161400i | 0.187796 | + | 0.00667876i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.12562 | + | 14.7893i | −0.0878087 | + | 0.610941i | ||||
\(587\) | −6.73339 | + | 16.2558i | −0.277917 | + | 0.670950i | −0.999778 | − | 0.0210878i | \(-0.993287\pi\) |
0.721861 | + | 0.692038i | \(0.243287\pi\) | |||||||
\(588\) | −35.8368 | + | 44.4799i | −1.47789 | + | 1.83432i | ||||
\(589\) | −1.66795 | + | 0.690887i | −0.0687266 | + | 0.0284675i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 15.5684i | − | 0.640397i | ||||||
\(592\) | 30.3100 | − | 21.0537i | 1.24573 | − | 0.865300i | ||||
\(593\) | − | 6.43191i | − | 0.264127i | −0.991241 | − | 0.132063i | \(-0.957840\pi\) | ||
0.991241 | − | 0.132063i | \(-0.0421603\pi\) | |||||||
\(594\) | 8.48010 | + | 5.03090i | 0.347943 | + | 0.206420i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.363166 | − | 3.37475i | −0.0148759 | − | 0.138235i | ||||
\(597\) | 16.0917 | − | 38.8489i | 0.658591 | − | 1.58998i | ||||
\(598\) | −31.6856 | − | 4.55407i | −1.29572 | − | 0.186230i | ||||
\(599\) | −18.1680 | + | 18.1680i | −0.742322 | + | 0.742322i | −0.973024 | − | 0.230702i | \(-0.925898\pi\) |
0.230702 | + | 0.973024i | \(0.425898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.2457 | − | 10.2457i | −0.417933 | − | 0.417933i | 0.466558 | − | 0.884491i | \(-0.345494\pi\) |
−0.884491 | + | 0.466558i | \(0.845494\pi\) | |||||||
\(602\) | −17.8418 | − | 23.8314i | −0.727178 | − | 0.971294i | ||||
\(603\) | 59.2601 | + | 24.5463i | 2.41326 | + | 0.999604i | ||||
\(604\) | 4.86985 | − | 16.5914i | 0.198151 | − | 0.675092i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −33.5154 | + | 8.55608i | −1.36147 | + | 0.347567i | ||||
\(607\) | −28.5016 | −1.15684 | −0.578422 | − | 0.815738i | \(-0.696331\pi\) | ||||
−0.578422 | + | 0.815738i | \(0.696331\pi\) | |||||||
\(608\) | −12.7312 | + | 0.913770i | −0.516317 | + | 0.0370583i | ||||
\(609\) | 86.0556 | 3.48715 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.37235 | − | 12.9700i | −0.217342 | − | 0.524710i | ||||
\(612\) | 25.1042 | + | 7.36850i | 1.01478 | + | 0.297854i | ||||
\(613\) | −11.9350 | − | 4.94365i | −0.482051 | − | 0.199672i | 0.128406 | − | 0.991722i | \(-0.459014\pi\) |
−0.610457 | + | 0.792050i | \(0.709014\pi\) | |||||||
\(614\) | 3.85088 | + | 5.14364i | 0.155409 | + | 0.207580i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.9157 | − | 7.26554i | −0.641261 | − | 0.292737i | ||||
\(617\) | 34.4226 | − | 34.4226i | 1.38580 | − | 1.38580i | 0.551870 | − | 0.833930i | \(-0.313915\pi\) |
0.833930 | − | 0.551870i | \(-0.186085\pi\) | |||||||
\(618\) | 37.7770 | + | 5.42958i | 1.51961 | + | 0.218410i | ||||
\(619\) | −13.3861 | + | 32.3170i | −0.538034 | + | 1.29893i | 0.388059 | + | 0.921635i | \(0.373146\pi\) |
−0.926093 | + | 0.377295i | \(0.876854\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.9778 | − | 8.27508i | 0.801682 | − | 0.332067i | ||||
\(622\) | −38.8354 | − | 23.0395i | −1.55716 | − | 0.923799i | ||||
\(623\) | − | 52.7798i | − | 2.11458i | ||||||
\(624\) | −53.1891 | + | 11.5818i | −2.12927 | + | 0.463643i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.0699 | + | 32.1443i | −0.762187 | + | 1.28475i | ||||
\(627\) | 8.59762 | − | 3.56125i | 0.343356 | − | 0.142223i | ||||
\(628\) | 19.4536 | + | 15.6734i | 0.776282 | + | 0.625439i | ||||
\(629\) | −9.84699 | + | 23.7727i | −0.392625 | + | 0.947881i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.3075 | + | 30.3075i | −1.20652 | + | 1.20652i | −0.234377 | + | 0.972146i | \(0.575305\pi\) |
−0.972146 | + | 0.234377i | \(0.924695\pi\) | |||||||
\(632\) | 12.5513 | − | 11.6892i | 0.499264 | − | 0.464972i | ||||
\(633\) | 28.7294 | + | 28.7294i | 1.14189 | + | 1.14189i | ||||
\(634\) | −30.4034 | + | 22.7621i | −1.20747 | + | 0.903998i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −28.6056 | + | 15.6236i | −1.13429 | + | 0.619516i | ||||
\(637\) | 19.3405 | + | 46.6922i | 0.766300 | + | 1.85001i | ||||
\(638\) | 3.88157 | + | 15.2047i | 0.153673 | + | 0.601959i | ||||
\(639\) | −19.2571 | −0.761801 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.6617 | −1.09257 | −0.546286 | − | 0.837599i | \(-0.683959\pi\) | ||||
−0.546286 | + | 0.837599i | \(0.683959\pi\) | |||||||
\(642\) | −2.37521 | − | 9.30401i | −0.0937419 | − | 0.367200i | ||||
\(643\) | 11.7066 | + | 28.2623i | 0.461664 | + | 1.11455i | 0.967714 | + | 0.252051i | \(0.0811051\pi\) |
−0.506050 | + | 0.862504i | \(0.668895\pi\) | |||||||
\(644\) | −33.6737 | + | 18.3916i | −1.32693 | + | 0.724732i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.12416 | − | 5.33364i | 0.280296 | − | 0.209849i | ||||
\(647\) | −33.6047 | − | 33.6047i | −1.32114 | − | 1.32114i | −0.912855 | − | 0.408284i | \(-0.866127\pi\) |
−0.408284 | − | 0.912855i | \(-0.633873\pi\) | |||||||
\(648\) | −2.21628 | + | 2.06405i | −0.0870636 | + | 0.0810836i | ||||
\(649\) | −15.5232 | + | 15.5232i | −0.609340 | + | 0.609340i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.53169 | + | 8.52626i | −0.138418 | + | 0.334170i | ||||
\(652\) | 1.87012 | + | 1.50673i | 0.0732397 | + | 0.0590081i | ||||
\(653\) | −14.2736 | + | 5.91232i | −0.558570 | + | 0.231367i | −0.644064 | − | 0.764972i | \(-0.722753\pi\) |
0.0854945 | + | 0.996339i | \(0.472753\pi\) | |||||||
\(654\) | 9.34904 | − | 15.7588i | 0.365577 | − | 0.616217i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.6823 | + | 49.0584i | 0.417076 | + | 1.91541i | ||||
\(657\) | 7.53079i | 0.293804i | ||||||||
\(658\) | −14.4718 | − | 8.58550i | −0.564168 | − | 0.334698i | ||||
\(659\) | −3.69353 | + | 1.52991i | −0.143880 | + | 0.0595969i | −0.453461 | − | 0.891276i | \(-0.649811\pi\) |
0.309582 | + | 0.950873i | \(0.399811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.19176 | − | 22.1909i | 0.357518 | − | 0.863125i | −0.638130 | − | 0.769929i | \(-0.720292\pi\) |
0.995648 | − | 0.0931960i | \(-0.0297083\pi\) | |||||||
\(662\) | 18.1993 | + | 2.61573i | 0.707337 | + | 0.101663i | ||||
\(663\) | 26.8379 | − | 26.8379i | 1.04230 | − | 1.04230i | ||||
\(664\) | 0.814067 | + | 0.371624i | 0.0315919 | + | 0.0144218i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 36.6785 | + | 48.9916i | 1.42126 | + | 1.89839i | ||||
\(667\) | 31.7945 | + | 13.1697i | 1.23109 | + | 0.509933i | ||||
\(668\) | −9.10577 | − | 2.67270i | −0.352313 | − | 0.103410i | ||||
\(669\) | 11.5590 | + | 27.9060i | 0.446898 | + | 1.07891i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.3581 | 0.708708 | ||||||||
\(672\) | −42.7152 | + | 49.3210i | −1.64777 | + | 1.90260i | ||||
\(673\) | −4.29624 | −0.165608 | −0.0828040 | − | 0.996566i | \(-0.526388\pi\) | ||||
−0.0828040 | + | 0.996566i | \(0.526388\pi\) | |||||||
\(674\) | 41.3644 | − | 10.5599i | 1.59330 | − | 0.406751i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.24207 | + | 21.2665i | −0.240080 | + | 0.817941i | ||||
\(677\) | −23.8398 | − | 9.87475i | −0.916236 | − | 0.379518i | −0.125796 | − | 0.992056i | \(-0.540148\pi\) |
−0.790441 | + | 0.612539i | \(0.790148\pi\) | |||||||
\(678\) | −1.39278 | − | 1.86034i | −0.0534893 | − | 0.0714458i | ||||
\(679\) | 39.7781 | + | 39.7781i | 1.52654 | + | 1.52654i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.40495 | + | 2.40495i | −0.0921581 | + | 0.0921581i | ||||
\(682\) | −1.66575 | − | 0.239414i | −0.0637850 | − | 0.00916762i | ||||
\(683\) | 2.54520 | − | 6.14467i | 0.0973895 | − | 0.235119i | −0.867675 | − | 0.497132i | \(-0.834386\pi\) |
0.965064 | + | 0.262013i | \(0.0843864\pi\) | |||||||
\(684\) | −2.26476 | − | 21.0454i | −0.0865951 | − | 0.804690i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.6874 | + | 9.89999i | 0.637130 | + | 0.377983i | ||||
\(687\) | 6.84912i | 0.261310i | ||||||||
\(688\) | −11.5496 | − | 16.6274i | −0.440323 | − | 0.633913i | ||||
\(689\) | 28.8388i | 1.09867i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.14914 | + | 2.96127i | −0.271966 | + | 0.112652i | −0.514498 | − | 0.857491i | \(-0.672022\pi\) |
0.242533 | + | 0.970143i | \(0.422022\pi\) | |||||||
\(692\) | −14.0650 | + | 17.4572i | −0.534673 | + | 0.663625i | ||||
\(693\) | 11.1031 | − | 26.8052i | 0.421770 | − | 1.01824i | ||||
\(694\) | −0.516020 | + | 3.59028i | −0.0195879 | + | 0.136285i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 58.4847 | + | 2.07995i | 2.21686 | + | 0.0788401i | ||||
\(697\) | −24.7537 | − | 24.7537i | −0.937614 | − | 0.937614i | ||||
\(698\) | 16.1446 | − | 12.0870i | 0.611083 | − | 0.457499i | ||||
\(699\) | 11.4810 | + | 4.75557i | 0.434250 | + | 0.179872i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.82186 | − | 4.39835i | −0.0688106 | − | 0.166124i | 0.885733 | − | 0.464195i | \(-0.153656\pi\) |
−0.954543 | + | 0.298072i | \(0.903656\pi\) | |||||||
\(702\) | −8.04769 | − | 31.5239i | −0.303740 | − | 1.18979i | ||||
\(703\) | 20.8176 | 0.785149 | ||||||||
\(704\) | −10.6409 | − | 5.32245i | −0.401045 | − | 0.200598i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.14040 | − | 4.46712i | −0.0429196 | − | 0.168122i | ||||
\(707\) | 14.0381 | + | 33.8910i | 0.527958 | + | 1.27460i | ||||
\(708\) | 39.2436 | + | 71.8520i | 1.47486 | + | 2.70036i | ||||
\(709\) | −35.5634 | − | 14.7309i | −1.33561 | − | 0.553229i | −0.403361 | − | 0.915041i | \(-0.632158\pi\) |
−0.932251 | + | 0.361812i | \(0.882158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.1122 | + | 20.1122i | 0.754267 | + | 0.754267i | ||||
\(712\) | 1.27568 | − | 35.8699i | 0.0478080 | − | 1.34428i | ||||
\(713\) | −2.60967 | + | 2.60967i | −0.0977329 | + | 0.0977329i | ||||
\(714\) | 6.47202 | − | 45.0300i | 0.242209 | − | 1.68521i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.58194 | + | 6.92819i | −0.208607 | + | 0.258919i | ||||
\(717\) | 22.2518 | − | 9.21701i | 0.831010 | − | 0.344215i | ||||
\(718\) | −5.88253 | + | 9.91562i | −0.219534 | + | 0.370048i | ||||
\(719\) | 43.7997i | 1.63345i | 0.577026 | + | 0.816726i | \(0.304213\pi\) | ||||
−0.577026 | + | 0.816726i | \(0.695787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 40.4746i | − | 1.50735i | ||||||
\(722\) | 16.9170 | + | 10.0362i | 0.629587 | + | 0.373508i | ||||
\(723\) | 19.9065 | − | 8.24555i | 0.740331 | − | 0.306655i | ||||
\(724\) | −0.0302924 | − | 0.281494i | −0.00112581 | − | 0.0104617i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −34.1154 | − | 4.90329i | −1.26614 | − | 0.181978i | ||||
\(727\) | −10.7411 | + | 10.7411i | −0.398366 | + | 0.398366i | −0.877656 | − | 0.479290i | \(-0.840894\pi\) |
0.479290 | + | 0.877656i | \(0.340894\pi\) | |||||||
\(728\) | 20.1825 | + | 54.0865i | 0.748014 | + | 2.00458i | ||||
\(729\) | −31.1301 | − | 31.1301i | −1.15296 | − | 1.15296i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0412 | + | 5.40184i | 0.482346 | + | 0.199794i | ||||
\(732\) | 19.2818 | − | 65.6921i | 0.712674 | − | 2.42805i | ||||
\(733\) | 1.01052 | + | 2.43961i | 0.0373244 | + | 0.0901091i | 0.941443 | − | 0.337174i | \(-0.109471\pi\) |
−0.904118 | + | 0.427283i | \(0.859471\pi\) | |||||||
\(734\) | −4.26892 | + | 1.08981i | −0.157569 | + | 0.0402255i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23.3297 | + | 11.6854i | −0.859944 | + | 0.430728i | ||||
\(737\) | 20.3379 | 0.749155 | ||||||||
\(738\) | −80.6745 | + | 20.5953i | −2.96967 | + | 0.758122i | ||||
\(739\) | −13.5424 | − | 32.6942i | −0.498165 | − | 1.20268i | −0.950471 | − | 0.310813i | \(-0.899399\pi\) |
0.452306 | − | 0.891863i | \(-0.350601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28.3691 | − | 11.7509i | −1.04217 | − | 0.431679i | ||||
\(742\) | 20.7163 | + | 27.6708i | 0.760520 | + | 1.01583i | ||||
\(743\) | 16.8110 | + | 16.8110i | 0.616735 | + | 0.616735i | 0.944692 | − | 0.327958i | \(-0.106360\pi\) |
−0.327958 | + | 0.944692i | \(0.606360\pi\) | |||||||
\(744\) | −2.60627 | + | 5.70921i | −0.0955505 | + | 0.209310i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.6689 | − | 1.67713i | −0.427228 | − | 0.0614041i | ||||
\(747\) | −0.567908 | + | 1.37105i | −0.0207787 | + | 0.0501641i | ||||
\(748\) | 8.24802 | − | 0.887593i | 0.301577 | − | 0.0324536i | ||||
\(749\) | −9.40829 | + | 3.89704i | −0.343772 | + | 0.142395i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4107i | 0.817778i | 0.912584 | + | 0.408889i | \(0.134084\pi\) | ||||
−0.912584 | + | 0.408889i | \(0.865916\pi\) | |||||||
\(752\) | −9.62771 | − | 6.18462i | −0.351087 | − | 0.225530i | ||||
\(753\) | 52.0909i | 1.89830i | ||||||||
\(754\) | 26.4191 | − | 44.5321i | 0.962126 | − | 1.62176i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −30.3669 | − | 24.4661i | −1.10443 | − | 0.889825i | ||||
\(757\) | −12.4687 | + | 30.1022i | −0.453184 | + | 1.09408i | 0.517921 | + | 0.855429i | \(0.326706\pi\) |
−0.971105 | + | 0.238654i | \(0.923294\pi\) | |||||||
\(758\) | 2.86206 | − | 19.9132i | 0.103955 | − | 0.723279i | ||||
\(759\) | 13.4518 | − | 13.4518i | 0.488271 | − | 0.488271i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.4349 | + | 30.4349i | 1.10326 | + | 1.10326i | 0.994014 | + | 0.109249i | \(0.0348445\pi\) |
0.109249 | + | 0.994014i | \(0.465155\pi\) | |||||||
\(762\) | 10.0836 | − | 7.54928i | 0.365290 | − | 0.273482i | ||||
\(763\) | −17.9529 | − | 7.43633i | −0.649938 | − | 0.269213i | ||||
\(764\) | 1.52007 | − | 0.830218i | 0.0549941 | − | 0.0300362i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.14494 | − | 31.9049i | −0.294289 | − | 1.15277i | ||||
\(767\) | 72.4377 | 2.61557 | ||||||||
\(768\) | −30.2220 | + | 32.4869i | −1.09054 | + | 1.17227i | ||||
\(769\) | 7.75534 | 0.279665 | 0.139832 | − | 0.990175i | \(-0.455344\pi\) | ||||
0.139832 | + | 0.990175i | \(0.455344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.6969 | + | 40.3098i | 0.601323 | + | 1.45172i | ||||
\(772\) | −29.2104 | + | 15.9539i | −1.05131 | + | 0.574194i | ||||
\(773\) | −16.8461 | − | 6.97787i | −0.605911 | − | 0.250976i | 0.0585684 | − | 0.998283i | \(-0.481346\pi\) |
−0.664479 | + | 0.747307i | \(0.731346\pi\) | |||||||
\(774\) | 26.8757 | − | 20.1210i | 0.966027 | − | 0.723235i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 26.0724 | + | 27.9953i | 0.935945 | + | 1.00497i | ||||
\(777\) | 75.2472 | − | 75.2472i | 2.69948 | − | 2.69948i | ||||
\(778\) | −2.18532 | + | 15.2047i | −0.0783477 | + | 0.545115i | ||||
\(779\) | −10.8383 | + | 26.1660i | −0.388322 | + | 0.937493i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.64113 | + | 2.33663i | −0.201855 | + | 0.0836112i | ||||
\(782\) | 9.28246 | − | 15.6465i | 0.331940 | − | 0.559519i | ||||
\(783\) | 34.9772i | 1.24998i | ||||||||
\(784\) | 34.6599 | + | 22.2647i | 1.23785 | + | 0.795168i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27.8921 | + | 16.5473i | 0.994878 | + | 0.590221i | ||||
\(787\) | −15.0743 | + | 6.24398i | −0.537341 | + | 0.222574i | −0.634815 | − | 0.772664i | \(-0.718924\pi\) |
0.0974741 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(788\) | −11.1634 | + | 1.20132i | −0.397679 | + | 0.0427954i | ||||
\(789\) | 8.18241 | − | 19.7541i | 0.291302 | − | 0.703264i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.74271 | + | 1.74271i | −0.0619635 | + | 0.0619635i | ||||
\(792\) | 8.19368 | − | 17.9488i | 0.291150 | − | 0.637784i | ||||
\(793\) | −42.8332 | − | 42.8332i | −1.52105 | − | 1.52105i | ||||
\(794\) | −14.0629 | − | 18.7839i | −0.499075 | − | 0.666616i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.0985 | − | 8.54092i | −1.03137 | − | 0.302725i | ||||
\(797\) | 0.0914925 | + | 0.220883i | 0.00324083 | + | 0.00782406i | 0.925492 | − | 0.378768i | \(-0.123652\pi\) |
−0.922251 | + | 0.386592i | \(0.873652\pi\) | |||||||
\(798\) | −35.6614 | + | 9.10394i | −1.26240 | + | 0.322276i | ||||
\(799\) | 7.97853 | 0.282260 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 59.5221 | 2.10311 | ||||||||
\(802\) | −33.8797 | + | 8.64910i | −1.19633 | + | 0.305410i | ||||
\(803\) | 0.913775 | + | 2.20605i | 0.0322464 | + | 0.0778497i | ||||
\(804\) | 21.3611 | − | 72.7763i | 0.753348 | − | 2.56662i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.32794 | + | 4.44514i | 0.117222 | + | 0.156573i | ||||
\(807\) | 16.0887 | + | 16.0887i | 0.566348 | + | 0.566348i | ||||
\(808\) | 8.72138 | + | 23.3721i | 0.306817 | + | 0.822229i | ||||
\(809\) | −24.8428 | + | 24.8428i | −0.873427 | + | 0.873427i | −0.992844 | − | 0.119417i | \(-0.961897\pi\) |
0.119417 | + | 0.992844i | \(0.461897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.55425 | − | 10.9949i | 0.159921 | − | 0.386085i | −0.823526 | − | 0.567279i | \(-0.807996\pi\) |
0.983447 | + | 0.181194i | \(0.0579962\pi\) | |||||||
\(812\) | −6.64043 | − | 61.7066i | −0.233033 | − | 2.16548i | ||||
\(813\) | 53.1084 | − | 21.9982i | 1.86259 | − | 0.771512i | ||||
\(814\) | 16.6891 | + | 9.90094i | 0.584951 | + | 0.347028i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.48685 | − | 30.4467i | 0.192078 | − | 1.06585i | ||||
\(817\) | − | 11.4200i | − | 0.399537i | ||||||
\(818\) | 13.4945 | − | 22.7465i | 0.471826 | − | 0.795311i | ||||
\(819\) | −88.4475 | + | 36.6362i | −3.09061 | + | 1.28017i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.5757 | − | 35.1889i | 0.508696 | − | 1.22810i | −0.435939 | − | 0.899976i | \(-0.643584\pi\) |
0.944635 | − | 0.328124i | \(-0.106416\pi\) | |||||||
\(822\) | 2.74068 | − | 19.0687i | 0.0955922 | − | 0.665096i | ||||
\(823\) | 20.9180 | − | 20.9180i | 0.729157 | − | 0.729157i | −0.241295 | − | 0.970452i | \(-0.577572\pi\) |
0.970452 | + | 0.241295i | \(0.0775722\pi\) | |||||||
\(824\) | 0.978264 | − | 27.5072i | 0.0340794 | − | 0.958258i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 69.5040 | − | 52.0355i | 2.41835 | − | 1.81055i | ||||
\(827\) | −43.4150 | − | 17.9831i | −1.50969 | − | 0.625333i | −0.534194 | − | 0.845362i | \(-0.679385\pi\) |
−0.975493 | + | 0.220029i | \(0.929385\pi\) | |||||||
\(828\) | −20.7411 | − | 37.9754i | −0.720803 | − | 1.31974i | ||||
\(829\) | −11.8059 | − | 28.5019i | −0.410035 | − | 0.989911i | −0.985128 | − | 0.171823i | \(-0.945034\pi\) |
0.575093 | − | 0.818088i | \(-0.304966\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 65.3667 | 2.26755 | ||||||||
\(832\) | 12.4091 | + | 37.2458i | 0.430208 | + | 1.29127i | ||||
\(833\) | −28.7228 | −0.995187 | ||||||||
\(834\) | 18.6608 | + | 73.0969i | 0.646171 | + | 2.53114i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.21705 | − | 5.89017i | −0.111264 | − | 0.203716i | ||||
\(837\) | −3.46549 | − | 1.43545i | −0.119785 | − | 0.0496165i | ||||
\(838\) | −4.28448 | + | 3.20766i | −0.148005 | + | 0.110807i | ||||
\(839\) | −8.76568 | − | 8.76568i | −0.302625 | − | 0.302625i | 0.539415 | − | 0.842040i | \(-0.318645\pi\) |
−0.842040 | + | 0.539415i | \(0.818645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.8556 | + | 18.8556i | −0.650194 | + | 0.650194i | ||||
\(842\) | −0.643786 | + | 4.47923i | −0.0221863 | + | 0.154364i | ||||
\(843\) | 2.11688 | − | 5.11060i | 0.0729091 | − | 0.176018i | ||||
\(844\) | 18.3837 | − | 22.8175i | 0.632793 | − | 0.785410i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.68226 | − | 16.3205i | 0.332883 | − | 0.561109i | ||||
\(847\) | 36.5515i | 1.25592i | ||||||||
\(848\) | 13.4103 | + | 19.3062i | 0.460512 | + | 0.662979i | ||||
\(849\) | 5.53135i | 0.189836i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.3168 | − | 16.2856i | 1.34776 | − | 0.558262i | ||||
\(852\) | 2.43638 | + | 22.6402i | 0.0834689 | + | 0.775640i | ||||
\(853\) | 11.2155 | − | 27.0766i | 0.384011 | − | 0.927084i | −0.607171 | − | 0.794571i | \(-0.707696\pi\) |
0.991181 | − | 0.132512i | \(-0.0423044\pi\) | |||||||
\(854\) | −71.8677 | − | 10.3293i | −2.45926 | − | 0.353462i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.48821 | + | 2.42109i | −0.221762 | + | 0.0827513i | ||||
\(857\) | 37.4118 | + | 37.4118i | 1.27796 | + | 1.27796i | 0.941806 | + | 0.336157i | \(0.109127\pi\) |
0.336157 | + | 0.941806i | \(0.390873\pi\) | |||||||
\(858\) | −17.1542 | − | 22.9130i | −0.585636 | − | 0.782236i | ||||
\(859\) | 13.0928 | + | 5.42323i | 0.446722 | + | 0.185038i | 0.594692 | − | 0.803954i | \(-0.297274\pi\) |
−0.147970 | + | 0.988992i | \(0.547274\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 55.4034 | + | 133.756i | 1.88814 | + | 4.55838i | ||||
\(862\) | −44.9581 | + | 11.4773i | −1.53128 | + | 0.390918i | ||||
\(863\) | 10.9648 | 0.373246 | 0.186623 | − | 0.982432i | \(-0.440246\pi\) | ||||
0.186623 | + | 0.982432i | \(0.440246\pi\) | |||||||
\(864\) | −20.0465 | − | 17.3615i | −0.681995 | − | 0.590651i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.98268 | + | 0.761445i | −0.101356 | + | 0.0258749i | ||||
\(867\) | −9.78650 | − | 23.6267i | −0.332367 | − | 0.802405i | ||||
\(868\) | 6.38632 | + | 1.87449i | 0.216766 | + | 0.0636245i | ||||
\(869\) | 8.33199 | + | 3.45122i | 0.282643 | + | 0.117075i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.4524 | − | 47.4524i | −1.60786 | − | 1.60786i | ||||
\(872\) | −12.0213 | − | 5.48776i | −0.407094 | − | 0.185839i | ||||
\(873\) | −44.8596 | + | 44.8596i | −1.51827 | + | 1.51827i | ||||
\(874\) | −14.5689 | − | 2.09394i | −0.492799 | − | 0.0708285i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.85379 | − | 0.952782i | 0.299142 | − | 0.0321915i | ||||
\(877\) | 20.1301 | − | 8.33816i | 0.679745 | − | 0.281560i | −0.0159754 | − | 0.999872i | \(-0.505085\pi\) |
0.695720 | + | 0.718313i | \(0.255085\pi\) | |||||||
\(878\) | 30.5024 | + | 18.0959i | 1.02941 | + | 0.610706i | ||||
\(879\) | 29.2988i | 0.988225i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0921i | 1.04752i | 0.851866 | + | 0.523760i | \(0.175471\pi\) | ||||
−0.851866 | + | 0.523760i | \(0.824529\pi\) | |||||||
\(882\) | −34.8563 | + | 58.7539i | −1.17367 | + | 1.97835i | ||||
\(883\) | −22.3815 | + | 9.27074i | −0.753199 | + | 0.311985i | −0.726046 | − | 0.687646i | \(-0.758644\pi\) |
−0.0271529 | + | 0.999631i | \(0.508644\pi\) | |||||||
\(884\) | −21.3152 | − | 17.1734i | −0.716909 | − | 0.577602i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.97857 | + | 41.5967i | −0.200854 | + | 1.39747i | ||||
\(887\) | 0.745073 | − | 0.745073i | 0.0250171 | − | 0.0250171i | −0.694488 | − | 0.719505i | \(-0.744369\pi\) |
0.719505 | + | 0.694488i | \(0.244369\pi\) | |||||||
\(888\) | 52.9579 | − | 49.3205i | 1.77715 | − | 1.65509i | ||||
\(889\) | −9.44601 | − | 9.44601i | −0.316809 | − | 0.316809i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.47124 | − | 0.609409i | −0.0492885 | − | 0.0204160i | ||||
\(892\) | 19.1182 | − | 10.4418i | 0.640124 | − | 0.349618i | ||||
\(893\) | −2.47018 | − | 5.96354i | −0.0826614 | − | 0.199562i | ||||
\(894\) | −1.64636 | − | 6.44901i | −0.0550625 | − | 0.215687i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 38.6620 | + | 26.8233i | 1.29161 | + | 0.896104i | ||||
\(897\) | −62.7717 | −2.09589 | ||||||||
\(898\) | 9.49186 | + | 37.1809i | 0.316747 | + | 1.24074i | ||||
\(899\) | −2.28451 | − | 5.51529i | −0.0761926 | − | 0.183945i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.1423 | − | 6.27213i | −0.504462 | − | 0.208955i | ||||
\(902\) | −21.1335 | + | 15.8220i | −0.703670 | + | 0.526816i | ||||
\(903\) | −41.2789 | − | 41.2789i | −1.37368 | − | 1.37368i | ||||
\(904\) | −1.22649 | + | 1.14225i | −0.0407925 | + | 0.0379907i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.82378 | − | 33.5621i | 0.160259 | − | 1.11503i | ||||
\(907\) | 17.4912 | − | 42.2276i | 0.580787 | − | 1.40214i | −0.311314 | − | 0.950307i | \(-0.600769\pi\) |
0.892101 | − | 0.451836i | \(-0.149231\pi\) | |||||||
\(908\) | 1.91006 | + | 1.53891i | 0.0633877 | + | 0.0510705i | ||||
\(909\) | −38.2204 | + | 15.8314i | −1.26769 | + | 0.525095i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.5610i | − | 1.07880i | −0.842051 | − | 0.539398i | \(-0.818652\pi\) | ||
0.842051 | − | 0.539398i | \(-0.181348\pi\) | |||||||
\(912\) | −24.4561 | + | 5.32525i | −0.809821 | + | 0.176337i | ||||
\(913\) | 0.470540i | 0.0155726i | ||||||||
\(914\) | 19.8427 | + | 11.7719i | 0.656337 | + | 0.389378i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.91120 | − | 0.528509i | 0.162271 | − | 0.0174624i | ||||
\(917\) | 13.1619 | − | 31.7756i | 0.434643 | − | 1.04932i | ||||
\(918\) | 18.3024 | + | 2.63055i | 0.604069 | + | 0.0868210i | ||||
\(919\) | −30.1203 | + | 30.1203i | −0.993576 | + | 0.993576i | −0.999979 | − | 0.00640371i | \(-0.997962\pi\) |
0.00640371 | + | 0.999979i | \(0.497962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.90943 | + | 8.90943i | 0.293576 | + | 0.293576i | ||||
\(922\) | 29.1428 | + | 38.9262i | 0.959769 | + | 1.28197i | ||||
\(923\) | 18.6137 | + | 7.71006i | 0.612678 | + | 0.253780i | ||||
\(924\) | −32.9190 | − | 9.66228i | −1.08295 | − | 0.317866i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.6470 | + | 3.22864i | −0.415607 | + | 0.106100i | ||||
\(927\) | 45.6451 | 1.49918 | ||||||||
\(928\) | −3.02150 | − | 42.0973i | −0.0991857 | − | 1.38191i | ||||
\(929\) | 46.0639 | 1.51131 | 0.755654 | − | 0.654971i | \(-0.227319\pi\) | ||||
0.755654 | + | 0.654971i | \(0.227319\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.89268 | + | 21.4688i | 0.291446 | + | 0.703613i | ||||
\(932\) | 2.52409 | − | 8.59945i | 0.0826792 | − | 0.281684i | ||||
\(933\) | −81.8063 | − | 33.8853i | −2.67822 | − | 1.10935i | ||||
\(934\) | −12.5745 | − | 16.7957i | −0.411449 | − | 0.549574i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −60.9958 | + | 22.7607i | −1.99371 | + | 0.743958i | ||||
\(937\) | 8.50147 | − | 8.50147i | 0.277731 | − | 0.277731i | −0.554472 | − | 0.832203i | \(-0.687080\pi\) |
0.832203 | + | 0.554472i | \(0.187080\pi\) | |||||||
\(938\) | −79.6179 | − | 11.4432i | −2.59962 | − | 0.373635i | ||||
\(939\) | −28.0471 | + | 67.7116i | −0.915281 | + | 2.20968i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.7142 | − | 8.99431i | 0.707862 | − | 0.293206i | 0.000442416 | − | 1.00000i | \(-0.499859\pi\) |
0.707420 | + | 0.706794i | \(0.249859\pi\) | |||||||
\(942\) | 42.1315 | + | 24.9949i | 1.37272 | + | 0.814379i | ||||
\(943\) | 57.8968i | 1.88538i | ||||||||
\(944\) | 48.4937 | − | 33.6842i | 1.57833 | − | 1.09633i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.43143 | − | 9.15524i | 0.176591 | − | 0.297663i | ||||
\(947\) | −11.7836 | + | 4.88093i | −0.382916 | + | 0.158609i | −0.565834 | − | 0.824519i | \(-0.691446\pi\) |
0.182918 | + | 0.983128i | \(0.441446\pi\) | |||||||
\(948\) | 21.1009 | − | 26.1900i | 0.685326 | − | 0.850613i | ||||
\(949\) | 3.01513 | − | 7.27918i | 0.0978754 | − | 0.236292i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −52.6625 | + | 52.6625i | −1.70770 | + | 1.70770i | ||||
\(952\) | −32.7884 | − | 1.16608i | −1.06268 | − | 0.0377930i | ||||
\(953\) | −9.27815 | − | 9.27815i | −0.300549 | − | 0.300549i | 0.540680 | − | 0.841228i | \(-0.318167\pi\) |
−0.841228 | + | 0.540680i | \(0.818167\pi\) | |||||||
\(954\) | −31.2057 | + | 23.3627i | −1.01032 | + | 0.756396i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.32615 | − | 15.2446i | −0.269287 | − | 0.493044i | ||||
\(957\) | 11.7757 | + | 28.4292i | 0.380656 | + | 0.918985i | ||||
\(958\) | −0.651870 | − | 2.55346i | −0.0210610 | − | 0.0824987i | ||||
\(959\) | −20.4303 | −0.659730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3598 | −0.979348 | ||||||||
\(962\) | −15.8381 | − | 62.0399i | −0.510639 | − | 2.00025i | ||||
\(963\) | −4.39487 | − | 10.6102i | −0.141623 | − | 0.341908i | ||||
\(964\) | −7.44859 | − | 13.6378i | −0.239903 | − | 0.439244i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −60.2294 | + | 45.0919i | −1.93785 | + | 1.45081i | ||||
\(967\) | −14.0727 | − | 14.0727i | −0.452549 | − | 0.452549i | 0.443651 | − | 0.896200i | \(-0.353683\pi\) |
−0.896200 | + | 0.443651i | \(0.853683\pi\) | |||||||
\(968\) | −0.883442 | + | 24.8410i | −0.0283949 | + | 0.798419i | ||||
\(969\) | 12.3399 | − | 12.3399i | 0.396416 | − | 0.396416i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.57164 | + | 3.79427i | −0.0504363 | + | 0.121764i | −0.947089 | − | 0.320970i | \(-0.895991\pi\) |
0.896653 | + | 0.442734i | \(0.145991\pi\) | |||||||
\(972\) | −21.3733 | + | 26.5281i | −0.685549 | + | 0.850890i | ||||
\(973\) | 73.9162 | − | 30.6171i | 2.36965 | − | 0.981539i | ||||
\(974\) | −25.7117 | + | 43.3397i | −0.823855 | + | 1.38869i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −48.5927 | − | 8.75699i | −1.55542 | − | 0.280305i | ||||
\(977\) | 45.4460i | 1.45394i | 0.686667 | + | 0.726972i | \(0.259073\pi\) | ||||
−0.686667 | + | 0.726972i | \(0.740927\pi\) | |||||||
\(978\) | 4.05021 | + | 2.40283i | 0.129512 | + | 0.0768340i | ||||
\(979\) | 17.4362 | − | 7.22232i | 0.557264 | − | 0.230827i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.38629 | − | 20.2463i | 0.267754 | − | 0.646415i | ||||
\(982\) | −13.2771 | − | 1.90827i | −0.423688 | − | 0.0608954i | ||||
\(983\) | −14.0959 | + | 14.0959i | −0.449588 | + | 0.449588i | −0.895218 | − | 0.445629i | \(-0.852980\pi\) |
0.445629 | + | 0.895218i | \(0.352980\pi\) | |||||||
\(984\) | 34.4202 | + | 92.2415i | 1.09728 | + | 2.94055i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.6364 | + | 23.5570i | 0.561657 | + | 0.750207i | ||||
\(987\) | −30.4846 | − | 12.6271i | −0.970334 | − | 0.401926i | ||||
\(988\) | −6.23694 | + | 21.2490i | −0.198423 | + | 0.676020i | ||||
\(989\) | −8.93390 | − | 21.5683i | −0.284081 | − | 0.685833i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.5618 | −1.63792 | −0.818958 | − | 0.573854i | \(-0.805448\pi\) | ||||
−0.818958 | + | 0.573854i | \(0.805448\pi\) | |||||||
\(992\) | 4.29493 | + | 1.42829i | 0.136364 | + | 0.0453483i | ||||
\(993\) | 36.0543 | 1.14415 | ||||||||
\(994\) | 23.3984 | − | 5.97333i | 0.742151 | − | 0.189463i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.68376 | + | 0.494214i | 0.0533521 | + | 0.0156598i | ||||
\(997\) | −19.0528 | − | 7.89192i | −0.603407 | − | 0.249939i | 0.0599995 | − | 0.998198i | \(-0.480890\pi\) |
−0.663407 | + | 0.748259i | \(0.730890\pi\) | |||||||
\(998\) | −6.33792 | − | 8.46558i | −0.200623 | − | 0.267973i | ||||
\(999\) | 30.5841 | + | 30.5841i | 0.967640 | + | 0.967640i |
(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 | 800.2.y.e.101.8 | yes | 64 | |
5.2 | odd | 4 | 800.2.ba.f.549.16 | 64 | |||
5.3 | odd | 4 | 800.2.ba.h.549.1 | 64 | |||
5.4 | even | 2 | 800.2.y.d.101.9 | ✓ | 64 | ||
32.13 | even | 8 | inner | 800.2.y.e.301.8 | yes | 64 | |
160.13 | odd | 8 | 800.2.ba.f.749.16 | 64 | |||
160.77 | odd | 8 | 800.2.ba.h.749.1 | 64 | |||
160.109 | even | 8 | 800.2.y.d.301.9 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
800.2.y.d.101.9 | ✓ | 64 | 5.4 | even | 2 | ||
800.2.y.d.301.9 | yes | 64 | 160.109 | even | 8 | ||
800.2.y.e.101.8 | yes | 64 | 1.1 | even | 1 | trivial | |
800.2.y.e.301.8 | yes | 64 | 32.13 | even | 8 | inner | |
800.2.ba.f.549.16 | 64 | 5.2 | odd | 4 | |||
800.2.ba.f.749.16 | 64 | 160.13 | odd | 8 | |||
800.2.ba.h.549.1 | 64 | 5.3 | odd | 4 | |||
800.2.ba.h.749.1 | 64 | 160.77 | odd | 8 |