Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(41,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bl (of order \(6\), degree \(2\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.10 | ||
Character | \(\chi\) | \(=\) | 315.41 |
Dual form | 315.2.bl.j.146.10 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.94805 | − | 1.12471i | 1.37748 | − | 0.795289i | 0.385626 | − | 0.922655i | \(-0.373986\pi\) |
0.991856 | + | 0.127366i | \(0.0406523\pi\) | |||||||
\(3\) | 0.913713 | + | 1.47144i | 0.527533 | + | 0.849535i | ||||
\(4\) | 1.52994 | − | 2.64993i | 0.764970 | − | 1.32497i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 3.43490 | + | 1.83878i | 1.40229 | + | 0.750677i | ||||
\(7\) | 0.315547 | − | 2.62687i | 0.119266 | − | 0.992862i | ||||
\(8\) | − | 2.38412i | − | 0.842912i | ||||||
\(9\) | −1.33026 | + | 2.68894i | −0.443419 | + | 0.896315i | ||||
\(10\) | 2.24942i | 0.711328i | ||||||||
\(11\) | 2.13353 | − | 1.23180i | 0.643284 | − | 0.371400i | −0.142594 | − | 0.989781i | \(-0.545544\pi\) |
0.785878 | + | 0.618381i | \(0.212211\pi\) | |||||||
\(12\) | 5.29714 | − | 0.170069i | 1.52915 | − | 0.0490946i | ||||
\(13\) | −0.336443 | − | 0.194245i | −0.0933124 | − | 0.0538740i | 0.452618 | − | 0.891705i | \(-0.350490\pi\) |
−0.545930 | + | 0.837831i | \(0.683824\pi\) | |||||||
\(14\) | −2.33976 | − | 5.47217i | −0.625327 | − | 1.46250i | ||||
\(15\) | −1.73116 | + | 0.0555801i | −0.446983 | + | 0.0143507i | ||||
\(16\) | 0.378445 | + | 0.655486i | 0.0946113 | + | 0.163872i | ||||
\(17\) | −4.81075 | −1.16678 | −0.583389 | − | 0.812193i | \(-0.698274\pi\) | ||||
−0.583389 | + | 0.812193i | \(0.698274\pi\) | |||||||
\(18\) | 0.432869 | + | 6.73436i | 0.102028 | + | 1.58730i | ||||
\(19\) | 1.11761i | 0.256396i | 0.991749 | + | 0.128198i | \(0.0409194\pi\) | ||||
−0.991749 | + | 0.128198i | \(0.959081\pi\) | |||||||
\(20\) | 1.52994 | + | 2.64993i | 0.342105 | + | 0.592543i | ||||
\(21\) | 4.15359 | − | 1.93590i | 0.906388 | − | 0.422447i | ||||
\(22\) | 2.77082 | − | 4.79920i | 0.590741 | − | 1.02319i | ||||
\(23\) | −1.85078 | − | 1.06855i | −0.385915 | − | 0.222808i | 0.294474 | − | 0.955660i | \(-0.404856\pi\) |
−0.680388 | + | 0.732852i | \(0.738189\pi\) | |||||||
\(24\) | 3.50808 | − | 2.17840i | 0.716083 | − | 0.444664i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −0.873878 | −0.171382 | ||||||||
\(27\) | −5.17209 | + | 0.499535i | −0.995368 | + | 0.0961355i | ||||
\(28\) | −6.47826 | − | 4.85513i | −1.22428 | − | 0.917533i | ||||
\(29\) | −4.02738 | + | 2.32521i | −0.747865 | + | 0.431780i | −0.824922 | − | 0.565247i | \(-0.808781\pi\) |
0.0770570 | + | 0.997027i | \(0.475448\pi\) | |||||||
\(30\) | −3.30988 | + | 2.05532i | −0.604298 | + | 0.375249i | ||||
\(31\) | −5.61553 | − | 3.24213i | −1.00858 | − | 0.582303i | −0.0978037 | − | 0.995206i | \(-0.531182\pi\) |
−0.910775 | + | 0.412902i | \(0.864515\pi\) | |||||||
\(32\) | 5.60387 | + | 3.23540i | 0.990634 | + | 0.571943i | ||||
\(33\) | 3.76195 | + | 2.01385i | 0.654871 | + | 0.350566i | ||||
\(34\) | −9.37160 | + | 5.41070i | −1.60722 | + | 0.927927i | ||||
\(35\) | 2.11716 | + | 1.58671i | 0.357865 | + | 0.268202i | ||||
\(36\) | 5.09031 | + | 7.63902i | 0.848385 | + | 1.27317i | ||||
\(37\) | 4.29543 | 0.706164 | 0.353082 | − | 0.935592i | \(-0.385134\pi\) | ||||
0.353082 | + | 0.935592i | \(0.385134\pi\) | |||||||
\(38\) | 1.25698 | + | 2.17716i | 0.203909 | + | 0.353181i | ||||
\(39\) | −0.0215924 | − | 0.672539i | −0.00345755 | − | 0.107692i | ||||
\(40\) | 2.06470 | + | 1.19206i | 0.326458 | + | 0.188481i | ||||
\(41\) | 0.476591 | − | 0.825479i | 0.0744310 | − | 0.128918i | −0.826408 | − | 0.563072i | \(-0.809619\pi\) |
0.900839 | + | 0.434154i | \(0.142953\pi\) | |||||||
\(42\) | 5.91409 | − | 8.44281i | 0.912565 | − | 1.30275i | ||||
\(43\) | −5.21348 | − | 9.03002i | −0.795049 | − | 1.37706i | −0.922808 | − | 0.385259i | \(-0.874112\pi\) |
0.127760 | − | 0.991805i | \(-0.459221\pi\) | |||||||
\(44\) | − | 7.53829i | − | 1.13644i | ||||||
\(45\) | −1.66357 | − | 2.49651i | −0.247990 | − | 0.372157i | ||||
\(46\) | −4.80723 | −0.708787 | ||||||||
\(47\) | 2.81296 | + | 4.87220i | 0.410313 | + | 0.710683i | 0.994924 | − | 0.100631i | \(-0.0320861\pi\) |
−0.584611 | + | 0.811314i | \(0.698753\pi\) | |||||||
\(48\) | −0.618716 | + | 1.15578i | −0.0893040 | + | 0.166823i | ||||
\(49\) | −6.80086 | − | 1.65780i | −0.971551 | − | 0.236829i | ||||
\(50\) | −1.94805 | − | 1.12471i | −0.275496 | − | 0.159058i | ||||
\(51\) | −4.39565 | − | 7.07872i | −0.615514 | − | 0.991219i | ||||
\(52\) | −1.02947 | + | 0.594368i | −0.142762 | + | 0.0824239i | ||||
\(53\) | 9.72792i | 1.33623i | 0.744057 | + | 0.668117i | \(0.232899\pi\) | ||||
−0.744057 | + | 0.668117i | \(0.767101\pi\) | |||||||
\(54\) | −9.51367 | + | 6.79021i | −1.29465 | + | 0.924031i | ||||
\(55\) | 2.46359i | 0.332190i | ||||||||
\(56\) | −6.26275 | − | 0.752301i | −0.836896 | − | 0.100530i | ||||
\(57\) | −1.64449 | + | 1.02117i | −0.217818 | + | 0.135257i | ||||
\(58\) | −5.23036 | + | 9.05925i | −0.686780 | + | 1.18954i | ||||
\(59\) | 6.18688 | − | 10.7160i | 0.805463 | − | 1.39510i | −0.110515 | − | 0.993875i | \(-0.535250\pi\) |
0.915978 | − | 0.401229i | \(-0.131417\pi\) | |||||||
\(60\) | −2.50129 | + | 4.67249i | −0.322915 | + | 0.603216i | ||||
\(61\) | −0.631916 | + | 0.364837i | −0.0809085 | + | 0.0467125i | −0.539908 | − | 0.841724i | \(-0.681541\pi\) |
0.459000 | + | 0.888436i | \(0.348208\pi\) | |||||||
\(62\) | −14.5858 | −1.85240 | ||||||||
\(63\) | 6.64374 | + | 4.34289i | 0.837032 | + | 0.547153i | ||||
\(64\) | 13.0417 | 1.63022 | ||||||||
\(65\) | 0.336443 | − | 0.194245i | 0.0417306 | − | 0.0240932i | ||||
\(66\) | 9.59347 | − | 0.308005i | 1.18087 | − | 0.0379128i | ||||
\(67\) | 5.73742 | − | 9.93750i | 0.700937 | − | 1.21406i | −0.267201 | − | 0.963641i | \(-0.586099\pi\) |
0.968138 | − | 0.250418i | \(-0.0805679\pi\) | |||||||
\(68\) | −7.36016 | + | 12.7482i | −0.892551 | + | 1.54594i | ||||
\(69\) | −0.118780 | − | 3.69966i | −0.0142995 | − | 0.445386i | ||||
\(70\) | 5.90892 | + | 0.709797i | 0.706251 | + | 0.0848370i | ||||
\(71\) | 15.1436i | 1.79721i | 0.438754 | + | 0.898607i | \(0.355420\pi\) | ||||
−0.438754 | + | 0.898607i | \(0.644580\pi\) | |||||||
\(72\) | 6.41075 | + | 3.17148i | 0.755514 | + | 0.373763i | ||||
\(73\) | − | 10.5746i | − | 1.23766i | −0.785524 | − | 0.618831i | \(-0.787607\pi\) | ||
0.785524 | − | 0.618831i | \(-0.212393\pi\) | |||||||
\(74\) | 8.36772 | − | 4.83111i | 0.972728 | − | 0.561605i | ||||
\(75\) | 0.817446 | − | 1.52702i | 0.0943905 | − | 0.176325i | ||||
\(76\) | 2.96158 | + | 1.70987i | 0.339717 | + | 0.196136i | ||||
\(77\) | −2.56253 | − | 5.99319i | −0.292028 | − | 0.682988i | ||||
\(78\) | −0.798474 | − | 1.28586i | −0.0904093 | − | 0.145595i | ||||
\(79\) | 7.35947 | + | 12.7470i | 0.828005 | + | 1.43415i | 0.899601 | + | 0.436713i | \(0.143857\pi\) |
−0.0715959 | + | 0.997434i | \(0.522809\pi\) | |||||||
\(80\) | −0.756890 | −0.0846229 | ||||||||
\(81\) | −5.46084 | − | 7.15397i | −0.606760 | − | 0.794885i | ||||
\(82\) | − | 2.14410i | − | 0.236777i | ||||||
\(83\) | 5.97335 | + | 10.3461i | 0.655660 | + | 1.13564i | 0.981728 | + | 0.190291i | \(0.0609430\pi\) |
−0.326067 | + | 0.945347i | \(0.605724\pi\) | |||||||
\(84\) | 1.22475 | − | 13.9685i | 0.133631 | − | 1.52409i | ||||
\(85\) | 2.40538 | − | 4.16623i | 0.260900 | − | 0.451891i | ||||
\(86\) | −20.3123 | − | 11.7273i | −2.19033 | − | 1.26459i | ||||
\(87\) | −7.10126 | − | 3.80146i | −0.761335 | − | 0.407559i | ||||
\(88\) | −2.93674 | − | 5.08659i | −0.313058 | − | 0.542232i | ||||
\(89\) | 14.2521 | 1.51072 | 0.755362 | − | 0.655308i | \(-0.227461\pi\) | ||||
0.755362 | + | 0.655308i | \(0.227461\pi\) | |||||||
\(90\) | −6.04856 | − | 2.99230i | −0.637574 | − | 0.315416i | ||||
\(91\) | −0.616420 | + | 0.822497i | −0.0646184 | + | 0.0862211i | ||||
\(92\) | −5.66317 | + | 3.26963i | −0.590426 | + | 0.340883i | ||||
\(93\) | −0.360396 | − | 11.2253i | −0.0373713 | − | 1.16401i | ||||
\(94\) | 10.9596 | + | 6.32753i | 1.13040 | + | 0.652635i | ||||
\(95\) | −0.967875 | − | 0.558803i | −0.0993019 | − | 0.0573320i | ||||
\(96\) | 0.359648 | + | 11.2020i | 0.0367064 | + | 1.14330i | ||||
\(97\) | 3.46717 | − | 2.00177i | 0.352038 | − | 0.203249i | −0.313545 | − | 0.949573i | \(-0.601517\pi\) |
0.665582 | + | 0.746324i | \(0.268183\pi\) | |||||||
\(98\) | −15.1130 | + | 4.41951i | −1.52664 | + | 0.446437i | ||||
\(99\) | 0.474084 | + | 7.37555i | 0.0476472 | + | 0.741271i | ||||
\(100\) | −3.05988 | −0.305988 | ||||||||
\(101\) | 3.71469 | + | 6.43403i | 0.369625 | + | 0.640210i | 0.989507 | − | 0.144485i | \(-0.0461527\pi\) |
−0.619882 | + | 0.784695i | \(0.712819\pi\) | |||||||
\(102\) | −16.5245 | − | 8.84590i | −1.63616 | − | 0.875874i | ||||
\(103\) | 7.59032 | + | 4.38227i | 0.747896 | + | 0.431798i | 0.824933 | − | 0.565230i | \(-0.191213\pi\) |
−0.0770370 | + | 0.997028i | \(0.524546\pi\) | |||||||
\(104\) | −0.463103 | + | 0.802118i | −0.0454110 | + | 0.0786542i | ||||
\(105\) | −0.400260 | + | 4.56506i | −0.0390614 | + | 0.445504i | ||||
\(106\) | 10.9411 | + | 18.9505i | 1.06269 | + | 1.84064i | ||||
\(107\) | − | 4.06484i | − | 0.392963i | −0.980508 | − | 0.196482i | \(-0.937048\pi\) | ||
0.980508 | − | 0.196482i | \(-0.0629516\pi\) | |||||||
\(108\) | −6.58925 | + | 14.4699i | −0.634051 | + | 1.39237i | ||||
\(109\) | 11.3809 | 1.09009 | 0.545046 | − | 0.838406i | \(-0.316512\pi\) | ||||
0.545046 | + | 0.838406i | \(0.316512\pi\) | |||||||
\(110\) | 2.77082 | + | 4.79920i | 0.264188 | + | 0.457586i | ||||
\(111\) | 3.92479 | + | 6.32045i | 0.372524 | + | 0.599911i | ||||
\(112\) | 1.84129 | − | 0.787288i | 0.173986 | − | 0.0743917i | ||||
\(113\) | −7.59510 | − | 4.38503i | −0.714487 | − | 0.412509i | 0.0982332 | − | 0.995163i | \(-0.468681\pi\) |
−0.812720 | + | 0.582654i | \(0.802014\pi\) | |||||||
\(114\) | −2.05503 | + | 3.83887i | −0.192471 | + | 0.359543i | ||||
\(115\) | 1.85078 | − | 1.06855i | 0.172586 | − | 0.0996427i | ||||
\(116\) | 14.2297i | 1.32120i | ||||||||
\(117\) | 0.969870 | − | 0.646280i | 0.0896645 | − | 0.0597486i | ||||
\(118\) | − | 27.8338i | − | 2.56231i | ||||||
\(119\) | −1.51802 | + | 12.6372i | −0.139157 | + | 1.15845i | ||||
\(120\) | 0.132509 | + | 4.12728i | 0.0120964 | + | 0.376768i | ||||
\(121\) | −2.46536 | + | 4.27013i | −0.224124 | + | 0.388194i | ||||
\(122\) | −0.820670 | + | 1.42144i | −0.0743000 | + | 0.128691i | ||||
\(123\) | 1.65011 | − | 0.0529780i | 0.148785 | − | 0.00477686i | ||||
\(124\) | −17.1829 | + | 9.92053i | −1.54307 | + | 0.890889i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 17.8268 | + | 0.987916i | 1.58814 | + | 0.0880106i | ||||
\(127\) | −5.13475 | −0.455635 | −0.227818 | − | 0.973704i | \(-0.573159\pi\) | ||||
−0.227818 | + | 0.973704i | \(0.573159\pi\) | |||||||
\(128\) | 14.1983 | − | 8.19737i | 1.25496 | − | 0.724552i | ||||
\(129\) | 8.52348 | − | 15.9222i | 0.750450 | − | 1.40187i | ||||
\(130\) | 0.436939 | − | 0.756800i | 0.0383221 | − | 0.0663758i | ||||
\(131\) | −6.25464 | + | 10.8334i | −0.546470 | + | 0.946514i | 0.452042 | + | 0.891996i | \(0.350696\pi\) |
−0.998513 | + | 0.0545179i | \(0.982638\pi\) | |||||||
\(132\) | 11.0921 | − | 6.88784i | 0.965446 | − | 0.599509i | ||||
\(133\) | 2.93580 | + | 0.352657i | 0.254566 | + | 0.0305793i | ||||
\(134\) | − | 25.8117i | − | 2.22979i | ||||||
\(135\) | 2.15343 | − | 4.72892i | 0.185338 | − | 0.407001i | ||||
\(136\) | 11.4694i | 0.983492i | ||||||||
\(137\) | −6.12680 | + | 3.53731i | −0.523448 | + | 0.302213i | −0.738344 | − | 0.674424i | \(-0.764392\pi\) |
0.214896 | + | 0.976637i | \(0.431059\pi\) | |||||||
\(138\) | −4.39243 | − | 7.07353i | −0.373908 | − | 0.602139i | ||||
\(139\) | 9.58572 | + | 5.53432i | 0.813050 | + | 0.469415i | 0.848014 | − | 0.529974i | \(-0.177798\pi\) |
−0.0349638 | + | 0.999389i | \(0.511132\pi\) | |||||||
\(140\) | 7.44379 | − | 3.18277i | 0.629115 | − | 0.268993i | ||||
\(141\) | −4.59889 | + | 8.59089i | −0.387296 | + | 0.723483i | ||||
\(142\) | 17.0321 | + | 29.5005i | 1.42931 | + | 2.47563i | ||||
\(143\) | −0.957082 | −0.0800352 | ||||||||
\(144\) | −2.26599 | + | 0.145653i | −0.188833 | + | 0.0121377i | ||||
\(145\) | − | 4.65041i | − | 0.386196i | ||||||
\(146\) | −11.8933 | − | 20.5999i | −0.984299 | − | 1.70486i | ||||
\(147\) | −3.77469 | − | 11.5218i | −0.311331 | − | 0.950302i | ||||
\(148\) | 6.57175 | − | 11.3826i | 0.540194 | − | 0.935644i | ||||
\(149\) | −7.40128 | − | 4.27313i | −0.606336 | − | 0.350068i | 0.165194 | − | 0.986261i | \(-0.447175\pi\) |
−0.771530 | + | 0.636193i | \(0.780508\pi\) | |||||||
\(150\) | −0.125023 | − | 3.89410i | −0.0102081 | − | 0.317952i | ||||
\(151\) | −7.86677 | − | 13.6256i | −0.640188 | − | 1.10884i | −0.985390 | − | 0.170311i | \(-0.945523\pi\) |
0.345202 | − | 0.938528i | \(-0.387810\pi\) | |||||||
\(152\) | 2.66450 | 0.216120 | ||||||||
\(153\) | 6.39953 | − | 12.9358i | 0.517372 | − | 1.04580i | ||||
\(154\) | −11.7325 | − | 8.79296i | −0.945436 | − | 0.708557i | ||||
\(155\) | 5.61553 | − | 3.24213i | 0.451050 | − | 0.260414i | ||||
\(156\) | −1.81522 | − | 0.971726i | −0.145334 | − | 0.0778004i | ||||
\(157\) | −17.2311 | − | 9.94836i | −1.37519 | − | 0.793966i | −0.383613 | − | 0.923494i | \(-0.625320\pi\) |
−0.991576 | + | 0.129528i | \(0.958654\pi\) | |||||||
\(158\) | 28.6733 | + | 16.5545i | 2.28112 | + | 1.31701i | ||||
\(159\) | −14.3140 | + | 8.88853i | −1.13518 | + | 0.704906i | ||||
\(160\) | −5.60387 | + | 3.23540i | −0.443025 | + | 0.255781i | ||||
\(161\) | −3.39094 | + | 4.52458i | −0.267244 | + | 0.356587i | ||||
\(162\) | −18.6841 | − | 7.79446i | −1.46796 | − | 0.612391i | ||||
\(163\) | 0.220738 | 0.0172895 | 0.00864477 | − | 0.999963i | \(-0.497248\pi\) | ||||
0.00864477 | + | 0.999963i | \(0.497248\pi\) | |||||||
\(164\) | −1.45831 | − | 2.52587i | −0.113875 | − | 0.197237i | ||||
\(165\) | −3.62502 | + | 2.25102i | −0.282207 | + | 0.175241i | ||||
\(166\) | 23.2728 | + | 13.4366i | 1.80632 | + | 1.04288i | ||||
\(167\) | 12.6948 | − | 21.9881i | 0.982356 | − | 1.70149i | 0.329215 | − | 0.944255i | \(-0.393216\pi\) |
0.653141 | − | 0.757236i | \(-0.273451\pi\) | |||||||
\(168\) | −4.61540 | − | 9.90264i | −0.356086 | − | 0.764005i | ||||
\(169\) | −6.42454 | − | 11.1276i | −0.494195 | − | 0.855971i | ||||
\(170\) | − | 10.8214i | − | 0.829963i | ||||||
\(171\) | −3.00518 | − | 1.48670i | −0.229812 | − | 0.113691i | ||||
\(172\) | −31.9053 | −2.43275 | ||||||||
\(173\) | −7.26041 | − | 12.5754i | −0.551999 | − | 0.956090i | −0.998130 | − | 0.0611226i | \(-0.980532\pi\) |
0.446131 | − | 0.894967i | \(-0.352801\pi\) | |||||||
\(174\) | −18.1092 | + | 0.581408i | −1.37285 | + | 0.0440765i | ||||
\(175\) | −2.43271 | + | 1.04016i | −0.183895 | + | 0.0786288i | ||||
\(176\) | 1.61485 | + | 0.932334i | 0.121724 | + | 0.0702773i | ||||
\(177\) | 21.4209 | − | 0.687735i | 1.61010 | − | 0.0516934i | ||||
\(178\) | 27.7639 | − | 16.0295i | 2.08099 | − | 1.20146i | ||||
\(179\) | 15.0447i | 1.12449i | 0.826971 | + | 0.562245i | \(0.190062\pi\) | ||||
−0.826971 | + | 0.562245i | \(0.809938\pi\) | |||||||
\(180\) | −9.16074 | + | 0.588832i | −0.682801 | + | 0.0438889i | ||||
\(181\) | − | 18.1625i | − | 1.35001i | −0.737813 | − | 0.675006i | \(-0.764141\pi\) | ||
0.737813 | − | 0.675006i | \(-0.235859\pi\) | |||||||
\(182\) | −0.275750 | + | 2.29556i | −0.0204399 | + | 0.170158i | ||||
\(183\) | −1.11422 | − | 0.596468i | −0.0823658 | − | 0.0440922i | ||||
\(184\) | −2.54754 | + | 4.41248i | −0.187807 | + | 0.325292i | ||||
\(185\) | −2.14771 | + | 3.71995i | −0.157903 | + | 0.273496i | ||||
\(186\) | −13.3272 | − | 21.4621i | −0.977201 | − | 1.57368i | ||||
\(187\) | −10.2639 | + | 5.92586i | −0.750570 | + | 0.433342i | ||||
\(188\) | 17.2147 | 1.25551 | ||||||||
\(189\) | −0.319826 | + | 13.7440i | −0.0232639 | + | 0.999729i | ||||
\(190\) | −2.51396 | −0.182382 | ||||||||
\(191\) | −1.71849 | + | 0.992168i | −0.124345 | + | 0.0717908i | −0.560882 | − | 0.827895i | \(-0.689538\pi\) |
0.436537 | + | 0.899686i | \(0.356205\pi\) | |||||||
\(192\) | 11.9164 | + | 19.1901i | 0.859993 | + | 1.38493i | ||||
\(193\) | 6.61042 | − | 11.4496i | 0.475829 | − | 0.824159i | −0.523788 | − | 0.851849i | \(-0.675482\pi\) |
0.999617 | + | 0.0276894i | \(0.00881495\pi\) | |||||||
\(194\) | 4.50282 | − | 7.79911i | 0.323284 | − | 0.559943i | ||||
\(195\) | 0.593232 | + | 0.317570i | 0.0424822 | + | 0.0227417i | ||||
\(196\) | −14.7980 | + | 15.4855i | −1.05700 | + | 1.10611i | ||||
\(197\) | − | 16.1651i | − | 1.15172i | −0.817550 | − | 0.575858i | \(-0.804668\pi\) | ||
0.817550 | − | 0.575858i | \(-0.195332\pi\) | |||||||
\(198\) | 9.21889 | + | 13.8348i | 0.655158 | + | 0.983193i | ||||
\(199\) | 27.3385i | 1.93798i | 0.247107 | + | 0.968988i | \(0.420520\pi\) | ||||
−0.247107 | + | 0.968988i | \(0.579480\pi\) | |||||||
\(200\) | −2.06470 | + | 1.19206i | −0.145997 | + | 0.0842912i | ||||
\(201\) | 19.8648 | − | 0.637773i | 1.40115 | − | 0.0449850i | ||||
\(202\) | 14.4728 | + | 8.35589i | 1.01830 | + | 0.587918i | ||||
\(203\) | 4.83718 | + | 11.3131i | 0.339504 | + | 0.794023i | ||||
\(204\) | −25.4832 | + | 0.818158i | −1.78418 | + | 0.0572825i | ||||
\(205\) | 0.476591 | + | 0.825479i | 0.0332865 | + | 0.0576540i | ||||
\(206\) | 19.7151 | 1.37362 | ||||||||
\(207\) | 5.33528 | − | 3.55520i | 0.370828 | − | 0.247104i | ||||
\(208\) | − | 0.294045i | − | 0.0203883i | ||||||
\(209\) | 1.37666 | + | 2.38445i | 0.0952257 | + | 0.164936i | ||||
\(210\) | 4.35464 | + | 9.34316i | 0.300499 | + | 0.644739i | ||||
\(211\) | −0.788116 | + | 1.36506i | −0.0542561 | + | 0.0939744i | −0.891878 | − | 0.452276i | \(-0.850612\pi\) |
0.837622 | + | 0.546251i | \(0.183945\pi\) | |||||||
\(212\) | 25.7784 | + | 14.8831i | 1.77047 | + | 1.02218i | ||||
\(213\) | −22.2829 | + | 13.8369i | −1.52680 | + | 0.948089i | ||||
\(214\) | −4.57176 | − | 7.91853i | −0.312519 | − | 0.541299i | ||||
\(215\) | 10.4270 | 0.711113 | ||||||||
\(216\) | 1.19095 | + | 12.3308i | 0.0810337 | + | 0.839008i | ||||
\(217\) | −10.2886 | + | 13.7282i | −0.698436 | + | 0.931931i | ||||
\(218\) | 22.1706 | − | 12.8002i | 1.50158 | − | 0.866939i | ||||
\(219\) | 15.5598 | − | 9.66214i | 1.05144 | − | 0.652907i | ||||
\(220\) | 6.52835 | + | 3.76915i | 0.440141 | + | 0.254116i | ||||
\(221\) | 1.61854 | + | 0.934466i | 0.108875 | + | 0.0628590i | ||||
\(222\) | 14.7544 | + | 7.89833i | 0.990248 | + | 0.530101i | ||||
\(223\) | −12.6487 | + | 7.30272i | −0.847019 | + | 0.489026i | −0.859644 | − | 0.510894i | \(-0.829314\pi\) |
0.0126252 | + | 0.999920i | \(0.495981\pi\) | |||||||
\(224\) | 10.2672 | − | 13.6997i | 0.686009 | − | 0.915350i | ||||
\(225\) | 2.99382 | − | 0.192436i | 0.199588 | − | 0.0128291i | ||||
\(226\) | −19.7275 | −1.31226 | ||||||||
\(227\) | −1.45581 | − | 2.52154i | −0.0966257 | − | 0.167361i | 0.813660 | − | 0.581341i | \(-0.197472\pi\) |
−0.910286 | + | 0.413980i | \(0.864138\pi\) | |||||||
\(228\) | 0.190070 | + | 5.92012i | 0.0125877 | + | 0.392069i | ||||
\(229\) | 16.2387 | + | 9.37541i | 1.07308 | + | 0.619545i | 0.929022 | − | 0.370024i | \(-0.120651\pi\) |
0.144061 | + | 0.989569i | \(0.453984\pi\) | |||||||
\(230\) | 2.40361 | − | 4.16318i | 0.158490 | − | 0.274512i | ||||
\(231\) | 6.47719 | − | 9.24667i | 0.426168 | − | 0.608386i | ||||
\(232\) | 5.54356 | + | 9.60173i | 0.363953 | + | 0.630384i | ||||
\(233\) | 5.14191i | 0.336858i | 0.985714 | + | 0.168429i | \(0.0538693\pi\) | ||||
−0.985714 | + | 0.168429i | \(0.946131\pi\) | |||||||
\(234\) | 1.16248 | − | 2.34981i | 0.0759938 | − | 0.153612i | ||||
\(235\) | −5.62593 | −0.366995 | ||||||||
\(236\) | −18.9311 | − | 32.7897i | −1.23231 | − | 2.13443i | ||||
\(237\) | −12.0319 | + | 22.4761i | −0.781558 | + | 1.45998i | ||||
\(238\) | 11.2560 | + | 26.3253i | 0.729618 | + | 1.70641i | ||||
\(239\) | 14.7909 | + | 8.53953i | 0.956743 | + | 0.552376i | 0.895169 | − | 0.445726i | \(-0.147055\pi\) |
0.0615742 | + | 0.998103i | \(0.480388\pi\) | |||||||
\(240\) | −0.691580 | − | 1.11372i | −0.0446413 | − | 0.0718901i | ||||
\(241\) | −18.1230 | + | 10.4633i | −1.16740 | + | 0.674000i | −0.953067 | − | 0.302760i | \(-0.902092\pi\) |
−0.214335 | + | 0.976760i | \(0.568759\pi\) | |||||||
\(242\) | 11.0913i | 0.712973i | ||||||||
\(243\) | 5.53698 | − | 14.5720i | 0.355197 | − | 0.934791i | ||||
\(244\) | 2.23271i | 0.142935i | ||||||||
\(245\) | 4.83613 | − | 5.06082i | 0.308969 | − | 0.323324i | ||||
\(246\) | 3.15491 | − | 1.95910i | 0.201150 | − | 0.124907i | ||||
\(247\) | 0.217090 | − | 0.376010i | 0.0138131 | − | 0.0239250i | ||||
\(248\) | −7.72961 | + | 13.3881i | −0.490831 | + | 0.850143i | ||||
\(249\) | −9.76578 | + | 18.2428i | −0.618881 | + | 1.15609i | ||||
\(250\) | 1.94805 | − | 1.12471i | 0.123206 | − | 0.0711328i | ||||
\(251\) | −3.52350 | −0.222401 | −0.111201 | − | 0.993798i | \(-0.535470\pi\) | ||||
−0.111201 | + | 0.993798i | \(0.535470\pi\) | |||||||
\(252\) | 21.6729 | − | 10.9611i | 1.36527 | − | 0.690485i | ||||
\(253\) | −5.26493 | −0.331004 | ||||||||
\(254\) | −10.0028 | + | 5.77510i | −0.627629 | + | 0.362362i | ||||
\(255\) | 8.32817 | − | 0.267382i | 0.521531 | − | 0.0167441i | ||||
\(256\) | 5.39757 | − | 9.34886i | 0.337348 | − | 0.584304i | ||||
\(257\) | 0.354048 | − | 0.613230i | 0.0220849 | − | 0.0382522i | −0.854772 | − | 0.519004i | \(-0.826303\pi\) |
0.876857 | + | 0.480752i | \(0.159636\pi\) | |||||||
\(258\) | −1.30361 | − | 40.6036i | −0.0811592 | − | 2.52787i | ||||
\(259\) | 1.35541 | − | 11.2835i | 0.0842210 | − | 0.701124i | ||||
\(260\) | − | 1.18874i | − | 0.0737222i | ||||||
\(261\) | −0.894907 | − | 13.9225i | −0.0553934 | − | 0.861782i | ||||
\(262\) | 28.1386i | 1.73841i | ||||||||
\(263\) | 8.83427 | − | 5.10047i | 0.544744 | − | 0.314508i | −0.202255 | − | 0.979333i | \(-0.564827\pi\) |
0.747000 | + | 0.664825i | \(0.231494\pi\) | |||||||
\(264\) | 4.80125 | − | 8.96891i | 0.295497 | − | 0.551998i | ||||
\(265\) | −8.42463 | − | 4.86396i | −0.517521 | − | 0.298791i | ||||
\(266\) | 6.11574 | − | 2.61493i | 0.374980 | − | 0.160332i | ||||
\(267\) | 13.0224 | + | 20.9711i | 0.796956 | + | 1.28341i | ||||
\(268\) | −17.5558 | − | 30.4076i | −1.07239 | − | 1.85744i | ||||
\(269\) | −30.0939 | −1.83486 | −0.917429 | − | 0.397900i | \(-0.869739\pi\) | ||||
−0.917429 | + | 0.397900i | \(0.869739\pi\) | |||||||
\(270\) | −1.12366 | − | 11.6342i | −0.0683839 | − | 0.708034i | ||||
\(271\) | 6.23015i | 0.378455i | 0.981933 | + | 0.189227i | \(0.0605983\pi\) | ||||
−0.981933 | + | 0.189227i | \(0.939402\pi\) | |||||||
\(272\) | −1.82061 | − | 3.15338i | −0.110390 | − | 0.191202i | ||||
\(273\) | −1.77348 | − | 0.155497i | −0.107336 | − | 0.00941113i | ||||
\(274\) | −7.95689 | + | 13.7817i | −0.480693 | + | 0.832585i | ||||
\(275\) | −2.13353 | − | 1.23180i | −0.128657 | − | 0.0742800i | ||||
\(276\) | −9.98557 | − | 5.34549i | −0.601061 | − | 0.321761i | ||||
\(277\) | −0.132848 | − | 0.230100i | −0.00798208 | − | 0.0138254i | 0.862007 | − | 0.506897i | \(-0.169207\pi\) |
−0.869989 | + | 0.493071i | \(0.835874\pi\) | |||||||
\(278\) | 24.8980 | 1.49328 | ||||||||
\(279\) | 16.1880 | − | 10.7870i | 0.969150 | − | 0.645800i | ||||
\(280\) | 3.78289 | − | 5.04755i | 0.226071 | − | 0.301649i | ||||
\(281\) | 12.0611 | − | 6.96348i | 0.719505 | − | 0.415406i | −0.0950655 | − | 0.995471i | \(-0.530306\pi\) |
0.814570 | + | 0.580065i | \(0.196973\pi\) | |||||||
\(282\) | 0.703370 | + | 21.9079i | 0.0418851 | + | 1.30460i | ||||
\(283\) | −13.7248 | − | 7.92403i | −0.815856 | − | 0.471035i | 0.0331293 | − | 0.999451i | \(-0.489453\pi\) |
−0.848985 | + | 0.528416i | \(0.822786\pi\) | |||||||
\(284\) | 40.1295 | + | 23.1688i | 2.38125 | + | 1.37482i | ||||
\(285\) | −0.0621167 | − | 1.93475i | −0.00367948 | − | 0.114605i | ||||
\(286\) | −1.86445 | + | 1.07644i | −0.110247 | + | 0.0636511i | ||||
\(287\) | −2.01804 | − | 1.51242i | −0.119121 | − | 0.0892752i | ||||
\(288\) | −16.1544 | + | 10.7646i | −0.951906 | + | 0.634309i | ||||
\(289\) | 6.14333 | 0.361372 | ||||||||
\(290\) | −5.23036 | − | 9.05925i | −0.307137 | − | 0.531978i | ||||
\(291\) | 6.11348 | + | 3.27268i | 0.358378 | + | 0.191848i | ||||
\(292\) | −28.0220 | − | 16.1785i | −1.63986 | − | 0.946775i | ||||
\(293\) | −3.37071 | + | 5.83823i | −0.196919 | + | 0.341073i | −0.947528 | − | 0.319673i | \(-0.896427\pi\) |
0.750609 | + | 0.660747i | \(0.229760\pi\) | |||||||
\(294\) | −20.3120 | − | 18.1996i | −1.18462 | − | 1.06142i | ||||
\(295\) | 6.18688 | + | 10.7160i | 0.360214 | + | 0.623909i | ||||
\(296\) | − | 10.2408i | − | 0.595234i | ||||||
\(297\) | −10.4195 | + | 7.43672i | −0.604600 | + | 0.431522i | ||||
\(298\) | −19.2241 | −1.11362 | ||||||||
\(299\) | 0.415121 | + | 0.719011i | 0.0240071 | + | 0.0415815i | ||||
\(300\) | −2.79585 | − | 4.50242i | −0.161419 | − | 0.259948i | ||||
\(301\) | −25.3658 | + | 10.8457i | −1.46206 | + | 0.625137i | ||||
\(302\) | −30.6498 | − | 17.6956i | −1.76370 | − | 1.01827i | ||||
\(303\) | −6.07311 | + | 11.3448i | −0.348891 | + | 0.651741i | ||||
\(304\) | −0.732575 | + | 0.422953i | −0.0420161 | + | 0.0242580i | ||||
\(305\) | − | 0.729673i | − | 0.0417810i | ||||||
\(306\) | −2.08243 | − | 32.3973i | −0.119044 | − | 1.85203i | ||||
\(307\) | − | 1.61431i | − | 0.0921335i | −0.998938 | − | 0.0460668i | \(-0.985331\pi\) | ||
0.998938 | − | 0.0460668i | \(-0.0146687\pi\) | |||||||
\(308\) | −19.8021 | − | 2.37869i | −1.12833 | − | 0.135538i | ||||
\(309\) | 0.487135 | + | 15.1728i | 0.0277121 | + | 0.863151i | ||||
\(310\) | 7.29290 | − | 12.6317i | 0.414209 | − | 0.717431i | ||||
\(311\) | −7.87129 | + | 13.6335i | −0.446340 | + | 0.773083i | −0.998144 | − | 0.0608901i | \(-0.980606\pi\) |
0.551805 | + | 0.833973i | \(0.313939\pi\) | |||||||
\(312\) | −1.60341 | + | 0.0514787i | −0.0907752 | + | 0.00291441i | ||||
\(313\) | 3.38500 | − | 1.95433i | 0.191332 | − | 0.110465i | −0.401274 | − | 0.915958i | \(-0.631433\pi\) |
0.592606 | + | 0.805493i | \(0.298099\pi\) | |||||||
\(314\) | −44.7560 | −2.52573 | ||||||||
\(315\) | −7.08293 | + | 3.58220i | −0.399078 | + | 0.201834i | ||||
\(316\) | 45.0382 | 2.53360 | ||||||||
\(317\) | −21.3367 | + | 12.3187i | −1.19839 | + | 0.691889i | −0.960195 | − | 0.279330i | \(-0.909888\pi\) |
−0.238191 | + | 0.971218i | \(0.576554\pi\) | |||||||
\(318\) | −17.8875 | + | 33.4145i | −1.00308 | + | 1.87379i | ||||
\(319\) | −5.72836 | + | 9.92180i | −0.320726 | + | 0.555514i | ||||
\(320\) | −6.52087 | + | 11.2945i | −0.364528 | + | 0.631380i | ||||
\(321\) | 5.98116 | − | 3.71410i | 0.333836 | − | 0.207301i | ||||
\(322\) | −1.51691 | + | 12.6279i | −0.0845339 | + | 0.703728i | ||||
\(323\) | − | 5.37653i | − | 0.299158i | ||||||
\(324\) | −27.3123 | + | 3.52571i | −1.51735 | + | 0.195873i | ||||
\(325\) | 0.388491i | 0.0215496i | ||||||||
\(326\) | 0.430010 | − | 0.248266i | 0.0238160 | − | 0.0137502i | ||||
\(327\) | 10.3989 | + | 16.7463i | 0.575059 | + | 0.926071i | ||||
\(328\) | −1.96804 | − | 1.13625i | −0.108667 | − | 0.0627388i | ||||
\(329\) | 13.6862 | − | 5.85187i | 0.754546 | − | 0.322624i | ||||
\(330\) | −4.52999 | + | 8.46219i | −0.249368 | + | 0.465828i | ||||
\(331\) | −4.61821 | − | 7.99898i | −0.253840 | − | 0.439664i | 0.710740 | − | 0.703455i | \(-0.248360\pi\) |
−0.964580 | + | 0.263791i | \(0.915027\pi\) | |||||||
\(332\) | 36.5555 | 2.00624 | ||||||||
\(333\) | −5.71402 | + | 11.5502i | −0.313126 | + | 0.632945i | ||||
\(334\) | − | 57.1120i | − | 3.12503i | ||||||
\(335\) | 5.73742 | + | 9.93750i | 0.313469 | + | 0.542943i | ||||
\(336\) | 2.84086 | + | 1.98999i | 0.154982 | + | 0.108563i | ||||
\(337\) | 1.28651 | − | 2.22831i | 0.0700809 | − | 0.121384i | −0.828856 | − | 0.559462i | \(-0.811008\pi\) |
0.898937 | + | 0.438079i | \(0.144341\pi\) | |||||||
\(338\) | −25.0307 | − | 14.4515i | −1.36149 | − | 0.786056i | ||||
\(339\) | −0.487442 | − | 15.1824i | −0.0264742 | − | 0.824594i | ||||
\(340\) | −7.36016 | − | 12.7482i | −0.399161 | − | 0.691367i | ||||
\(341\) | −15.9745 | −0.865070 | ||||||||
\(342\) | −7.52636 | + | 0.483777i | −0.406979 | + | 0.0261597i | ||||
\(343\) | −6.50081 | + | 17.3418i | −0.351011 | + | 0.936371i | ||||
\(344\) | −21.5286 | + | 12.4295i | −1.16074 | + | 0.670156i | ||||
\(345\) | 3.26339 | + | 1.74696i | 0.175695 | + | 0.0940532i | ||||
\(346\) | −28.2873 | − | 16.3317i | −1.52074 | − | 0.877998i | ||||
\(347\) | −16.4541 | − | 9.49979i | −0.883303 | − | 0.509975i | −0.0115570 | − | 0.999933i | \(-0.503679\pi\) |
−0.871746 | + | 0.489958i | \(0.837012\pi\) | |||||||
\(348\) | −20.9381 | + | 13.0019i | −1.12240 | + | 0.696974i | ||||
\(349\) | 9.19557 | − | 5.30906i | 0.492227 | − | 0.284188i | −0.233271 | − | 0.972412i | \(-0.574943\pi\) |
0.725498 | + | 0.688224i | \(0.241609\pi\) | |||||||
\(350\) | −3.56916 | + | 4.76238i | −0.190780 | + | 0.254560i | ||||
\(351\) | 1.83714 | + | 0.836589i | 0.0980594 | + | 0.0446538i | ||||
\(352\) | 15.9414 | 0.849679 | ||||||||
\(353\) | −0.838153 | − | 1.45172i | −0.0446104 | − | 0.0772674i | 0.842858 | − | 0.538136i | \(-0.180871\pi\) |
−0.887468 | + | 0.460869i | \(0.847538\pi\) | |||||||
\(354\) | 40.9556 | − | 25.4321i | 2.17677 | − | 1.35170i | ||||
\(355\) | −13.1147 | − | 7.57180i | −0.696058 | − | 0.401869i | ||||
\(356\) | 21.8049 | − | 37.7672i | 1.15566 | − | 2.00166i | ||||
\(357\) | −19.9819 | + | 9.31311i | −1.05755 | + | 0.492902i | ||||
\(358\) | 16.9209 | + | 29.3078i | 0.894295 | + | 1.54896i | ||||
\(359\) | 20.7692i | 1.09616i | 0.836428 | + | 0.548078i | \(0.184640\pi\) | ||||
−0.836428 | + | 0.548078i | \(0.815360\pi\) | |||||||
\(360\) | −5.95196 | + | 3.96613i | −0.313696 | + | 0.209034i | ||||
\(361\) | 17.7510 | 0.934261 | ||||||||
\(362\) | −20.4276 | − | 35.3816i | −1.07365 | − | 1.85962i | ||||
\(363\) | −8.53586 | + | 0.274050i | −0.448017 | + | 0.0143839i | ||||
\(364\) | 1.23648 | + | 2.89184i | 0.0648090 | + | 0.151574i | ||||
\(365\) | 9.15786 | + | 5.28729i | 0.479344 | + | 0.276750i | ||||
\(366\) | −2.84142 | + | 0.0912259i | −0.148523 | + | 0.00476846i | ||||
\(367\) | 25.5963 | − | 14.7780i | 1.33612 | − | 0.771407i | 0.349886 | − | 0.936792i | \(-0.386220\pi\) |
0.986229 | + | 0.165385i | \(0.0528868\pi\) | |||||||
\(368\) | − | 1.61755i | − | 0.0843205i | ||||||
\(369\) | 1.58568 | + | 2.37962i | 0.0825472 | + | 0.123878i | ||||
\(370\) | 9.66221i | 0.502314i | ||||||||
\(371\) | 25.5540 | + | 3.06962i | 1.32670 | + | 0.159367i | ||||
\(372\) | −30.2976 | − | 16.2190i | −1.57086 | − | 0.840915i | ||||
\(373\) | −5.41206 | + | 9.37397i | −0.280226 | + | 0.485366i | −0.971440 | − | 0.237284i | \(-0.923743\pi\) |
0.691214 | + | 0.722650i | \(0.257076\pi\) | |||||||
\(374\) | −13.3297 | + | 23.0878i | −0.689264 | + | 1.19384i | ||||
\(375\) | 0.913713 | + | 1.47144i | 0.0471839 | + | 0.0759847i | ||||
\(376\) | 11.6159 | − | 6.70643i | 0.599043 | − | 0.345858i | ||||
\(377\) | 1.80664 | 0.0930468 | ||||||||
\(378\) | 14.8350 | + | 27.1338i | 0.763029 | + | 1.39561i | ||||
\(379\) | 30.6805 | 1.57595 | 0.787976 | − | 0.615706i | \(-0.211129\pi\) | ||||
0.787976 | + | 0.615706i | \(0.211129\pi\) | |||||||
\(380\) | −2.96158 | + | 1.70987i | −0.151926 | + | 0.0877145i | ||||
\(381\) | −4.69169 | − | 7.55546i | −0.240362 | − | 0.387078i | ||||
\(382\) | −2.23180 | + | 3.86559i | −0.114189 | + | 0.197781i | ||||
\(383\) | −7.24288 | + | 12.5450i | −0.370094 | + | 0.641022i | −0.989580 | − | 0.143986i | \(-0.954008\pi\) |
0.619486 | + | 0.785008i | \(0.287341\pi\) | |||||||
\(384\) | 25.0350 | + | 13.4018i | 1.27756 | + | 0.683908i | ||||
\(385\) | 6.47152 | + | 0.777379i | 0.329819 | + | 0.0396189i | ||||
\(386\) | − | 29.7392i | − | 1.51369i | ||||||
\(387\) | 31.2165 | − | 2.00652i | 1.58682 | − | 0.101997i | ||||
\(388\) | − | 12.2504i | − | 0.621918i | ||||||
\(389\) | −16.0958 | + | 9.29294i | −0.816092 | + | 0.471171i | −0.849067 | − | 0.528285i | \(-0.822835\pi\) |
0.0329752 | + | 0.999456i | \(0.489502\pi\) | |||||||
\(390\) | 1.51282 | − | 0.0485703i | 0.0766047 | − | 0.00245945i | ||||
\(391\) | 8.90365 | + | 5.14052i | 0.450277 | + | 0.259967i | ||||
\(392\) | −3.95239 | + | 16.2140i | −0.199626 | + | 0.818932i | ||||
\(393\) | −21.6555 | + | 0.695267i | −1.09238 | + | 0.0350716i | ||||
\(394\) | −18.1810 | − | 31.4905i | −0.915947 | − | 1.58647i | ||||
\(395\) | −14.7189 | −0.740590 | ||||||||
\(396\) | 20.2700 | + | 10.0279i | 1.01861 | + | 0.503919i | ||||
\(397\) | 10.0525i | 0.504521i | 0.967659 | + | 0.252261i | \(0.0811740\pi\) | ||||
−0.967659 | + | 0.252261i | \(0.918826\pi\) | |||||||
\(398\) | 30.7479 | + | 53.2569i | 1.54125 | + | 2.66953i | ||||
\(399\) | 2.16357 | + | 4.64208i | 0.108314 | + | 0.232395i | ||||
\(400\) | 0.378445 | − | 0.655486i | 0.0189223 | − | 0.0327743i | ||||
\(401\) | −16.3738 | − | 9.45340i | −0.817667 | − | 0.472080i | 0.0319444 | − | 0.999490i | \(-0.489830\pi\) |
−0.849611 | + | 0.527410i | \(0.823163\pi\) | |||||||
\(402\) | 37.9803 | − | 23.5845i | 1.89428 | − | 1.17629i | ||||
\(403\) | 1.25954 | + | 2.18158i | 0.0627420 | + | 0.108672i | ||||
\(404\) | 22.7330 | 1.13101 | ||||||||
\(405\) | 8.92594 | − | 1.15224i | 0.443533 | − | 0.0572552i | ||||
\(406\) | 22.1470 | + | 16.5981i | 1.09914 | + | 0.823749i | ||||
\(407\) | 9.16443 | − | 5.29109i | 0.454264 | − | 0.262269i | ||||
\(408\) | −16.8765 | + | 10.4797i | −0.835511 | + | 0.518824i | ||||
\(409\) | 4.97809 | + | 2.87410i | 0.246151 | + | 0.142115i | 0.618000 | − | 0.786178i | \(-0.287943\pi\) |
−0.371850 | + | 0.928293i | \(0.621276\pi\) | |||||||
\(410\) | 1.85685 | + | 1.07205i | 0.0917032 | + | 0.0529449i | ||||
\(411\) | −10.8031 | − | 5.78312i | −0.532876 | − | 0.285260i | ||||
\(412\) | 23.2255 | − | 13.4092i | 1.14424 | − | 0.660625i | ||||
\(413\) | −26.1972 | − | 19.6335i | −1.28908 | − | 0.966102i | ||||
\(414\) | 6.39484 | − | 12.9264i | 0.314289 | − | 0.635296i | ||||
\(415\) | −11.9467 | −0.586440 | ||||||||
\(416\) | −1.25692 | − | 2.17705i | −0.0616256 | − | 0.106739i | ||||
\(417\) | 0.615196 | + | 19.1616i | 0.0301263 | + | 0.938346i | ||||
\(418\) | 5.36362 | + | 3.09669i | 0.262343 | + | 0.151464i | ||||
\(419\) | −3.76615 | + | 6.52317i | −0.183989 | + | 0.318678i | −0.943235 | − | 0.332125i | \(-0.892234\pi\) |
0.759247 | + | 0.650803i | \(0.225568\pi\) | |||||||
\(420\) | 11.4847 | + | 8.04494i | 0.560398 | + | 0.392553i | ||||
\(421\) | 4.57617 | + | 7.92615i | 0.223029 | + | 0.386297i | 0.955726 | − | 0.294257i | \(-0.0950723\pi\) |
−0.732697 | + | 0.680554i | \(0.761739\pi\) | |||||||
\(422\) | 3.54560i | 0.172597i | ||||||||
\(423\) | −16.8430 | + | 1.08263i | −0.818936 | + | 0.0526394i | ||||
\(424\) | 23.1925 | 1.12633 | ||||||||
\(425\) | 2.40538 | + | 4.16623i | 0.116678 | + | 0.202092i | ||||
\(426\) | −27.8457 | + | 52.0167i | −1.34913 | + | 2.52022i | ||||
\(427\) | 0.758978 | + | 1.77508i | 0.0367295 | + | 0.0859022i | ||||
\(428\) | −10.7716 | − | 6.21897i | −0.520663 | − | 0.300605i | ||||
\(429\) | −0.874498 | − | 1.40829i | −0.0422212 | − | 0.0679927i | ||||
\(430\) | 20.3123 | − | 11.7273i | 0.979545 | − | 0.565541i | ||||
\(431\) | − | 5.09485i | − | 0.245410i | −0.992443 | − | 0.122705i | \(-0.960843\pi\) | ||
0.992443 | − | 0.122705i | \(-0.0391570\pi\) | |||||||
\(432\) | −2.28479 | − | 3.20118i | −0.109927 | − | 0.154017i | ||||
\(433\) | 35.8805i | 1.72430i | 0.506649 | + | 0.862152i | \(0.330884\pi\) | ||||
−0.506649 | + | 0.862152i | \(0.669116\pi\) | |||||||
\(434\) | −4.60251 | + | 38.3150i | −0.220927 | + | 1.83918i | ||||
\(435\) | 6.84279 | − | 4.24914i | 0.328087 | − | 0.203731i | ||||
\(436\) | 17.4121 | − | 30.1586i | 0.833888 | − | 1.44434i | ||||
\(437\) | 1.19422 | − | 2.06844i | 0.0571271 | − | 0.0989471i | ||||
\(438\) | 19.4443 | − | 36.3227i | 0.929085 | − | 1.73556i | ||||
\(439\) | 0.641214 | − | 0.370205i | 0.0306035 | − | 0.0176689i | −0.484620 | − | 0.874725i | \(-0.661042\pi\) |
0.515224 | + | 0.857056i | \(0.327709\pi\) | |||||||
\(440\) | 5.87348 | 0.280007 | ||||||||
\(441\) | 13.5046 | − | 16.0818i | 0.643077 | − | 0.765801i | ||||
\(442\) | 4.20401 | 0.199964 | ||||||||
\(443\) | −14.9440 | + | 8.62790i | −0.710009 | + | 0.409924i | −0.811064 | − | 0.584957i | \(-0.801111\pi\) |
0.101056 | + | 0.994881i | \(0.467778\pi\) | |||||||
\(444\) | 22.7535 | − | 0.730517i | 1.07983 | − | 0.0346688i | ||||
\(445\) | −7.12607 | + | 12.3427i | −0.337808 | + | 0.585101i | ||||
\(446\) | −16.4269 | + | 28.4522i | −0.777835 | + | 1.34725i | ||||
\(447\) | −0.475002 | − | 14.7949i | −0.0224668 | − | 0.699776i | ||||
\(448\) | 4.11528 | − | 34.2589i | 0.194429 | − | 1.61858i | ||||
\(449\) | − | 20.5062i | − | 0.967747i | −0.875138 | − | 0.483874i | \(-0.839229\pi\) | ||
0.875138 | − | 0.483874i | \(-0.160771\pi\) | |||||||
\(450\) | 5.61569 | − | 3.74205i | 0.264726 | − | 0.176402i | ||||
\(451\) | − | 2.34825i | − | 0.110575i | ||||||
\(452\) | −23.2401 | + | 13.4177i | −1.09312 | + | 0.631115i | ||||
\(453\) | 12.8613 | − | 24.0254i | 0.604277 | − | 1.12881i | ||||
\(454\) | −5.67200 | − | 3.27473i | −0.266200 | − | 0.153691i | ||||
\(455\) | −0.404093 | − | 0.945084i | −0.0189442 | − | 0.0443062i | ||||
\(456\) | 2.43459 | + | 3.92065i | 0.114010 | + | 0.183601i | ||||
\(457\) | 4.57715 | + | 7.92786i | 0.214110 | + | 0.370849i | 0.952997 | − | 0.302980i | \(-0.0979816\pi\) |
−0.738887 | + | 0.673829i | \(0.764648\pi\) | |||||||
\(458\) | 42.1785 | 1.97087 | ||||||||
\(459\) | 24.8816 | − | 2.40314i | 1.16137 | − | 0.112169i | ||||
\(460\) | − | 6.53927i | − | 0.304895i | ||||||
\(461\) | −5.07463 | − | 8.78951i | −0.236349 | − | 0.409368i | 0.723315 | − | 0.690518i | \(-0.242618\pi\) |
−0.959664 | + | 0.281150i | \(0.909284\pi\) | |||||||
\(462\) | 2.21810 | − | 25.2979i | 0.103195 | − | 1.17697i | ||||
\(463\) | −0.613755 | + | 1.06305i | −0.0285236 | + | 0.0494043i | −0.879935 | − | 0.475094i | \(-0.842414\pi\) |
0.851411 | + | 0.524499i | \(0.175747\pi\) | |||||||
\(464\) | −3.04828 | − | 1.75993i | −0.141513 | − | 0.0817025i | ||||
\(465\) | 9.90157 | + | 5.30053i | 0.459174 | + | 0.245806i | ||||
\(466\) | 5.78315 | + | 10.0167i | 0.267899 | + | 0.464015i | ||||
\(467\) | 23.2327 | 1.07508 | 0.537540 | − | 0.843238i | \(-0.319354\pi\) | ||||
0.537540 | + | 0.843238i | \(0.319354\pi\) | |||||||
\(468\) | −0.228756 | − | 3.55886i | −0.0105742 | − | 0.164508i | ||||
\(469\) | −24.2941 | − | 18.2072i | −1.12180 | − | 0.840729i | ||||
\(470\) | −10.9596 | + | 6.32753i | −0.505529 | + | 0.291867i | ||||
\(471\) | −1.10586 | − | 34.4444i | −0.0509555 | − | 1.58711i | ||||
\(472\) | −25.5482 | − | 14.7502i | −1.17595 | − | 0.678935i | ||||
\(473\) | −22.2463 | − | 12.8439i | −1.02288 | − | 0.590562i | ||||
\(474\) | 1.84021 | + | 57.3170i | 0.0845234 | + | 2.63266i | ||||
\(475\) | 0.967875 | − | 0.558803i | 0.0444092 | − | 0.0256396i | ||||
\(476\) | 31.1653 | + | 23.3568i | 1.42846 | + | 1.07056i | ||||
\(477\) | −26.1578 | − | 12.9406i | −1.19769 | − | 0.592511i | ||||
\(478\) | 38.4179 | 1.75720 | ||||||||
\(479\) | −15.6175 | − | 27.0504i | −0.713583 | − | 1.23596i | −0.963503 | − | 0.267696i | \(-0.913738\pi\) |
0.249920 | − | 0.968266i | \(-0.419596\pi\) | |||||||
\(480\) | −9.88101 | − | 5.28952i | −0.451005 | − | 0.241433i | ||||
\(481\) | −1.44517 | − | 0.834367i | −0.0658939 | − | 0.0380438i | ||||
\(482\) | −23.5363 | + | 40.7661i | −1.07205 | + | 1.85684i | ||||
\(483\) | −9.75598 | − | 0.855396i | −0.443913 | − | 0.0389219i | ||||
\(484\) | 7.54371 | + | 13.0661i | 0.342896 | + | 0.593913i | ||||
\(485\) | 4.00354i | 0.181791i | ||||||||
\(486\) | −5.60288 | − | 34.6144i | −0.254152 | − | 1.57014i | ||||
\(487\) | −10.7164 | −0.485605 | −0.242802 | − | 0.970076i | \(-0.578067\pi\) | ||||
−0.242802 | + | 0.970076i | \(0.578067\pi\) | |||||||
\(488\) | 0.869813 | + | 1.50656i | 0.0393746 | + | 0.0681988i | ||||
\(489\) | 0.201691 | + | 0.324802i | 0.00912080 | + | 0.0146881i | ||||
\(490\) | 3.72909 | − | 15.2980i | 0.168463 | − | 0.691092i | ||||
\(491\) | −0.912341 | − | 0.526740i | −0.0411734 | − | 0.0237715i | 0.479272 | − | 0.877666i | \(-0.340901\pi\) |
−0.520445 | + | 0.853895i | \(0.674234\pi\) | |||||||
\(492\) | 2.38418 | − | 4.45373i | 0.107487 | − | 0.200790i | ||||
\(493\) | 19.3747 | − | 11.1860i | 0.872593 | − | 0.503792i | ||||
\(494\) | − | 0.976651i | − | 0.0439416i | ||||||
\(495\) | −6.62446 | − | 3.27721i | −0.297747 | − | 0.147299i | ||||
\(496\) | − | 4.90787i | − | 0.220370i | ||||||
\(497\) | 39.7802 | + | 4.77852i | 1.78439 | + | 0.214346i | ||||
\(498\) | 1.49361 | + | 46.5216i | 0.0669304 | + | 2.08468i | ||||
\(499\) | −2.52065 | + | 4.36589i | −0.112840 | + | 0.195444i | −0.916914 | − | 0.399085i | \(-0.869328\pi\) |
0.804074 | + | 0.594529i | \(0.202661\pi\) | |||||||
\(500\) | 1.52994 | − | 2.64993i | 0.0684210 | − | 0.118509i | ||||
\(501\) | 43.9536 | − | 1.41116i | 1.96370 | − | 0.0630461i | ||||
\(502\) | −6.86396 | + | 3.96291i | −0.306354 | + | 0.176873i | ||||
\(503\) | 34.8769 | 1.55508 | 0.777542 | − | 0.628831i | \(-0.216466\pi\) | ||||
0.777542 | + | 0.628831i | \(0.216466\pi\) | |||||||
\(504\) | 10.3540 | − | 15.8394i | 0.461202 | − | 0.705545i | ||||
\(505\) | −7.42938 | −0.330603 | ||||||||
\(506\) | −10.2564 | + | 5.92152i | −0.455951 | + | 0.263244i | ||||
\(507\) | 10.5034 | − | 19.6208i | 0.466473 | − | 0.871389i | ||||
\(508\) | −7.85586 | + | 13.6067i | −0.348547 | + | 0.603702i | ||||
\(509\) | 3.07394 | − | 5.32422i | 0.136250 | − | 0.235992i | −0.789824 | − | 0.613333i | \(-0.789828\pi\) |
0.926074 | + | 0.377341i | \(0.123162\pi\) | |||||||
\(510\) | 15.9230 | − | 9.88765i | 0.705082 | − | 0.437832i | ||||
\(511\) | −27.7780 | − | 3.33678i | −1.22883 | − | 0.147610i | ||||
\(512\) | 8.50671i | 0.375947i | ||||||||
\(513\) | −0.558283 | − | 5.78035i | −0.0246488 | − | 0.255209i | ||||
\(514\) | − | 1.59280i | − | 0.0702556i | ||||||
\(515\) | −7.59032 | + | 4.38227i | −0.334469 | + | 0.193106i | ||||
\(516\) | −29.1523 | − | 46.9466i | −1.28336 | − | 2.06671i | ||||
\(517\) | 12.0031 | + | 6.92999i | 0.527896 | + | 0.304781i | ||||
\(518\) | −10.0503 | − | 23.5053i | −0.441583 | − | 1.03276i | ||||
\(519\) | 11.8700 | − | 22.1736i | 0.521034 | − | 0.973311i | ||||
\(520\) | −0.463103 | − | 0.802118i | −0.0203084 | − | 0.0351752i | ||||
\(521\) | 20.2902 | 0.888932 | 0.444466 | − | 0.895796i | \(-0.353394\pi\) | ||||
0.444466 | + | 0.895796i | \(0.353394\pi\) | |||||||
\(522\) | −17.4021 | − | 26.1153i | −0.761669 | − | 1.14303i | ||||
\(523\) | 15.6812i | 0.685690i | 0.939392 | + | 0.342845i | \(0.111391\pi\) | ||||
−0.939392 | + | 0.342845i | \(0.888609\pi\) | |||||||
\(524\) | 19.1385 | + | 33.1488i | 0.836067 | + | 1.44811i | ||||
\(525\) | −3.75333 | − | 2.62917i | −0.163809 | − | 0.114746i | ||||
\(526\) | 11.4731 | − | 19.8720i | 0.500250 | − | 0.866459i | ||||
\(527\) | 27.0149 | + | 15.5971i | 1.17679 | + | 0.679419i | ||||
\(528\) | 0.103638 | + | 3.22803i | 0.00451029 | + | 0.140482i | ||||
\(529\) | −9.21641 | − | 15.9633i | −0.400713 | − | 0.694056i | ||||
\(530\) | −21.8822 | −0.950501 | ||||||||
\(531\) | 20.5846 | + | 30.8912i | 0.893294 | + | 1.34056i | ||||
\(532\) | 5.42612 | − | 7.24014i | 0.235252 | − | 0.313900i | ||||
\(533\) | −0.320691 | + | 0.185151i | −0.0138907 | + | 0.00801978i | ||||
\(534\) | 48.9547 | + | 26.2065i | 2.11848 | + | 1.13407i | ||||
\(535\) | 3.52026 | + | 2.03242i | 0.152194 | + | 0.0878692i | ||||
\(536\) | −23.6921 | − | 13.6787i | −1.02334 | − | 0.590828i | ||||
\(537\) | −22.1373 | + | 13.7465i | −0.955294 | + | 0.593205i | ||||
\(538\) | −58.6245 | + | 33.8469i | −2.52748 | + | 1.45924i | ||||
\(539\) | −16.5519 | + | 4.84030i | −0.712942 | + | 0.208486i | ||||
\(540\) | −9.23672 | − | 12.9414i | −0.397485 | − | 0.556910i | ||||
\(541\) | 19.2258 | 0.826583 | 0.413291 | − | 0.910599i | \(-0.364379\pi\) | ||||
0.413291 | + | 0.910599i | \(0.364379\pi\) | |||||||
\(542\) | 7.00711 | + | 12.1367i | 0.300981 | + | 0.521314i | ||||
\(543\) | 26.7250 | − | 16.5954i | 1.14688 | − | 0.712175i | ||||
\(544\) | −26.9588 | − | 15.5647i | −1.15585 | − | 0.667331i | ||||
\(545\) | −5.69045 | + | 9.85615i | −0.243752 | + | 0.422191i | ||||
\(546\) | −3.62973 | + | 1.69174i | −0.155338 | + | 0.0723996i | ||||
\(547\) | −12.9816 | − | 22.4848i | −0.555053 | − | 0.961379i | −0.997899 | − | 0.0647821i | \(-0.979365\pi\) |
0.442847 | − | 0.896597i | \(-0.353969\pi\) | |||||||
\(548\) | 21.6475i | 0.924735i | ||||||||
\(549\) | −0.140416 | − | 2.18451i | −0.00599279 | − | 0.0932327i | ||||
\(550\) | −5.54164 | −0.236296 | ||||||||
\(551\) | −2.59866 | − | 4.50102i | −0.110707 | − | 0.191750i | ||||
\(552\) | −8.82041 | + | 0.283186i | −0.375421 | + | 0.0120532i | ||||
\(553\) | 35.8069 | − | 15.3101i | 1.52266 | − | 0.651051i | ||||
\(554\) | −0.517591 | − | 0.298831i | −0.0219903 | − | 0.0126961i | ||||
\(555\) | −7.43607 | + | 0.238740i | −0.315643 | + | 0.0101340i | ||||
\(556\) | 29.3312 | − | 16.9344i | 1.24392 | − | 0.718177i | ||||
\(557\) | − | 5.78189i | − | 0.244987i | −0.992469 | − | 0.122493i | \(-0.960911\pi\) | ||
0.992469 | − | 0.122493i | \(-0.0390890\pi\) | |||||||
\(558\) | 19.4029 | − | 39.2204i | 0.821388 | − | 1.66033i | ||||
\(559\) | 4.05078i | 0.171330i | ||||||||
\(560\) | −0.238834 | + | 1.98825i | −0.0100926 | + | 0.0840189i | ||||
\(561\) | −18.0978 | − | 9.68814i | −0.764089 | − | 0.409033i | ||||
\(562\) | 15.6638 | − | 27.1305i | 0.660737 | − | 1.14443i | ||||
\(563\) | 18.8450 | − | 32.6404i | 0.794220 | − | 1.37563i | −0.129113 | − | 0.991630i | \(-0.541213\pi\) |
0.923333 | − | 0.384000i | \(-0.125454\pi\) | |||||||
\(564\) | 15.7293 | + | 25.3303i | 0.662322 | + | 1.06660i | ||||
\(565\) | 7.59510 | − | 4.38503i | 0.319528 | − | 0.184480i | ||||
\(566\) | −35.6489 | −1.49844 | ||||||||
\(567\) | −20.5157 | + | 12.0875i | −0.861577 | + | 0.507626i | ||||
\(568\) | 36.1041 | 1.51489 | ||||||||
\(569\) | 11.9150 | − | 6.87915i | 0.499504 | − | 0.288389i | −0.229005 | − | 0.973425i | \(-0.573547\pi\) |
0.728509 | + | 0.685037i | \(0.240214\pi\) | |||||||
\(570\) | −2.29704 | − | 3.69914i | −0.0962125 | − | 0.154940i | ||||
\(571\) | −10.5199 | + | 18.2211i | −0.440246 | + | 0.762528i | −0.997707 | − | 0.0676747i | \(-0.978442\pi\) |
0.557462 | + | 0.830203i | \(0.311775\pi\) | |||||||
\(572\) | −1.46428 | + | 2.53620i | −0.0612245 | + | 0.106044i | ||||
\(573\) | −3.03012 | − | 1.62209i | −0.126585 | − | 0.0677636i | ||||
\(574\) | −5.63228 | − | 0.676566i | −0.235087 | − | 0.0282393i | ||||
\(575\) | 2.13710i | 0.0891231i | ||||||||
\(576\) | −17.3489 | + | 35.0685i | −0.722869 | + | 1.46119i | ||||
\(577\) | − | 12.0259i | − | 0.500643i | −0.968163 | − | 0.250321i | \(-0.919464\pi\) | ||
0.968163 | − | 0.250321i | \(-0.0805363\pi\) | |||||||
\(578\) | 11.9675 | − | 6.90946i | 0.497784 | − | 0.287396i | ||||
\(579\) | 22.8874 | − | 0.734816i | 0.951167 | − | 0.0305379i | ||||
\(580\) | −12.3233 | − | 7.11485i | −0.511697 | − | 0.295428i | ||||
\(581\) | 29.0628 | − | 12.4265i | 1.20573 | − | 0.515538i | ||||
\(582\) | 15.5902 | − | 0.500535i | 0.646234 | − | 0.0207478i | ||||
\(583\) | 11.9828 | + | 20.7548i | 0.496277 | + | 0.859577i | ||||
\(584\) | −25.2110 | −1.04324 | ||||||||
\(585\) | 0.0747596 | + | 1.16307i | 0.00309093 | + | 0.0480871i | ||||
\(586\) | 15.1643i | 0.626429i | ||||||||
\(587\) | −0.136440 | − | 0.236321i | −0.00563148 | − | 0.00975402i | 0.863196 | − | 0.504869i | \(-0.168459\pi\) |
−0.868827 | + | 0.495115i | \(0.835126\pi\) | |||||||
\(588\) | −36.3070 | − | 7.62499i | −1.49728 | − | 0.314449i | ||||
\(589\) | 3.62342 | − | 6.27595i | 0.149300 | − | 0.258596i | ||||
\(590\) | 24.1047 | + | 13.9169i | 0.992377 | + | 0.572949i | ||||
\(591\) | 23.7859 | − | 14.7703i | 0.978423 | − | 0.607568i | ||||
\(592\) | 1.62558 | + | 2.81559i | 0.0668111 | + | 0.115720i | ||||
\(593\) | −3.61889 | −0.148610 | −0.0743050 | − | 0.997236i | \(-0.523674\pi\) | ||||
−0.0743050 | + | 0.997236i | \(0.523674\pi\) | |||||||
\(594\) | −11.9336 | + | 26.2060i | −0.489640 | + | 1.07525i | ||||
\(595\) | −10.1851 | − | 7.63324i | −0.417550 | − | 0.312933i | ||||
\(596\) | −22.6470 | + | 13.0753i | −0.927658 | + | 0.535584i | ||||
\(597\) | −40.2269 | + | 24.9796i | −1.64638 | + | 1.02235i | ||||
\(598\) | 1.61736 | + | 0.933781i | 0.0661386 | + | 0.0381852i | ||||
\(599\) | −21.6954 | − | 12.5258i | −0.886448 | − | 0.511791i | −0.0136692 | − | 0.999907i | \(-0.504351\pi\) |
−0.872779 | + | 0.488115i | \(0.837685\pi\) | |||||||
\(600\) | −3.64059 | − | 1.94888i | −0.148626 | − | 0.0795629i | ||||
\(601\) | 17.6859 | − | 10.2110i | 0.721424 | − | 0.416515i | −0.0938524 | − | 0.995586i | \(-0.529918\pi\) |
0.815277 | + | 0.579072i | \(0.196585\pi\) | |||||||
\(602\) | −37.2155 | + | 49.6571i | −1.51679 | + | 2.02387i | ||||
\(603\) | 19.0891 | + | 28.6470i | 0.777370 | + | 1.16660i | ||||
\(604\) | −48.1427 | −1.95890 | ||||||||
\(605\) | −2.46536 | − | 4.27013i | −0.100231 | − | 0.173606i | ||||
\(606\) | 0.928843 | + | 28.9307i | 0.0377317 | + | 1.17523i | ||||
\(607\) | 20.8266 | + | 12.0243i | 0.845327 | + | 0.488050i | 0.859071 | − | 0.511856i | \(-0.171042\pi\) |
−0.0137445 | + | 0.999906i | \(0.504375\pi\) | |||||||
\(608\) | −3.61590 | + | 6.26292i | −0.146644 | + | 0.253995i | ||||
\(609\) | −12.2267 | + | 17.4545i | −0.495451 | + | 0.707293i | ||||
\(610\) | −0.820670 | − | 1.42144i | −0.0332280 | − | 0.0575525i | ||||
\(611\) | − | 2.18562i | − | 0.0884207i | ||||||
\(612\) | −24.4882 | − | 36.7494i | −0.989878 | − | 1.48551i | ||||
\(613\) | 19.0207 | 0.768239 | 0.384120 | − | 0.923283i | \(-0.374505\pi\) | ||||
0.384120 | + | 0.923283i | \(0.374505\pi\) | |||||||
\(614\) | −1.81563 | − | 3.14476i | −0.0732728 | − | 0.126912i | ||||
\(615\) | −0.779174 | + | 1.45552i | −0.0314193 | + | 0.0586924i | ||||
\(616\) | −14.2885 | + | 6.10937i | −0.575699 | + | 0.246154i | ||||
\(617\) | −28.5311 | − | 16.4725i | −1.14862 | − | 0.663157i | −0.200070 | − | 0.979782i | \(-0.564117\pi\) |
−0.948551 | + | 0.316625i | \(0.897450\pi\) | |||||||
\(618\) | 18.0140 | + | 29.0096i | 0.724628 | + | 1.16694i | ||||
\(619\) | −17.7455 | + | 10.2454i | −0.713253 | + | 0.411797i | −0.812264 | − | 0.583290i | \(-0.801765\pi\) |
0.0990114 | + | 0.995086i | \(0.468432\pi\) | |||||||
\(620\) | − | 19.8411i | − | 0.796836i | ||||||
\(621\) | 10.1062 | + | 4.60210i | 0.405547 | + | 0.184676i | ||||
\(622\) | 35.4116i | 1.41988i | ||||||||
\(623\) | 4.49722 | − | 37.4385i | 0.180177 | − | 1.49994i | ||||
\(624\) | 0.432668 | − | 0.268673i | 0.0173206 | − | 0.0107555i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 4.39611 | − | 7.61429i | 0.175704 | − | 0.304328i | ||||
\(627\) | −2.25069 | + | 4.20437i | −0.0898840 | + | 0.167907i | ||||
\(628\) | −52.7250 | + | 30.4408i | −2.10396 | + | 1.21472i | ||||
\(629\) | −20.6642 | −0.823937 | ||||||||
\(630\) | −9.76898 | + | 14.9445i | −0.389206 | + | 0.595405i | ||||
\(631\) | −47.0272 | −1.87212 | −0.936061 | − | 0.351838i | \(-0.885557\pi\) | ||||
−0.936061 | + | 0.351838i | \(0.885557\pi\) | |||||||
\(632\) | 30.3903 | − | 17.5458i | 1.20886 | − | 0.697935i | ||||
\(633\) | −2.72871 | + | 0.0876072i | −0.108456 | + | 0.00348207i | ||||
\(634\) | −27.7100 | + | 47.9951i | −1.10050 | + | 1.90613i | ||||
\(635\) | 2.56737 | − | 4.44682i | 0.101883 | − | 0.176467i | ||||
\(636\) | 1.65441 | + | 51.5302i | 0.0656018 | + | 2.04330i | ||||
\(637\) | 1.96608 | + | 1.87879i | 0.0778989 | + | 0.0744404i | ||||
\(638\) | 25.7709i | 1.02028i | ||||||||
\(639\) | −40.7203 | − | 20.1449i | −1.61087 | − | 0.796918i | ||||
\(640\) | 16.3947i | 0.648059i | ||||||||
\(641\) | −1.78047 | + | 1.02796i | −0.0703244 | + | 0.0406018i | −0.534750 | − | 0.845010i | \(-0.679594\pi\) |
0.464426 | + | 0.885612i | \(0.346261\pi\) | |||||||
\(642\) | 7.47434 | − | 13.9623i | 0.294989 | − | 0.551049i | ||||
\(643\) | −38.6058 | − | 22.2891i | −1.52246 | − | 0.878995i | −0.999647 | − | 0.0265505i | \(-0.991548\pi\) |
−0.522817 | − | 0.852445i | \(-0.675119\pi\) | |||||||
\(644\) | 6.80189 | + | 15.9081i | 0.268032 | + | 0.626868i | ||||
\(645\) | 9.52726 | + | 15.3426i | 0.375135 | + | 0.604115i | ||||
\(646\) | −6.04703 | − | 10.4738i | −0.237917 | − | 0.412084i | ||||
\(647\) | 8.06386 | 0.317023 | 0.158512 | − | 0.987357i | \(-0.449330\pi\) | ||||
0.158512 | + | 0.987357i | \(0.449330\pi\) | |||||||
\(648\) | −17.0559 | + | 13.0193i | −0.670019 | + | 0.511445i | ||||
\(649\) | − | 30.4839i | − | 1.19660i | ||||||
\(650\) | 0.436939 | + | 0.756800i | 0.0171382 | + | 0.0296842i | ||||
\(651\) | −29.6010 | − | 2.59539i | −1.16016 | − | 0.101721i | ||||
\(652\) | 0.337716 | − | 0.584942i | 0.0132260 | − | 0.0229081i | ||||
\(653\) | −10.8478 | − | 6.26301i | −0.424509 | − | 0.245090i | 0.272496 | − | 0.962157i | \(-0.412151\pi\) |
−0.697005 | + | 0.717067i | \(0.745484\pi\) | |||||||
\(654\) | 39.0923 | + | 20.9269i | 1.52863 | + | 0.818308i | ||||
\(655\) | −6.25464 | − | 10.8334i | −0.244389 | − | 0.423294i | ||||
\(656\) | 0.721454 | 0.0281680 | ||||||||
\(657\) | 28.4345 | + | 14.0669i | 1.10933 | + | 0.548803i | ||||
\(658\) | 20.0799 | − | 26.7928i | 0.782794 | − | 1.04449i | ||||
\(659\) | 5.31567 | − | 3.06900i | 0.207069 | − | 0.119551i | −0.392880 | − | 0.919590i | \(-0.628521\pi\) |
0.599949 | + | 0.800039i | \(0.295188\pi\) | |||||||
\(660\) | 0.418979 | + | 13.0500i | 0.0163088 | + | 0.507970i | ||||
\(661\) | −5.75735 | − | 3.32400i | −0.223935 | − | 0.129289i | 0.383836 | − | 0.923401i | \(-0.374603\pi\) |
−0.607771 | + | 0.794112i | \(0.707936\pi\) | |||||||
\(662\) | −17.9930 | − | 10.3883i | −0.699319 | − | 0.403752i | ||||
\(663\) | 0.103876 | + | 3.23542i | 0.00403419 | + | 0.125653i | ||||
\(664\) | 24.6664 | − | 14.2412i | 0.957242 | − | 0.552664i | ||||
\(665\) | −1.77331 | + | 2.36615i | −0.0687661 | + | 0.0917554i | ||||
\(666\) | 1.85936 | + | 28.9269i | 0.0720487 | + | 1.12090i | ||||
\(667\) | 9.93839 | 0.384816 | ||||||||
\(668\) | −38.8447 | − | 67.2810i | −1.50295 | − | 2.60318i | ||||
\(669\) | −22.3028 | − | 11.9392i | −0.862275 | − | 0.461594i | ||||
\(670\) | 22.3536 | + | 12.9058i | 0.863594 | + | 0.498596i | ||||
\(671\) | −0.898808 | + | 1.55678i | −0.0346981 | + | 0.0600989i | ||||
\(672\) | 29.5396 | + | 2.59000i | 1.13951 | + | 0.0999115i | ||||
\(673\) | 0.875991 | + | 1.51726i | 0.0337670 | + | 0.0584861i | 0.882415 | − | 0.470472i | \(-0.155916\pi\) |
−0.848648 | + | 0.528958i | \(0.822583\pi\) | |||||||
\(674\) | − | 5.78781i | − | 0.222938i | ||||||
\(675\) | 3.01865 | + | 4.22939i | 0.116188 | + | 0.162789i | ||||
\(676\) | −39.3166 | −1.51218 | ||||||||
\(677\) | −7.49127 | − | 12.9753i | −0.287913 | − | 0.498680i | 0.685398 | − | 0.728168i | \(-0.259628\pi\) |
−0.973311 | + | 0.229488i | \(0.926295\pi\) | |||||||
\(678\) | −18.0253 | − | 29.0278i | −0.692258 | − | 1.11481i | ||||
\(679\) | −4.16433 | − | 9.73944i | −0.159812 | − | 0.373765i | ||||
\(680\) | −9.93278 | − | 5.73469i | −0.380905 | − | 0.219915i | ||||
\(681\) | 2.38010 | − | 4.44611i | 0.0912055 | − | 0.170375i | ||||
\(682\) | −31.1193 | + | 17.9667i | −1.19162 | + | 0.687981i | ||||
\(683\) | − | 11.6024i | − | 0.443954i | −0.975052 | − | 0.221977i | \(-0.928749\pi\) | ||
0.975052 | − | 0.221977i | \(-0.0712509\pi\) | |||||||
\(684\) | −8.53741 | + | 5.68896i | −0.326436 | + | 0.217523i | ||||
\(685\) | − | 7.07462i | − | 0.270307i | ||||||
\(686\) | 6.84060 | + | 41.0943i | 0.261175 | + | 1.56899i | ||||
\(687\) | 1.04217 | + | 32.4607i | 0.0397614 | + | 1.23845i | ||||
\(688\) | 3.94603 | − | 6.83473i | 0.150441 | − | 0.260572i | ||||
\(689\) | 1.88960 | − | 3.27289i | 0.0719882 | − | 0.124687i | ||||
\(690\) | 8.32207 | − | 0.267186i | 0.316816 | − | 0.0101716i | ||||
\(691\) | 7.00564 | − | 4.04471i | 0.266507 | − | 0.153868i | −0.360792 | − | 0.932646i | \(-0.617494\pi\) |
0.627299 | + | 0.778778i | \(0.284160\pi\) | |||||||
\(692\) | −44.4320 | −1.68905 | ||||||||
\(693\) | 19.5242 | + | 1.08198i | 0.741662 | + | 0.0411010i | ||||
\(694\) | −42.7380 | −1.62231 | ||||||||
\(695\) | −9.58572 | + | 5.53432i | −0.363607 | + | 0.209929i | ||||
\(696\) | −9.06312 | + | 16.9302i | −0.343537 | + | 0.641739i | ||||
\(697\) | −2.29276 | + | 3.97118i | −0.0868445 | + | 0.150419i | ||||
\(698\) | 11.9423 | − | 20.6847i | 0.452023 | − | 0.782926i | ||||
\(699\) | −7.56600 | + | 4.69823i | −0.286172 | + | 0.177703i | ||||
\(700\) | −0.965536 | + | 8.03790i | −0.0364938 | + | 0.303804i | ||||
\(701\) | − | 39.1808i | − | 1.47984i | −0.672696 | − | 0.739919i | \(-0.734864\pi\) | ||
0.672696 | − | 0.739919i | \(-0.265136\pi\) | |||||||
\(702\) | 4.51977 | − | 0.436532i | 0.170588 | − | 0.0164758i | ||||
\(703\) | 4.80060i | 0.181058i | ||||||||
\(704\) | 27.8250 | − | 16.0647i | 1.04869 | − | 0.605463i | ||||
\(705\) | −5.14048 | − | 8.27820i | −0.193602 | − | 0.311775i | ||||
\(706\) | −3.26553 | − | 1.88536i | −0.122900 | − | 0.0709563i | ||||
\(707\) | 18.0735 | − | 7.72775i | 0.679724 | − | 0.290632i | ||||
\(708\) | 30.9503 | − | 57.8163i | 1.16318 | − | 2.17287i | ||||
\(709\) | 7.25588 | + | 12.5676i | 0.272500 | + | 0.471984i | 0.969501 | − | 0.245086i | \(-0.0788161\pi\) |
−0.697001 | + | 0.717070i | \(0.745483\pi\) | |||||||
\(710\) | −34.0643 | −1.27841 | ||||||||
\(711\) | −44.0659 | + | 2.83246i | −1.65260 | + | 0.106225i | ||||
\(712\) | − | 33.9787i | − | 1.27341i | ||||||
\(713\) | 6.92874 | + | 12.0009i | 0.259484 | + | 0.449439i | ||||
\(714\) | −28.4512 | + | 40.6162i | −1.06476 | + | 1.52002i | ||||
\(715\) | 0.478541 | − | 0.828857i | 0.0178964 | − | 0.0309975i | ||||
\(716\) | 39.8674 | + | 23.0174i | 1.48991 | + | 0.860202i | ||||
\(717\) | 0.949256 | + | 29.5666i | 0.0354506 | + | 1.10418i | ||||
\(718\) | 23.3593 | + | 40.4595i | 0.871760 | + | 1.50993i | ||||
\(719\) | −19.8590 | −0.740618 | −0.370309 | − | 0.928909i | \(-0.620748\pi\) | ||||
−0.370309 | + | 0.928909i | \(0.620748\pi\) | |||||||
\(720\) | 1.00686 | − | 2.03523i | 0.0375234 | − | 0.0758487i | ||||
\(721\) | 13.9067 | − | 18.5559i | 0.517914 | − | 0.691059i | ||||
\(722\) | 34.5798 | − | 19.9647i | 1.28693 | − | 0.743008i | ||||
\(723\) | −31.9553 | − | 17.1063i | −1.18843 | − | 0.636192i | ||||
\(724\) | −48.1295 | − | 27.7876i | −1.78872 | − | 1.03272i | ||||
\(725\) | 4.02738 | + | 2.32521i | 0.149573 | + | 0.0863560i | ||||
\(726\) | −16.3201 | + | 10.1342i | −0.605695 | + | 0.376116i | ||||
\(727\) | 35.4470 | − | 20.4653i | 1.31466 | − | 0.759017i | 0.331793 | − | 0.943352i | \(-0.392346\pi\) |
0.982864 | + | 0.184335i | \(0.0590131\pi\) | |||||||
\(728\) | 1.96093 | + | 1.46962i | 0.0726768 | + | 0.0544676i | ||||
\(729\) | 26.5009 | − | 5.16727i | 0.981516 | − | 0.191380i | ||||
\(730\) | 23.7867 | 0.880384 | ||||||||
\(731\) | 25.0808 | + | 43.4412i | 0.927646 | + | 1.60673i | ||||
\(732\) | −3.28530 | + | 2.04006i | −0.121428 | + | 0.0754028i | ||||
\(733\) | −22.0712 | − | 12.7428i | −0.815217 | − | 0.470666i | 0.0335476 | − | 0.999437i | \(-0.489319\pi\) |
−0.848764 | + | 0.528772i | \(0.822653\pi\) | |||||||
\(734\) | 33.2420 | − | 57.5768i | 1.22698 | − | 2.12520i | ||||
\(735\) | 11.8655 | + | 2.49192i | 0.437666 | + | 0.0919160i | ||||
\(736\) | −6.91436 | − | 11.9760i | −0.254867 | − | 0.441442i | ||||
\(737\) | − | 28.2693i | − | 1.04131i | ||||||
\(738\) | 5.76537 | + | 2.85221i | 0.212226 | + | 0.104991i | ||||
\(739\) | 22.6712 | 0.833973 | 0.416986 | − | 0.908913i | \(-0.363086\pi\) | ||||
0.416986 | + | 0.908913i | \(0.363086\pi\) | |||||||
\(740\) | 6.57175 | + | 11.3826i | 0.241582 | + | 0.418433i | ||||
\(741\) | 0.751634 | − | 0.0241318i | 0.0276120 | − | 0.000886502i | ||||
\(742\) | 53.2329 | − | 22.7610i | 1.95424 | − | 0.835582i | ||||
\(743\) | 1.37485 | + | 0.793772i | 0.0504385 | + | 0.0291207i | 0.525007 | − | 0.851098i | \(-0.324063\pi\) |
−0.474569 | + | 0.880218i | \(0.657396\pi\) | |||||||
\(744\) | −26.7624 | + | 0.859225i | −0.981156 | + | 0.0315007i | ||||
\(745\) | 7.40128 | − | 4.27313i | 0.271162 | − | 0.156555i | ||||
\(746\) | 24.3480i | 0.891443i | ||||||||
\(747\) | −35.7663 | + | 2.29898i | −1.30862 | + | 0.0841152i | ||||
\(748\) | 36.2649i | 1.32597i | ||||||||
\(749\) | −10.6778 | − | 1.28265i | −0.390158 | − | 0.0468670i | ||||
\(750\) | 3.43490 | + | 1.83878i | 0.125425 | + | 0.0671426i | ||||
\(751\) | −18.8024 | + | 32.5667i | −0.686109 | + | 1.18838i | 0.286978 | + | 0.957937i | \(0.407349\pi\) |
−0.973087 | + | 0.230439i | \(0.925984\pi\) | |||||||
\(752\) | −2.12910 | + | 3.68772i | −0.0776404 | + | 0.134477i | ||||
\(753\) | −3.21947 | − | 5.18461i | −0.117324 | − | 0.188938i | ||||
\(754\) | 3.51943 | − | 2.03195i | 0.128170 | − | 0.0739991i | ||||
\(755\) | 15.7335 | 0.572602 | ||||||||
\(756\) | 35.9314 | + | 21.8750i | 1.30681 | + | 0.795587i | ||||
\(757\) | 10.5426 | 0.383178 | 0.191589 | − | 0.981475i | \(-0.438636\pi\) | ||||
0.191589 | + | 0.981475i | \(0.438636\pi\) | |||||||
\(758\) | 59.7672 | − | 34.5066i | 2.17084 | − | 1.25334i | ||||
\(759\) | −4.81064 | − | 7.74702i | −0.174615 | − | 0.281199i | ||||
\(760\) | −1.33225 | + | 2.30753i | −0.0483258 | + | 0.0837028i | ||||
\(761\) | −9.26305 | + | 16.0441i | −0.335785 | + | 0.581597i | −0.983635 | − | 0.180171i | \(-0.942335\pi\) |
0.647850 | + | 0.761768i | \(0.275668\pi\) | |||||||
\(762\) | −17.6373 | − | 9.44166i | −0.638934 | − | 0.342035i | ||||
\(763\) | 3.59121 | − | 29.8961i | 0.130010 | − | 1.08231i | ||||
\(764\) | 6.07183i | 0.219671i | ||||||||
\(765\) | 8.00300 | + | 12.0101i | 0.289349 | + | 0.434225i | ||||
\(766\) | 32.5845i | 1.17733i | ||||||||
\(767\) | −4.16306 | + | 2.40355i | −0.150319 | + | 0.0867870i | ||||
\(768\) | 18.6881 | − | 0.599995i | 0.674348 | − | 0.0216505i | ||||
\(769\) | 28.4505 | + | 16.4259i | 1.02595 | + | 0.592333i | 0.915822 | − | 0.401584i | \(-0.131540\pi\) |
0.110129 | + | 0.993917i | \(0.464874\pi\) | |||||||
\(770\) | 13.4812 | − | 5.76421i | 0.485829 | − | 0.207728i | ||||
\(771\) | 1.22583 | − | 0.0393561i | 0.0441471 | − | 0.00141738i | ||||
\(772\) | −20.2271 | − | 35.0344i | −0.727989 | − | 1.26091i | ||||
\(773\) | −27.5217 | −0.989887 | −0.494944 | − | 0.868925i | \(-0.664811\pi\) | ||||
−0.494944 | + | 0.868925i | \(0.664811\pi\) | |||||||
\(774\) | 58.5546 | − | 39.0183i | 2.10470 | − | 1.40248i | ||||
\(775\) | 6.48426i | 0.232921i | ||||||||
\(776\) | −4.77245 | − | 8.26613i | −0.171321 | − | 0.296737i | ||||
\(777\) | 17.8414 | − | 8.31550i | 0.640058 | − | 0.298317i | ||||
\(778\) | −20.9037 | + | 36.2063i | −0.749434 | + | 1.29806i | ||||
\(779\) | 0.922561 | + | 0.532641i | 0.0330542 | + | 0.0190838i | ||||
\(780\) | 1.74915 | − | 1.08616i | 0.0626296 | − | 0.0388909i | ||||
\(781\) | 18.6538 | + | 32.3093i | 0.667486 | + | 1.15612i | ||||
\(782\) | 23.1264 | 0.826997 | ||||||||
\(783\) | 19.6684 | − | 14.0380i | 0.702892 | − | 0.501676i | ||||
\(784\) | −1.48709 | − | 5.08526i | −0.0531102 | − | 0.181616i | ||||
\(785\) | 17.2311 | − | 9.94836i | 0.615003 | − | 0.355072i | ||||
\(786\) | −41.4042 | + | 25.7106i | −1.47684 | + | 0.917067i | ||||
\(787\) | −8.80451 | − | 5.08329i | −0.313847 | − | 0.181200i | 0.334800 | − | 0.942289i | \(-0.391331\pi\) |
−0.648647 | + | 0.761090i | \(0.724665\pi\) | |||||||
\(788\) | −42.8365 | − | 24.7316i | −1.52599 | − | 0.881028i | ||||
\(789\) | 15.5770 | + | 8.33871i | 0.554556 | + | 0.296866i | ||||
\(790\) | −28.6733 | + | 16.5545i | −1.02015 | + | 0.588983i | ||||
\(791\) | −13.9155 | + | 18.5676i | −0.494779 | + | 0.660189i | ||||
\(792\) | 17.5842 | − | 1.13027i | 0.624826 | − | 0.0401624i | ||||
\(793\) | 0.283471 | 0.0100664 | ||||||||
\(794\) | 11.3061 | + | 19.5828i | 0.401240 | + | 0.694968i | ||||
\(795\) | −0.540679 | − | 16.8406i | −0.0191759 | − | 0.597274i | ||||
\(796\) | 72.4453 | + | 41.8263i | 2.56776 | + | 1.48249i | ||||
\(797\) | −11.2524 | + | 19.4897i | −0.398580 | + | 0.690362i | −0.993551 | − | 0.113386i | \(-0.963830\pi\) |
0.594971 | + | 0.803747i | \(0.297164\pi\) | |||||||
\(798\) | 9.43573 | + | 6.60963i | 0.334021 | + | 0.233978i | ||||
\(799\) | −13.5325 | − | 23.4389i | −0.478744 | − | 0.829210i | ||||
\(800\) | − | 6.47079i | − | 0.228777i | ||||||
\(801\) | −18.9590 | + | 38.3232i | −0.669883 | + | 1.35408i | ||||
\(802\) | −42.5293 | −1.50176 | ||||||||
\(803\) | −13.0257 | − | 22.5612i | −0.459668 | − | 0.796168i | ||||
\(804\) | 28.7018 | − | 53.6161i | 1.01224 | − | 1.89089i | ||||
\(805\) | −2.22293 | − | 5.19893i | −0.0783479 | − | 0.183238i | ||||
\(806\) | 4.90729 | + | 2.83322i | 0.172852 | + | 0.0997960i | ||||
\(807\) | −27.4972 | − | 44.2813i | −0.967947 | − | 1.55878i | ||||
\(808\) | 15.3395 | − | 8.85625i | 0.539641 | − | 0.311562i | ||||
\(809\) | − | 24.8607i | − | 0.874056i | −0.899448 | − | 0.437028i | \(-0.856031\pi\) | ||
0.899448 | − | 0.437028i | \(-0.143969\pi\) | |||||||
\(810\) | 16.0923 | − | 12.2837i | 0.565425 | − | 0.431605i | ||||
\(811\) | 40.0552i | 1.40653i | 0.710928 | + | 0.703264i | \(0.248275\pi\) | ||||
−0.710928 | + | 0.703264i | \(0.751725\pi\) | |||||||
\(812\) | 37.3796 | + | 4.49014i | 1.31177 | + | 0.157573i | ||||
\(813\) | −9.16728 | + | 5.69257i | −0.321510 | + | 0.199647i | ||||
\(814\) | 11.9019 | − | 20.6146i | 0.417160 | − | 0.722543i | ||||
\(815\) | −0.110369 | + | 0.191165i | −0.00386606 | + | 0.00669621i | ||||
\(816\) | 2.97649 | − | 5.56019i | 0.104198 | − | 0.194646i | ||||
\(817\) | 10.0920 | − | 5.82662i | 0.353074 | − | 0.203848i | ||||
\(818\) | 12.9301 | 0.452091 | ||||||||
\(819\) | −1.39165 | − | 2.75165i | −0.0486282 | − | 0.0961504i | ||||
\(820\) | 2.91662 | 0.101853 | ||||||||
\(821\) | 29.4435 | − | 16.9992i | 1.02759 | − | 0.593277i | 0.111294 | − | 0.993788i | \(-0.464501\pi\) |
0.916292 | + | 0.400511i | \(0.131167\pi\) | |||||||
\(822\) | −27.5493 | + | 0.884490i | −0.960891 | + | 0.0308501i | ||||
\(823\) | 15.2864 | − | 26.4768i | 0.532850 | − | 0.922923i | −0.466414 | − | 0.884566i | \(-0.654454\pi\) |
0.999264 | − | 0.0383565i | \(-0.0122122\pi\) | |||||||
\(824\) | 10.4478 | − | 18.0962i | 0.363968 | − | 0.630411i | ||||
\(825\) | −0.136927 | − | 4.26487i | −0.00476718 | − | 0.148484i | ||||
\(826\) | −73.1156 | − | 8.78286i | −2.54402 | − | 0.305595i | ||||
\(827\) | 36.8463i | 1.28127i | 0.767845 | + | 0.640635i | \(0.221329\pi\) | ||||
−0.767845 | + | 0.640635i | \(0.778671\pi\) | |||||||
\(828\) | −1.25839 | − | 19.5774i | −0.0437321 | − | 0.680361i | ||||
\(829\) | 41.5579i | 1.44337i | 0.692224 | + | 0.721683i | \(0.256631\pi\) | ||||
−0.692224 | + | 0.721683i | \(0.743369\pi\) | |||||||
\(830\) | −23.2728 | + | 13.4366i | −0.807811 | + | 0.466390i | ||||
\(831\) | 0.217192 | − | 0.405723i | 0.00753432 | − | 0.0140744i | ||||
\(832\) | −4.38780 | − | 2.53330i | −0.152120 | − | 0.0878262i | ||||
\(833\) | 32.7172 | + | 7.97527i | 1.13359 | + | 0.276327i | ||||
\(834\) | 22.7496 | + | 36.6358i | 0.787755 | + | 1.26860i | ||||
\(835\) | 12.6948 | + | 21.9881i | 0.439323 | + | 0.760930i | ||||
\(836\) | 8.42484 | 0.291379 | ||||||||
\(837\) | 30.6636 | + | 13.9634i | 1.05989 | + | 0.482646i | ||||
\(838\) | 16.9433i | 0.585297i | ||||||||
\(839\) | −13.2465 | − | 22.9437i | −0.457321 | − | 0.792103i | 0.541497 | − | 0.840703i | \(-0.317858\pi\) |
−0.998818 | + | 0.0485991i | \(0.984524\pi\) | |||||||
\(840\) | 10.8836 | + | 0.954267i | 0.375521 | + | 0.0329253i | ||||
\(841\) | −3.68683 | + | 6.38578i | −0.127132 | + | 0.220199i | ||||
\(842\) | 17.8292 | + | 10.2937i | 0.614436 | + | 0.354745i | ||||
\(843\) | 21.2667 | + | 11.3845i | 0.732464 | + | 0.392104i | ||||
\(844\) | 2.41154 | + | 4.17691i | 0.0830086 | + | 0.143775i | ||||
\(845\) | 12.8491 | 0.442022 | ||||||||
\(846\) | −31.5935 | + | 21.0525i | −1.08621 | + | 0.723801i | ||||
\(847\) | 10.4391 | + | 7.82360i | 0.358693 | + | 0.268822i | ||||
\(848\) | −6.37652 | + | 3.68148i | −0.218971 | + | 0.126423i | ||||
\(849\) | −0.880837 | − | 27.4355i | −0.0302303 | − | 0.941584i | ||||
\(850\) | 9.37160 | + | 5.41070i | 0.321443 | + | 0.185585i | ||||
\(851\) | −7.94990 | − | 4.58987i | −0.272519 | − | 0.157339i | ||||
\(852\) | 2.57545 | + | 80.2177i | 0.0882335 | + | 2.74821i | ||||
\(853\) | −2.66454 | + | 1.53837i | −0.0912321 | + | 0.0526729i | −0.544922 | − | 0.838487i | \(-0.683441\pi\) |
0.453690 | + | 0.891160i | \(0.350107\pi\) | |||||||
\(854\) | 3.47498 | + | 2.60432i | 0.118911 | + | 0.0891181i | ||||
\(855\) | 2.79011 | − | 1.85921i | 0.0954198 | − | 0.0635837i | ||||
\(856\) | −9.69105 | −0.331233 | ||||||||
\(857\) | 0.835486 | + | 1.44710i | 0.0285397 | + | 0.0494321i | 0.879942 | − | 0.475080i | \(-0.157581\pi\) |
−0.851403 | + | 0.524512i | \(0.824248\pi\) | |||||||
\(858\) | −3.28748 | − | 1.75986i | −0.112233 | − | 0.0600806i | ||||
\(859\) | −30.7586 | − | 17.7585i | −1.04947 | − | 0.605911i | −0.126968 | − | 0.991907i | \(-0.540525\pi\) |
−0.922501 | + | 0.385996i | \(0.873858\pi\) | |||||||
\(860\) | 15.9526 | − | 27.6308i | 0.543980 | − | 0.942202i | ||||
\(861\) | 0.381521 | − | 4.35133i | 0.0130022 | − | 0.148293i | ||||
\(862\) | −5.73023 | − | 9.92504i | −0.195172 | − | 0.338048i | ||||
\(863\) | 29.1514i | 0.992325i | 0.868230 | + | 0.496162i | \(0.165258\pi\) | ||||
−0.868230 | + | 0.496162i | \(0.834742\pi\) | |||||||
\(864\) | −30.5999 | − | 13.9344i | −1.04103 | − | 0.474059i | ||||
\(865\) | 14.5208 | 0.493723 | ||||||||
\(866\) | 40.3551 | + | 69.8970i | 1.37132 | + | 2.37520i | ||||
\(867\) | 5.61324 | + | 9.03953i | 0.190636 | + | 0.306998i | ||||
\(868\) | 20.6379 | + | 48.2675i | 0.700496 | + | 1.63830i | ||||
\(869\) | 31.4033 | + | 18.1307i | 1.06528 | + | 0.615042i | ||||
\(870\) | 8.55107 | − | 15.9737i | 0.289908 | − | 0.541559i | ||||
\(871\) | −3.86062 | + | 2.22893i | −0.130812 | + | 0.0755245i | ||||
\(872\) | − | 27.1334i | − | 0.918852i | ||||||
\(873\) | 0.770426 | + | 11.9859i | 0.0260750 | + | 0.405661i | ||||
\(874\) | − | 5.37259i | − | 0.181730i | ||||||
\(875\) | 0.315547 | − | 2.62687i | 0.0106674 | − | 0.0888043i | ||||
\(876\) | −1.79841 | − | 56.0151i | −0.0607625 | − | 1.89257i | ||||
\(877\) | −3.35894 | + | 5.81786i | −0.113423 | + | 0.196455i | −0.917148 | − | 0.398546i | \(-0.869515\pi\) |
0.803725 | + | 0.595001i | \(0.202848\pi\) | |||||||
\(878\) | 0.832745 | − | 1.44236i | 0.0281038 | − | 0.0486772i | ||||
\(879\) | −11.6705 | + | 0.374689i | −0.393635 | + | 0.0126379i | ||||
\(880\) | −1.61485 | + | 0.932334i | −0.0544366 | + | 0.0314290i | ||||
\(881\) | 1.09027 | 0.0367322 | 0.0183661 | − | 0.999831i | \(-0.494154\pi\) | ||||
0.0183661 | + | 0.999831i | \(0.494154\pi\) | |||||||
\(882\) | 8.22033 | − | 46.5170i | 0.276793 | − | 1.56631i | ||||
\(883\) | −6.11832 | −0.205898 | −0.102949 | − | 0.994687i | \(-0.532828\pi\) | ||||
−0.102949 | + | 0.994687i | \(0.532828\pi\) | |||||||
\(884\) | 4.95255 | − | 2.85935i | 0.166572 | − | 0.0961705i | ||||
\(885\) | −10.1149 | + | 18.8950i | −0.340008 | + | 0.635147i | ||||
\(886\) | −19.4077 | + | 33.6152i | −0.652016 | + | 1.12932i | ||||
\(887\) | 22.6970 | − | 39.3124i | 0.762091 | − | 1.31998i | −0.179679 | − | 0.983725i | \(-0.557506\pi\) |
0.941771 | − | 0.336256i | \(-0.109161\pi\) | |||||||
\(888\) | 15.0687 | − | 9.35715i | 0.505672 | − | 0.314005i | ||||
\(889\) | −1.62025 | + | 13.4883i | −0.0543416 | + | 0.452383i | ||||
\(890\) | 32.0590i | 1.07462i | ||||||||
\(891\) | −20.4631 | − | 8.53659i | −0.685539 | − | 0.285986i | ||||
\(892\) | 44.6909i | 1.49636i | ||||||||
\(893\) | −5.44520 | + | 3.14379i | −0.182217 | + | 0.105203i | ||||
\(894\) | −17.5653 | − | 28.2871i | −0.587472 | − | 0.946061i | ||||
\(895\) | −13.0291 | − | 7.52233i | −0.435513 | − | 0.251444i | ||||
\(896\) | −17.0532 | − | 39.8836i | −0.569707 | − | 1.33242i | ||||
\(897\) | −0.678678 | + | 1.26779i | −0.0226604 | + | 0.0423304i | ||||
\(898\) | −23.0635 | − | 39.9472i | −0.769639 | − | 1.33305i | ||||
\(899\) | 30.1545 | 1.00571 | ||||||||
\(900\) | 4.07043 | − | 8.22785i | 0.135681 | − | 0.274262i | ||||
\(901\) | − | 46.7986i | − | 1.55909i | ||||||
\(902\) | −2.64110 | − | 4.57451i | −0.0879389 | − | 0.152315i | ||||
\(903\) | −39.1358 | − | 27.4142i | −1.30236 | − | 0.912288i | ||||
\(904\) | −10.4544 | + | 18.1076i | −0.347709 | + | 0.602250i | ||||
\(905\) | 15.7292 | + | 9.08127i | 0.522857 | + | 0.301872i | ||||
\(906\) | −1.96705 | − | 61.2680i | −0.0653510 | − | 2.03549i | ||||
\(907\) | 4.94352 | + | 8.56242i | 0.164147 | + | 0.284311i | 0.936352 | − | 0.351063i | \(-0.114180\pi\) |
−0.772205 | + | 0.635373i | \(0.780846\pi\) | |||||||
\(908\) | −8.90923 | −0.295663 | ||||||||
\(909\) | −22.2422 | + | 1.42968i | −0.737728 | + | 0.0474195i | ||||
\(910\) | −1.85014 | − | 1.38659i | −0.0613315 | − | 0.0459649i | ||||
\(911\) | −34.9512 | + | 20.1791i | −1.15798 | + | 0.668563i | −0.950820 | − | 0.309743i | \(-0.899757\pi\) |
−0.207165 | + | 0.978306i | \(0.566424\pi\) | |||||||
\(912\) | −1.29171 | − | 0.691481i | −0.0427729 | − | 0.0228972i | ||||
\(913\) | 25.4887 | + | 14.7159i | 0.843552 | + | 0.487025i | ||||
\(914\) | 17.8331 | + | 10.2959i | 0.589865 | + | 0.340559i | ||||
\(915\) | 1.07367 | − | 0.666712i | 0.0354944 | − | 0.0220408i | ||||
\(916\) | 49.6885 | − | 28.6877i | 1.64175 | − | 0.947867i | ||||
\(917\) | 26.4841 | + | 19.8485i | 0.874583 | + | 0.655456i | ||||
\(918\) | 45.7679 | − | 32.6660i | 1.51057 | − | 1.07814i | ||||
\(919\) | 20.1949 | 0.666167 | 0.333084 | − | 0.942897i | \(-0.391911\pi\) | ||||
0.333084 | + | 0.942897i | \(0.391911\pi\) | |||||||
\(920\) | −2.54754 | − | 4.41248i | −0.0839900 | − | 0.145475i | ||||
\(921\) | 2.37536 | − | 1.47502i | 0.0782706 | − | 0.0486034i | ||||
\(922\) | −19.7713 | − | 11.4150i | −0.651133 | − | 0.375932i | ||||
\(923\) | 2.94157 | − | 5.09495i | 0.0968230 | − | 0.167702i | ||||
\(924\) | −14.5933 | − | 31.3110i | −0.480086 | − | 1.03006i | ||||
\(925\) | −2.14771 | − | 3.71995i | −0.0706164 | − | 0.122311i | ||||
\(926\) | 2.76118i | 0.0907381i | ||||||||
\(927\) | −21.8808 | + | 14.5804i | −0.718658 | + | 0.478883i | ||||
\(928\) | −30.0919 | −0.987814 | ||||||||
\(929\) | −2.47705 | − | 4.29038i | −0.0812694 | − | 0.140763i | 0.822526 | − | 0.568727i | \(-0.192564\pi\) |
−0.903795 | + | 0.427965i | \(0.859231\pi\) | |||||||
\(930\) | 25.2503 | − | 0.810681i | 0.827991 | − | 0.0265833i | ||||
\(931\) | 1.85277 | − | 7.60068i | 0.0607220 | − | 0.249102i | ||||
\(932\) | 13.6257 | + | 7.86681i | 0.446325 | + | 0.257686i | ||||
\(933\) | −27.2529 | + | 0.874975i | −0.892220 | + | 0.0286454i | ||||
\(934\) | 45.2585 | − | 26.1300i | 1.48090 | − | 0.854999i | ||||
\(935\) | − | 11.8517i | − | 0.387593i | ||||||
\(936\) | −1.54081 | − | 2.31228i | −0.0503628 | − | 0.0755793i | ||||
\(937\) | − | 32.1771i | − | 1.05118i | −0.850738 | − | 0.525590i | \(-0.823845\pi\) | ||
0.850738 | − | 0.525590i | \(-0.176155\pi\) | |||||||
\(938\) | −67.8039 | − | 8.14480i | −2.21388 | − | 0.265937i | ||||
\(939\) | 5.96860 | + | 3.19512i | 0.194778 | + | 0.104269i | ||||
\(940\) | −8.60733 | + | 14.9083i | −0.280740 | + | 0.486256i | ||||
\(941\) | −9.92726 | + | 17.1945i | −0.323619 | + | 0.560525i | −0.981232 | − | 0.192831i | \(-0.938233\pi\) |
0.657613 | + | 0.753356i | \(0.271566\pi\) | |||||||
\(942\) | −40.8942 | − | 65.8557i | −1.33240 | − | 2.14569i | ||||
\(943\) | −1.76413 | + | 1.01852i | −0.0574480 | + | 0.0331676i | ||||
\(944\) | 9.36558 | 0.304824 | ||||||||
\(945\) | −11.7427 | − | 7.14898i | −0.381992 | − | 0.232556i | ||||
\(946\) | −57.7825 | −1.87867 | ||||||||
\(947\) | −9.34865 | + | 5.39744i | −0.303790 | + | 0.175393i | −0.644144 | − | 0.764904i | \(-0.722786\pi\) |
0.340354 | + | 0.940297i | \(0.389453\pi\) | |||||||
\(948\) | 41.1520 | + | 66.2709i | 1.33655 | + | 2.15238i | ||||
\(949\) | −2.05406 | + | 3.55774i | −0.0666777 | + | 0.115489i | ||||
\(950\) | 1.25698 | − | 2.17716i | 0.0407819 | − | 0.0706363i | ||||
\(951\) | −37.6218 | − | 20.1398i | −1.21997 | − | 0.653077i | ||||
\(952\) | 30.1286 | + | 3.61913i | 0.976472 | + | 0.117297i | ||||
\(953\) | 16.7368i | 0.542157i | 0.962557 | + | 0.271079i | \(0.0873804\pi\) | ||||
−0.962557 | + | 0.271079i | \(0.912620\pi\) | |||||||
\(954\) | −65.5113 | + | 4.21092i | −2.12101 | + | 0.136334i | ||||
\(955\) | − | 1.98434i | − | 0.0642116i | ||||||
\(956\) | 45.2584 | − | 26.1299i | 1.46376 | − | 0.845103i | ||||
\(957\) | −19.8334 | + | 0.636766i | −0.641122 | + | 0.0205837i | ||||
\(958\) | −60.8476 | − | 35.1304i | −1.96590 | − | 1.13501i | ||||
\(959\) | 7.35875 | + | 17.2105i | 0.237626 | + | 0.555755i | ||||
\(960\) | −22.5773 | + | 0.724862i | −0.728680 | + | 0.0233948i | ||||
\(961\) | 5.52279 | + | 9.56574i | 0.178154 | + | 0.308572i | ||||
\(962\) | −3.75368 | −0.121023 | ||||||||
\(963\) | 10.9301 | + | 5.40728i | 0.352219 | + | 0.174247i | ||||
\(964\) | 64.0329i | 2.06236i | ||||||||
\(965\) | 6.61042 | + | 11.4496i | 0.212797 | + | 0.368575i | ||||
\(966\) | −19.9672 | + | 9.30629i | −0.642436 | + | 0.299425i | ||||
\(967\) | −25.6781 | + | 44.4758i | −0.825752 | + | 1.43024i | 0.0755915 | + | 0.997139i | \(0.475915\pi\) |
−0.901343 | + | 0.433105i | \(0.857418\pi\) | |||||||
\(968\) | 10.1805 | + | 5.87771i | 0.327213 | + | 0.188917i | ||||
\(969\) | 7.91122 | − | 4.91260i | 0.254145 | − | 0.157816i | ||||
\(970\) | 4.50282 | + | 7.79911i | 0.144577 | + | 0.250414i | ||||
\(971\) | −5.95642 | −0.191151 | −0.0955753 | − | 0.995422i | \(-0.530469\pi\) | ||||
−0.0955753 | + | 0.995422i | \(0.530469\pi\) | |||||||
\(972\) | −30.1435 | − | 36.9669i | −0.966853 | − | 1.18571i | ||||
\(973\) | 17.5627 | − | 23.4341i | 0.563033 | − | 0.751262i | ||||
\(974\) | −20.8760 | + | 12.0528i | −0.668911 | + | 0.386196i | ||||
\(975\) | −0.571640 | + | 0.354969i | −0.0183071 | + | 0.0113681i | ||||
\(976\) | −0.478291 | − | 0.276141i | −0.0153097 | − | 0.00883907i | ||||
\(977\) | −18.8015 | − | 10.8550i | −0.601512 | − | 0.347283i | 0.168124 | − | 0.985766i | \(-0.446229\pi\) |
−0.769636 | + | 0.638483i | \(0.779562\pi\) | |||||||
\(978\) | 0.758214 | + | 0.405888i | 0.0242450 | + | 0.0129789i | ||||
\(979\) | 30.4074 | − | 17.5557i | 0.971824 | − | 0.561083i | ||||
\(980\) | −6.01185 | − | 20.5582i | −0.192041 | − | 0.656707i | ||||
\(981\) | −15.1395 | + | 30.6026i | −0.483367 | + | 0.977066i | ||||
\(982\) | −2.36972 | −0.0756207 | ||||||||
\(983\) | 6.84543 | + | 11.8566i | 0.218335 | + | 0.378168i | 0.954299 | − | 0.298853i | \(-0.0966040\pi\) |
−0.735964 | + | 0.677021i | \(0.763271\pi\) | |||||||
\(984\) | −0.126306 | − | 3.93405i | −0.00402648 | − | 0.125413i | ||||
\(985\) | 13.9994 | + | 8.08255i | 0.446058 | + | 0.257531i | ||||
\(986\) | 25.1620 | − | 43.5818i | 0.801320 | − | 1.38793i | ||||
\(987\) | 21.1160 | + | 14.7915i | 0.672128 | + | 0.470819i | ||||
\(988\) | −0.664269 | − | 1.15055i | −0.0211332 | − | 0.0366038i | ||||
\(989\) | 22.2834i | 0.708572i | ||||||||
\(990\) | −16.5907 | + | 1.06641i | −0.527287 | + | 0.0338928i | ||||
\(991\) | 25.1854 | 0.800040 | 0.400020 | − | 0.916506i | \(-0.369003\pi\) | ||||
0.400020 | + | 0.916506i | \(0.369003\pi\) | |||||||
\(992\) | −20.9791 | − | 36.3369i | −0.666088 | − | 1.15370i | ||||
\(993\) | 7.55027 | − | 14.1042i | 0.239601 | − | 0.447583i | ||||
\(994\) | 82.8684 | − | 35.4324i | 2.62843 | − | 1.12385i | ||||
\(995\) | −23.6759 | − | 13.6693i | −0.750575 | − | 0.433345i | ||||
\(996\) | 33.4012 | + | 53.7891i | 1.05836 | + | 1.70437i | ||||
\(997\) | −24.4950 | + | 14.1422i | −0.775766 | + | 0.447888i | −0.834927 | − | 0.550360i | \(-0.814490\pi\) |
0.0591620 | + | 0.998248i | \(0.481157\pi\) | |||||||
\(998\) | 11.3400i | 0.358961i | ||||||||
\(999\) | −22.2163 | + | 2.14571i | −0.702893 | + | 0.0678874i |
(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 | 315.2.bl.j.41.10 | yes | 24 | |
3.2 | odd | 2 | 945.2.bl.j.881.3 | 24 | |||
7.6 | odd | 2 | 315.2.bl.i.41.10 | ✓ | 24 | ||
9.2 | odd | 6 | 315.2.bl.i.146.10 | yes | 24 | ||
9.7 | even | 3 | 945.2.bl.i.251.3 | 24 | |||
21.20 | even | 2 | 945.2.bl.i.881.3 | 24 | |||
63.20 | even | 6 | inner | 315.2.bl.j.146.10 | yes | 24 | |
63.34 | odd | 6 | 945.2.bl.j.251.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bl.i.41.10 | ✓ | 24 | 7.6 | odd | 2 | ||
315.2.bl.i.146.10 | yes | 24 | 9.2 | odd | 6 | ||
315.2.bl.j.41.10 | yes | 24 | 1.1 | even | 1 | trivial | |
315.2.bl.j.146.10 | yes | 24 | 63.20 | even | 6 | inner | |
945.2.bl.i.251.3 | 24 | 9.7 | even | 3 | |||
945.2.bl.i.881.3 | 24 | 21.20 | even | 2 | |||
945.2.bl.j.251.3 | 24 | 63.34 | odd | 6 | |||
945.2.bl.j.881.3 | 24 | 3.2 | odd | 2 |