Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(89,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.k (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6 x^{19} + 19 x^{18} - 42 x^{17} + 62 x^{16} - 42 x^{15} - 25 x^{14} + 6 x^{13} + 445 x^{12} - 1764 x^{11} + 3864 x^{10} - 5292 x^{9} + 4005 x^{8} + 162 x^{7} - 2025 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.3 | ||
Root | \(1.69321 + 0.364755i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.353 |
Dual form | 462.2.k.g.89.3 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.530717 | − | 1.64874i | −0.306410 | − | 0.951900i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −0.417958 | − | 0.723925i | −0.186917 | − | 0.323749i | 0.757304 | − | 0.653063i | \(-0.226516\pi\) |
−0.944221 | + | 0.329313i | \(0.893183\pi\) | |||||||
\(6\) | 1.28398 | + | 1.16249i | 0.524184 | + | 0.474585i | ||||
\(7\) | −1.42670 | − | 2.22812i | −0.539240 | − | 0.842152i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.43668 | + | 1.75003i | −0.812226 | + | 0.583343i | ||||
\(10\) | 0.723925 | + | 0.417958i | 0.228925 | + | 0.132170i | ||||
\(11\) | 0.866025 | + | 0.500000i | 0.261116 | + | 0.150756i | ||||
\(12\) | −1.69321 | − | 0.364755i | −0.488787 | − | 0.105296i | ||||
\(13\) | − | 3.86332i | − | 1.07149i | −0.844379 | − | 0.535746i | \(-0.820031\pi\) | ||
0.844379 | − | 0.535746i | \(-0.179969\pi\) | |||||||
\(14\) | 2.34962 | + | 1.21626i | 0.627962 | + | 0.325060i | ||||
\(15\) | −0.971746 | + | 1.07330i | −0.250904 | + | 0.277126i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.06563 | + | 1.84573i | −0.258454 | + | 0.447656i | −0.965828 | − | 0.259184i | \(-0.916546\pi\) |
0.707374 | + | 0.706840i | \(0.249880\pi\) | |||||||
\(18\) | 1.23521 | − | 2.73391i | 0.291142 | − | 0.644388i | ||||
\(19\) | −2.35922 | + | 1.36210i | −0.541243 | + | 0.312487i | −0.745583 | − | 0.666413i | \(-0.767829\pi\) |
0.204339 | + | 0.978900i | \(0.434495\pi\) | |||||||
\(20\) | −0.835917 | −0.186917 | ||||||||
\(21\) | −2.91642 | + | 3.53475i | −0.636416 | + | 0.771346i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −6.08555 | + | 3.51349i | −1.26892 | + | 0.732614i | −0.974785 | − | 0.223148i | \(-0.928367\pi\) |
−0.294140 | + | 0.955762i | \(0.595033\pi\) | |||||||
\(24\) | 1.64874 | − | 0.530717i | 0.336547 | − | 0.108332i | ||||
\(25\) | 2.15062 | − | 3.72499i | 0.430124 | − | 0.744997i | ||||
\(26\) | 1.93166 | + | 3.34573i | 0.378829 | + | 0.656152i | ||||
\(27\) | 4.17853 | + | 3.08868i | 0.804158 | + | 0.594416i | ||||
\(28\) | −2.64296 | + | 0.121493i | −0.499473 | + | 0.0229600i | ||||
\(29\) | 7.25640i | 1.34748i | 0.738969 | + | 0.673740i | \(0.235313\pi\) | ||||
−0.738969 | + | 0.673740i | \(0.764687\pi\) | |||||||
\(30\) | 0.304905 | − | 1.41538i | 0.0556677 | − | 0.258412i | ||||
\(31\) | −4.85360 | − | 2.80223i | −0.871732 | − | 0.503295i | −0.00380865 | − | 0.999993i | \(-0.501212\pi\) |
−0.867923 | + | 0.496698i | \(0.834546\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0.364755 | − | 1.69321i | 0.0634957 | − | 0.294750i | ||||
\(34\) | − | 2.13127i | − | 0.365509i | ||||||
\(35\) | −1.01670 | + | 1.96408i | −0.171853 | + | 0.331991i | ||||
\(36\) | 0.297229 | + | 2.98524i | 0.0495382 | + | 0.497540i | ||||
\(37\) | 1.76131 | + | 3.05069i | 0.289558 | + | 0.501530i | 0.973704 | − | 0.227815i | \(-0.0731583\pi\) |
−0.684146 | + | 0.729345i | \(0.739825\pi\) | |||||||
\(38\) | 1.36210 | − | 2.35922i | 0.220962 | − | 0.382717i | ||||
\(39\) | −6.36960 | + | 2.05033i | −1.01995 | + | 0.328315i | ||||
\(40\) | 0.723925 | − | 0.417958i | 0.114463 | − | 0.0660850i | ||||
\(41\) | 0.835917 | 0.130548 | 0.0652741 | − | 0.997867i | \(-0.479208\pi\) | ||||
0.0652741 | + | 0.997867i | \(0.479208\pi\) | |||||||
\(42\) | 0.758320 | − | 4.51940i | 0.117011 | − | 0.697358i | ||||
\(43\) | −9.85086 | −1.50224 | −0.751121 | − | 0.660165i | \(-0.770486\pi\) | ||||
−0.751121 | + | 0.660165i | \(0.770486\pi\) | |||||||
\(44\) | 0.866025 | − | 0.500000i | 0.130558 | − | 0.0753778i | ||||
\(45\) | 2.28532 | + | 1.03253i | 0.340675 | + | 0.153921i | ||||
\(46\) | 3.51349 | − | 6.08555i | 0.518036 | − | 0.897265i | ||||
\(47\) | −5.84290 | − | 10.1202i | −0.852274 | − | 1.47618i | −0.879151 | − | 0.476543i | \(-0.841890\pi\) |
0.0268770 | − | 0.999639i | \(-0.491444\pi\) | |||||||
\(48\) | −1.16249 | + | 1.28398i | −0.167791 | + | 0.185327i | ||||
\(49\) | −2.92908 | + | 6.35771i | −0.418440 | + | 0.908245i | ||||
\(50\) | 4.30124i | 0.608288i | ||||||||
\(51\) | 3.60868 | + | 0.777390i | 0.505316 | + | 0.108856i | ||||
\(52\) | −3.34573 | − | 1.93166i | −0.463969 | − | 0.267873i | ||||
\(53\) | −7.26395 | − | 4.19384i | −0.997780 | − | 0.576069i | −0.0901894 | − | 0.995925i | \(-0.528747\pi\) |
−0.907591 | + | 0.419856i | \(0.862081\pi\) | |||||||
\(54\) | −5.16305 | − | 0.585609i | −0.702602 | − | 0.0796914i | ||||
\(55\) | − | 0.835917i | − | 0.112715i | ||||||
\(56\) | 2.22812 | − | 1.42670i | 0.297746 | − | 0.190650i | ||||
\(57\) | 3.49783 | + | 3.16686i | 0.463298 | + | 0.419460i | ||||
\(58\) | −3.62820 | − | 6.28423i | −0.476406 | − | 0.825159i | ||||
\(59\) | 3.60897 | − | 6.25091i | 0.469847 | − | 0.813799i | −0.529558 | − | 0.848274i | \(-0.677642\pi\) |
0.999406 | + | 0.0344741i | \(0.0109756\pi\) | |||||||
\(60\) | 0.443635 | + | 1.37821i | 0.0572731 | + | 0.177926i | ||||
\(61\) | −2.31656 | + | 1.33746i | −0.296605 | + | 0.171245i | −0.640917 | − | 0.767611i | \(-0.721446\pi\) |
0.344312 | + | 0.938855i | \(0.388112\pi\) | |||||||
\(62\) | 5.60445 | 0.711766 | ||||||||
\(63\) | 7.37568 | + | 2.93247i | 0.929248 | + | 0.369456i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.79675 | + | 1.61471i | −0.346895 | + | 0.200280i | ||||
\(66\) | 0.530717 | + | 1.64874i | 0.0653268 | + | 0.202946i | ||||
\(67\) | 6.35213 | − | 11.0022i | 0.776036 | − | 1.34413i | −0.158175 | − | 0.987411i | \(-0.550561\pi\) |
0.934211 | − | 0.356722i | \(-0.116106\pi\) | |||||||
\(68\) | 1.06563 | + | 1.84573i | 0.129227 | + | 0.223828i | ||||
\(69\) | 9.02254 | + | 8.16881i | 1.08619 | + | 0.983409i | ||||
\(70\) | −0.101558 | − | 2.20930i | −0.0121385 | − | 0.264061i | ||||
\(71\) | − | 2.66448i | − | 0.316215i | −0.987422 | − | 0.158108i | \(-0.949461\pi\) | ||
0.987422 | − | 0.158108i | \(-0.0505393\pi\) | |||||||
\(72\) | −1.75003 | − | 2.43668i | −0.206243 | − | 0.287165i | ||||
\(73\) | 10.7588 | + | 6.21158i | 1.25922 | + | 0.727011i | 0.972923 | − | 0.231130i | \(-0.0742422\pi\) |
0.286297 | + | 0.958141i | \(0.407576\pi\) | |||||||
\(74\) | −3.05069 | − | 1.76131i | −0.354635 | − | 0.204749i | ||||
\(75\) | −7.28290 | − | 1.56890i | −0.840957 | − | 0.181161i | ||||
\(76\) | 2.72420i | 0.312487i | ||||||||
\(77\) | −0.121493 | − | 2.64296i | −0.0138454 | − | 0.301193i | ||||
\(78\) | 4.49107 | − | 4.96044i | 0.508514 | − | 0.561659i | ||||
\(79\) | 2.81072 | + | 4.86831i | 0.316231 | + | 0.547728i | 0.979698 | − | 0.200477i | \(-0.0642492\pi\) |
−0.663467 | + | 0.748205i | \(0.730916\pi\) | |||||||
\(80\) | −0.417958 | + | 0.723925i | −0.0467292 | + | 0.0809373i | ||||
\(81\) | 2.87481 | − | 8.52851i | 0.319423 | − | 0.947612i | ||||
\(82\) | −0.723925 | + | 0.417958i | −0.0799442 | + | 0.0461558i | ||||
\(83\) | −3.41567 | −0.374918 | −0.187459 | − | 0.982272i | \(-0.560025\pi\) | ||||
−0.187459 | + | 0.982272i | \(0.560025\pi\) | |||||||
\(84\) | 1.60297 | + | 4.29307i | 0.174899 | + | 0.468413i | ||||
\(85\) | 1.78156 | 0.193238 | ||||||||
\(86\) | 8.53109 | − | 4.92543i | 0.919931 | − | 0.531123i | ||||
\(87\) | 11.9639 | − | 3.85110i | 1.28267 | − | 0.412881i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | 0.355752 | + | 0.616180i | 0.0377096 | + | 0.0653150i | 0.884264 | − | 0.466987i | \(-0.154660\pi\) |
−0.846555 | + | 0.532302i | \(0.821327\pi\) | |||||||
\(90\) | −2.49541 | + | 0.248459i | −0.263040 | + | 0.0261899i | ||||
\(91\) | −8.60795 | + | 5.51178i | −0.902359 | + | 0.577792i | ||||
\(92\) | 7.02699i | 0.732614i | ||||||||
\(93\) | −2.04425 | + | 9.48951i | −0.211979 | + | 0.984016i | ||||
\(94\) | 10.1202 | + | 5.84290i | 1.04382 | + | 0.602649i | ||||
\(95\) | 1.97212 | + | 1.13860i | 0.202335 | + | 0.116818i | ||||
\(96\) | 0.364755 | − | 1.69321i | 0.0372276 | − | 0.172812i | ||||
\(97\) | − | 9.84612i | − | 0.999722i | −0.866106 | − | 0.499861i | \(-0.833384\pi\) | ||
0.866106 | − | 0.499861i | \(-0.166616\pi\) | |||||||
\(98\) | −0.642202 | − | 6.97048i | −0.0648722 | − | 0.704125i | ||||
\(99\) | −2.98524 | + | 0.297229i | −0.300028 | + | 0.0298727i | ||||
\(100\) | −2.15062 | − | 3.72499i | −0.215062 | − | 0.372499i | ||||
\(101\) | 3.31704 | − | 5.74529i | 0.330058 | − | 0.571677i | −0.652465 | − | 0.757819i | \(-0.726265\pi\) |
0.982523 | + | 0.186142i | \(0.0595983\pi\) | |||||||
\(102\) | −3.51390 | + | 1.13110i | −0.347928 | + | 0.111996i | ||||
\(103\) | 13.2128 | − | 7.62843i | 1.30190 | − | 0.751651i | 0.321169 | − | 0.947022i | \(-0.395924\pi\) |
0.980729 | + | 0.195371i | \(0.0625910\pi\) | |||||||
\(104\) | 3.86332 | 0.378829 | ||||||||
\(105\) | 3.77784 | + | 0.633892i | 0.368680 | + | 0.0618616i | ||||
\(106\) | 8.38769 | 0.814684 | ||||||||
\(107\) | 3.22599 | − | 1.86253i | 0.311868 | − | 0.180057i | −0.335894 | − | 0.941900i | \(-0.609038\pi\) |
0.647762 | + | 0.761843i | \(0.275705\pi\) | |||||||
\(108\) | 4.76414 | − | 2.07437i | 0.458429 | − | 0.199606i | ||||
\(109\) | −9.01132 | + | 15.6081i | −0.863128 | + | 1.49498i | 0.00576622 | + | 0.999983i | \(0.498165\pi\) |
−0.868894 | + | 0.494998i | \(0.835169\pi\) | |||||||
\(110\) | 0.417958 | + | 0.723925i | 0.0398508 | + | 0.0690236i | ||||
\(111\) | 4.09502 | − | 4.52300i | 0.388682 | − | 0.429304i | ||||
\(112\) | −1.21626 | + | 2.34962i | −0.114926 | + | 0.222018i | ||||
\(113\) | − | 13.9774i | − | 1.31488i | −0.753506 | − | 0.657441i | \(-0.771639\pi\) | ||
0.753506 | − | 0.657441i | \(-0.228361\pi\) | |||||||
\(114\) | −4.61263 | − | 0.993664i | −0.432013 | − | 0.0930652i | ||||
\(115\) | 5.08701 | + | 2.93699i | 0.474366 | + | 0.273876i | ||||
\(116\) | 6.28423 | + | 3.62820i | 0.583476 | + | 0.336870i | ||||
\(117\) | 6.76091 | + | 9.41366i | 0.625047 | + | 0.870293i | ||||
\(118\) | 7.21793i | 0.664464i | ||||||||
\(119\) | 5.63285 | − | 0.258934i | 0.516363 | − | 0.0237364i | ||||
\(120\) | −1.07330 | − | 0.971746i | −0.0979788 | − | 0.0887079i | ||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 1.33746 | − | 2.31656i | 0.121088 | − | 0.209731i | ||||
\(123\) | −0.443635 | − | 1.37821i | −0.0400013 | − | 0.124269i | ||||
\(124\) | −4.85360 | + | 2.80223i | −0.435866 | + | 0.251647i | ||||
\(125\) | −7.77507 | −0.695423 | ||||||||
\(126\) | −7.85376 | + | 1.14825i | −0.699668 | + | 0.102294i | ||||
\(127\) | −10.4325 | −0.925737 | −0.462869 | − | 0.886427i | \(-0.653180\pi\) | ||||
−0.462869 | + | 0.886427i | \(0.653180\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 5.22802 | + | 16.2415i | 0.460301 | + | 1.42998i | ||||
\(130\) | 1.61471 | − | 2.79675i | 0.141619 | − | 0.245292i | ||||
\(131\) | 5.20268 | + | 9.01131i | 0.454561 | + | 0.787322i | 0.998663 | − | 0.0516968i | \(-0.0164629\pi\) |
−0.544102 | + | 0.839019i | \(0.683130\pi\) | |||||||
\(132\) | −1.28398 | − | 1.16249i | −0.111756 | − | 0.101182i | ||||
\(133\) | 6.40082 | + | 3.31334i | 0.555022 | + | 0.287303i | ||||
\(134\) | 12.7043i | 1.09748i | ||||||||
\(135\) | 0.489521 | − | 4.31588i | 0.0421313 | − | 0.371452i | ||||
\(136\) | −1.84573 | − | 1.06563i | −0.158270 | − | 0.0913773i | ||||
\(137\) | 5.61907 | + | 3.24417i | 0.480070 | + | 0.277168i | 0.720446 | − | 0.693511i | \(-0.243937\pi\) |
−0.240376 | + | 0.970680i | \(0.577271\pi\) | |||||||
\(138\) | −11.8982 | − | 2.56313i | −1.01284 | − | 0.218188i | ||||
\(139\) | − | 15.0423i | − | 1.27587i | −0.770091 | − | 0.637934i | \(-0.779789\pi\) | ||
0.770091 | − | 0.637934i | \(-0.220211\pi\) | |||||||
\(140\) | 1.19260 | + | 1.86253i | 0.100793 | + | 0.157412i | ||||
\(141\) | −13.5846 | + | 15.0044i | −1.14403 | + | 1.26360i | ||||
\(142\) | 1.33224 | + | 2.30750i | 0.111799 | + | 0.193641i | ||||
\(143\) | 1.93166 | − | 3.34573i | 0.161533 | − | 0.279784i | ||||
\(144\) | 2.73391 | + | 1.23521i | 0.227826 | + | 0.102934i | ||||
\(145\) | 5.25309 | − | 3.03287i | 0.436246 | − | 0.251866i | ||||
\(146\) | −12.4232 | −1.02815 | ||||||||
\(147\) | 12.0367 | + | 1.45513i | 0.992772 | + | 0.120017i | ||||
\(148\) | 3.52263 | 0.289558 | ||||||||
\(149\) | −4.20728 | + | 2.42908i | −0.344674 | + | 0.198998i | −0.662337 | − | 0.749206i | \(-0.730435\pi\) |
0.317663 | + | 0.948204i | \(0.397102\pi\) | |||||||
\(150\) | 7.09163 | − | 2.28274i | 0.579029 | − | 0.186385i | ||||
\(151\) | 8.45368 | − | 14.6422i | 0.687951 | − | 1.19157i | −0.284549 | − | 0.958662i | \(-0.591844\pi\) |
0.972500 | − | 0.232904i | \(-0.0748229\pi\) | |||||||
\(152\) | −1.36210 | − | 2.35922i | −0.110481 | − | 0.191358i | ||||
\(153\) | −0.633475 | − | 6.36234i | −0.0512134 | − | 0.514365i | ||||
\(154\) | 1.42670 | + | 2.22812i | 0.114966 | + | 0.179547i | ||||
\(155\) | 4.68486i | 0.376297i | ||||||||
\(156\) | −1.40916 | + | 6.54140i | −0.112823 | + | 0.523731i | ||||
\(157\) | 3.28571 | + | 1.89701i | 0.262229 | + | 0.151398i | 0.625351 | − | 0.780344i | \(-0.284956\pi\) |
−0.363122 | + | 0.931742i | \(0.618289\pi\) | |||||||
\(158\) | −4.86831 | − | 2.81072i | −0.387302 | − | 0.223609i | ||||
\(159\) | −3.05945 | + | 14.2021i | −0.242630 | + | 1.12630i | ||||
\(160\) | − | 0.835917i | − | 0.0660850i | ||||||
\(161\) | 16.5107 | + | 8.54667i | 1.30123 | + | 0.673572i | ||||
\(162\) | 1.77460 | + | 8.82331i | 0.139426 | + | 0.693225i | ||||
\(163\) | 3.12271 | + | 5.40870i | 0.244590 | + | 0.423642i | 0.962016 | − | 0.272992i | \(-0.0880134\pi\) |
−0.717426 | + | 0.696634i | \(0.754680\pi\) | |||||||
\(164\) | 0.417958 | − | 0.723925i | 0.0326371 | − | 0.0565291i | ||||
\(165\) | −1.37821 | + | 0.443635i | −0.107293 | + | 0.0345370i | ||||
\(166\) | 2.95806 | − | 1.70784i | 0.229590 | − | 0.132554i | ||||
\(167\) | 3.37801 | 0.261398 | 0.130699 | − | 0.991422i | \(-0.458278\pi\) | ||||
0.130699 | + | 0.991422i | \(0.458278\pi\) | |||||||
\(168\) | −3.53475 | − | 2.91642i | −0.272712 | − | 0.225007i | ||||
\(169\) | −1.92522 | −0.148094 | ||||||||
\(170\) | −1.54288 | + | 0.890781i | −0.118333 | + | 0.0683198i | ||||
\(171\) | 3.36496 | − | 7.44771i | 0.257325 | − | 0.569540i | ||||
\(172\) | −4.92543 | + | 8.53109i | −0.375560 | + | 0.650490i | ||||
\(173\) | −5.09256 | − | 8.82057i | −0.387180 | − | 0.670615i | 0.604889 | − | 0.796310i | \(-0.293217\pi\) |
−0.992069 | + | 0.125694i | \(0.959884\pi\) | |||||||
\(174\) | −8.43550 | + | 9.31710i | −0.639494 | + | 0.706328i | ||||
\(175\) | −11.3680 | + | 0.522570i | −0.859341 | + | 0.0395026i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | −12.2215 | − | 2.63278i | −0.918621 | − | 0.197892i | ||||
\(178\) | −0.616180 | − | 0.355752i | −0.0461846 | − | 0.0266647i | ||||
\(179\) | −16.5044 | − | 9.52883i | −1.23360 | − | 0.712218i | −0.265820 | − | 0.964023i | \(-0.585643\pi\) |
−0.967778 | + | 0.251805i | \(0.918976\pi\) | |||||||
\(180\) | 2.03686 | − | 1.46288i | 0.151819 | − | 0.109036i | ||||
\(181\) | − | 21.3997i | − | 1.59063i | −0.606199 | − | 0.795313i | \(-0.707306\pi\) | ||
0.606199 | − | 0.795313i | \(-0.292694\pi\) | |||||||
\(182\) | 4.69882 | − | 9.07732i | 0.348299 | − | 0.672856i | ||||
\(183\) | 3.43456 | + | 3.10958i | 0.253890 | + | 0.229867i | ||||
\(184\) | −3.51349 | − | 6.08555i | −0.259018 | − | 0.448633i | ||||
\(185\) | 1.47231 | − | 2.55012i | 0.108247 | − | 0.187489i | ||||
\(186\) | −2.97438 | − | 9.24028i | −0.218092 | − | 0.677530i | ||||
\(187\) | −1.84573 | + | 1.06563i | −0.134973 | + | 0.0779268i | ||||
\(188\) | −11.6858 | −0.852274 | ||||||||
\(189\) | 0.920469 | − | 13.7169i | 0.0669543 | − | 0.997756i | ||||
\(190\) | −2.27720 | −0.165206 | ||||||||
\(191\) | −7.70390 | + | 4.44785i | −0.557435 | + | 0.321835i | −0.752115 | − | 0.659032i | \(-0.770966\pi\) |
0.194680 | + | 0.980867i | \(0.437633\pi\) | |||||||
\(192\) | 0.530717 | + | 1.64874i | 0.0383012 | + | 0.118987i | ||||
\(193\) | 3.07676 | − | 5.32910i | 0.221470 | − | 0.383597i | −0.733785 | − | 0.679382i | \(-0.762248\pi\) |
0.955254 | + | 0.295785i | \(0.0955813\pi\) | |||||||
\(194\) | 4.92306 | + | 8.52699i | 0.353455 | + | 0.612202i | ||||
\(195\) | 4.14651 | + | 3.75416i | 0.296938 | + | 0.268841i | ||||
\(196\) | 4.04140 | + | 5.71551i | 0.288672 | + | 0.408251i | ||||
\(197\) | − | 19.4741i | − | 1.38748i | −0.720228 | − | 0.693738i | \(-0.755963\pi\) | ||
0.720228 | − | 0.693738i | \(-0.244037\pi\) | |||||||
\(198\) | 2.43668 | − | 1.75003i | 0.173167 | − | 0.124369i | ||||
\(199\) | −11.4944 | − | 6.63628i | −0.814815 | − | 0.470433i | 0.0338105 | − | 0.999428i | \(-0.489236\pi\) |
−0.848625 | + | 0.528995i | \(0.822569\pi\) | |||||||
\(200\) | 3.72499 | + | 2.15062i | 0.263396 | + | 0.152072i | ||||
\(201\) | −21.5109 | − | 4.63394i | −1.51726 | − | 0.326853i | ||||
\(202\) | 6.63409i | 0.466773i | ||||||||
\(203\) | 16.1682 | − | 10.3527i | 1.13478 | − | 0.726615i | ||||
\(204\) | 2.47758 | − | 2.73651i | 0.173465 | − | 0.191594i | ||||
\(205\) | −0.349379 | − | 0.605141i | −0.0244017 | − | 0.0422649i | ||||
\(206\) | −7.62843 | + | 13.2128i | −0.531498 | + | 0.920581i | ||||
\(207\) | 8.67982 | − | 19.2111i | 0.603289 | − | 1.33527i | ||||
\(208\) | −3.34573 | + | 1.93166i | −0.231985 | + | 0.133936i | ||||
\(209\) | −2.72420 | −0.188437 | ||||||||
\(210\) | −3.58865 | + | 1.33995i | −0.247641 | + | 0.0924656i | ||||
\(211\) | −16.8085 | −1.15715 | −0.578574 | − | 0.815630i | \(-0.696391\pi\) | ||||
−0.578574 | + | 0.815630i | \(0.696391\pi\) | |||||||
\(212\) | −7.26395 | + | 4.19384i | −0.498890 | + | 0.288034i | ||||
\(213\) | −4.39302 | + | 1.41408i | −0.301005 | + | 0.0968913i | ||||
\(214\) | −1.86253 | + | 3.22599i | −0.127320 | + | 0.220524i | ||||
\(215\) | 4.11725 | + | 7.13129i | 0.280794 | + | 0.486350i | ||||
\(216\) | −3.08868 | + | 4.17853i | −0.210158 | + | 0.284313i | ||||
\(217\) | 0.680901 | + | 14.8123i | 0.0462226 | + | 1.00553i | ||||
\(218\) | − | 18.0226i | − | 1.22065i | ||||||
\(219\) | 4.53141 | − | 21.0350i | 0.306204 | − | 1.42141i | ||||
\(220\) | −0.723925 | − | 0.417958i | −0.0488070 | − | 0.0281788i | ||||
\(221\) | 7.13065 | + | 4.11688i | 0.479659 | + | 0.276931i | ||||
\(222\) | −1.28490 | + | 5.96454i | −0.0862365 | + | 0.400314i | ||||
\(223\) | 5.99627i | 0.401540i | 0.979638 | + | 0.200770i | \(0.0643444\pi\) | ||||
−0.979638 | + | 0.200770i | \(0.935656\pi\) | |||||||
\(224\) | −0.121493 | − | 2.64296i | −0.00811758 | − | 0.176590i | ||||
\(225\) | 1.27846 | + | 12.8402i | 0.0852303 | + | 0.856016i | ||||
\(226\) | 6.98869 | + | 12.1048i | 0.464881 | + | 0.805197i | ||||
\(227\) | −3.71163 | + | 6.42873i | −0.246350 | + | 0.426690i | −0.962510 | − | 0.271246i | \(-0.912564\pi\) |
0.716161 | + | 0.697935i | \(0.245898\pi\) | |||||||
\(228\) | 4.49149 | − | 1.44578i | 0.297456 | − | 0.0957490i | ||||
\(229\) | −10.1281 | + | 5.84744i | −0.669281 | + | 0.386410i | −0.795804 | − | 0.605554i | \(-0.792952\pi\) |
0.126523 | + | 0.991964i | \(0.459618\pi\) | |||||||
\(230\) | −5.87398 | −0.387319 | ||||||||
\(231\) | −4.29307 | + | 1.60297i | −0.282463 | + | 0.105468i | ||||
\(232\) | −7.25640 | −0.476406 | ||||||||
\(233\) | −12.0947 | + | 6.98286i | −0.792348 | + | 0.457462i | −0.840788 | − | 0.541364i | \(-0.817908\pi\) |
0.0484405 | + | 0.998826i | \(0.484575\pi\) | |||||||
\(234\) | −10.5620 | − | 4.77201i | −0.690457 | − | 0.311956i | ||||
\(235\) | −4.88418 | + | 8.45964i | −0.318609 | + | 0.551846i | ||||
\(236\) | −3.60897 | − | 6.25091i | −0.234924 | − | 0.406900i | ||||
\(237\) | 6.53488 | − | 7.21785i | 0.424486 | − | 0.468849i | ||||
\(238\) | −4.74873 | + | 3.04067i | −0.307814 | + | 0.197097i | ||||
\(239\) | − | 9.25345i | − | 0.598556i | −0.954166 | − | 0.299278i | \(-0.903254\pi\) | ||
0.954166 | − | 0.299278i | \(-0.0967458\pi\) | |||||||
\(240\) | 1.41538 | + | 0.304905i | 0.0913625 | + | 0.0196815i | ||||
\(241\) | −4.12181 | − | 2.37973i | −0.265509 | − | 0.153292i | 0.361336 | − | 0.932436i | \(-0.382321\pi\) |
−0.626845 | + | 0.779144i | \(0.715654\pi\) | |||||||
\(242\) | −0.866025 | − | 0.500000i | −0.0556702 | − | 0.0321412i | ||||
\(243\) | −15.5870 | − | 0.213576i | −0.999906 | − | 0.0137009i | ||||
\(244\) | 2.67493i | 0.171245i | ||||||||
\(245\) | 5.82674 | − | 0.536827i | 0.372257 | − | 0.0342966i | ||||
\(246\) | 1.07330 | + | 0.971746i | 0.0684314 | + | 0.0619563i | ||||
\(247\) | 5.26222 | + | 9.11443i | 0.334827 | + | 0.579938i | ||||
\(248\) | 2.80223 | − | 4.85360i | 0.177942 | − | 0.308204i | ||||
\(249\) | 1.81275 | + | 5.63155i | 0.114879 | + | 0.356885i | ||||
\(250\) | 6.73341 | − | 3.88753i | 0.425858 | − | 0.245869i | ||||
\(251\) | −20.1964 | −1.27478 | −0.637392 | − | 0.770540i | \(-0.719987\pi\) | ||||
−0.637392 | + | 0.770540i | \(0.719987\pi\) | |||||||
\(252\) | 6.22743 | − | 4.92129i | 0.392291 | − | 0.310012i | ||||
\(253\) | −7.02699 | −0.441783 | ||||||||
\(254\) | 9.03483 | − | 5.21626i | 0.566896 | − | 0.327298i | ||||
\(255\) | −0.945506 | − | 2.93733i | −0.0592099 | − | 0.183943i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.1698 | + | 24.5429i | 0.883890 | + | 1.53094i | 0.846980 | + | 0.531624i | \(0.178418\pi\) |
0.0369100 | + | 0.999319i | \(0.488249\pi\) | |||||||
\(258\) | −12.6483 | − | 11.4515i | −0.787451 | − | 0.712941i | ||||
\(259\) | 4.28445 | − | 8.27683i | 0.266223 | − | 0.514297i | ||||
\(260\) | 3.22941i | 0.200280i | ||||||||
\(261\) | −12.6989 | − | 17.6815i | −0.786042 | − | 1.09446i | ||||
\(262\) | −9.01131 | − | 5.20268i | −0.556721 | − | 0.321423i | ||||
\(263\) | −16.5761 | − | 9.57022i | −1.02213 | − | 0.590125i | −0.107407 | − | 0.994215i | \(-0.534255\pi\) |
−0.914719 | + | 0.404090i | \(0.867588\pi\) | |||||||
\(264\) | 1.69321 | + | 0.364755i | 0.104210 | + | 0.0224491i | ||||
\(265\) | 7.01141i | 0.430707i | ||||||||
\(266\) | −7.19995 | + | 0.330971i | −0.441457 | + | 0.0202931i | ||||
\(267\) | 0.827116 | − | 0.913559i | 0.0506187 | − | 0.0559089i | ||||
\(268\) | −6.35213 | − | 11.0022i | −0.388018 | − | 0.672067i | ||||
\(269\) | −4.24434 | + | 7.35142i | −0.258782 | + | 0.448224i | −0.965916 | − | 0.258856i | \(-0.916655\pi\) |
0.707134 | + | 0.707080i | \(0.249988\pi\) | |||||||
\(270\) | 1.73400 | + | 3.98242i | 0.105528 | + | 0.242362i | ||||
\(271\) | 13.3069 | − | 7.68275i | 0.808338 | − | 0.466694i | −0.0380407 | − | 0.999276i | \(-0.512112\pi\) |
0.846378 | + | 0.532582i | \(0.178778\pi\) | |||||||
\(272\) | 2.13127 | 0.129227 | ||||||||
\(273\) | 13.6559 | + | 11.2671i | 0.826491 | + | 0.681914i | ||||
\(274\) | −6.48835 | −0.391975 | ||||||||
\(275\) | 3.72499 | − | 2.15062i | 0.224625 | − | 0.129687i | ||||
\(276\) | 11.5857 | − | 3.72934i | 0.697375 | − | 0.224480i | ||||
\(277\) | 10.1508 | − | 17.5818i | 0.609904 | − | 1.05638i | −0.381352 | − | 0.924430i | \(-0.624541\pi\) |
0.991256 | − | 0.131955i | \(-0.0421254\pi\) | |||||||
\(278\) | 7.52113 | + | 13.0270i | 0.451088 | + | 0.781307i | ||||
\(279\) | 16.7306 | − | 1.66581i | 1.00164 | − | 0.0997293i | ||||
\(280\) | −1.96408 | − | 1.01670i | −0.117377 | − | 0.0607592i | ||||
\(281\) | 11.7320i | 0.699870i | 0.936774 | + | 0.349935i | \(0.113796\pi\) | ||||
−0.936774 | + | 0.349935i | \(0.886204\pi\) | |||||||
\(282\) | 4.26245 | − | 19.7865i | 0.253825 | − | 1.17827i | ||||
\(283\) | 12.3521 | + | 7.13151i | 0.734258 | + | 0.423924i | 0.819978 | − | 0.572395i | \(-0.193986\pi\) |
−0.0857197 | + | 0.996319i | \(0.527319\pi\) | |||||||
\(284\) | −2.30750 | − | 1.33224i | −0.136925 | − | 0.0790538i | ||||
\(285\) | 0.830621 | − | 3.85578i | 0.0492017 | − | 0.228397i | ||||
\(286\) | 3.86332i | 0.228443i | ||||||||
\(287\) | −1.19260 | − | 1.86253i | −0.0703969 | − | 0.109941i | ||||
\(288\) | −2.98524 | + | 0.297229i | −0.175907 | + | 0.0175144i | ||||
\(289\) | 6.22885 | + | 10.7887i | 0.366403 | + | 0.634629i | ||||
\(290\) | −3.03287 | + | 5.25309i | −0.178096 | + | 0.308472i | ||||
\(291\) | −16.2337 | + | 5.22550i | −0.951635 | + | 0.306324i | ||||
\(292\) | 10.7588 | − | 6.21158i | 0.629610 | − | 0.363505i | ||||
\(293\) | −6.45384 | −0.377038 | −0.188519 | − | 0.982070i | \(-0.560369\pi\) | ||||
−0.188519 | + | 0.982070i | \(0.560369\pi\) | |||||||
\(294\) | −11.1517 | + | 4.75818i | −0.650379 | + | 0.277502i | ||||
\(295\) | −6.03359 | −0.351289 | ||||||||
\(296\) | −3.05069 | + | 1.76131i | −0.177317 | + | 0.102374i | ||||
\(297\) | 2.07437 | + | 4.76414i | 0.120367 | + | 0.276443i | ||||
\(298\) | 2.42908 | − | 4.20728i | 0.140713 | − | 0.243721i | ||||
\(299\) | 13.5737 | + | 23.5104i | 0.784990 | + | 1.35964i | ||||
\(300\) | −5.00016 | + | 5.52273i | −0.288684 | + | 0.318855i | ||||
\(301\) | 14.0542 | + | 21.9489i | 0.810070 | + | 1.26512i | ||||
\(302\) | 16.9074i | 0.972910i | ||||||||
\(303\) | −11.2329 | − | 2.41981i | −0.645313 | − | 0.139015i | ||||
\(304\) | 2.35922 | + | 1.36210i | 0.135311 | + | 0.0781217i | ||||
\(305\) | 1.93645 | + | 1.11801i | 0.110881 | + | 0.0640170i | ||||
\(306\) | 3.72978 | + | 5.19321i | 0.213217 | + | 0.296876i | ||||
\(307\) | 11.6367i | 0.664141i | 0.943255 | + | 0.332071i | \(0.107747\pi\) | ||||
−0.943255 | + | 0.332071i | \(0.892253\pi\) | |||||||
\(308\) | −2.34962 | − | 1.21626i | −0.133882 | − | 0.0693031i | ||||
\(309\) | −19.5896 | − | 17.7360i | −1.11441 | − | 1.00896i | ||||
\(310\) | −2.34243 | − | 4.05721i | −0.133041 | − | 0.230434i | ||||
\(311\) | 14.3269 | − | 24.8149i | 0.812405 | − | 1.40713i | −0.0987717 | − | 0.995110i | \(-0.531491\pi\) |
0.911177 | − | 0.412016i | \(-0.135175\pi\) | |||||||
\(312\) | −2.05033 | − | 6.36960i | −0.116077 | − | 0.360608i | ||||
\(313\) | 19.4240 | − | 11.2144i | 1.09791 | − | 0.633878i | 0.162238 | − | 0.986752i | \(-0.448129\pi\) |
0.935671 | + | 0.352874i | \(0.114796\pi\) | |||||||
\(314\) | −3.79402 | −0.214109 | ||||||||
\(315\) | −0.959842 | − | 6.56509i | −0.0540810 | − | 0.369901i | ||||
\(316\) | 5.62145 | 0.316231 | ||||||||
\(317\) | 9.12201 | − | 5.26659i | 0.512343 | − | 0.295801i | −0.221453 | − | 0.975171i | \(-0.571080\pi\) |
0.733796 | + | 0.679370i | \(0.237747\pi\) | |||||||
\(318\) | −4.45149 | − | 13.8291i | −0.249627 | − | 0.775498i | ||||
\(319\) | −3.62820 | + | 6.28423i | −0.203140 | + | 0.351849i | ||||
\(320\) | 0.417958 | + | 0.723925i | 0.0233646 | + | 0.0404687i | ||||
\(321\) | −4.78291 | − | 4.33034i | −0.266956 | − | 0.241696i | ||||
\(322\) | −18.5720 | + | 0.853729i | −1.03498 | + | 0.0475764i | ||||
\(323\) | − | 5.80599i | − | 0.323054i | ||||||
\(324\) | −5.94850 | − | 6.75391i | −0.330472 | − | 0.375217i | ||||
\(325\) | −14.3908 | − | 8.30853i | −0.798258 | − | 0.460875i | ||||
\(326\) | −5.40870 | − | 3.12271i | −0.299560 | − | 0.172951i | ||||
\(327\) | 30.5161 | + | 6.57384i | 1.68754 | + | 0.363534i | ||||
\(328\) | 0.835917i | 0.0461558i | ||||||||
\(329\) | −14.2130 | + | 27.4571i | −0.783589 | + | 1.51376i | ||||
\(330\) | 0.971746 | − | 1.07330i | 0.0534929 | − | 0.0590834i | ||||
\(331\) | 15.4645 | + | 26.7852i | 0.850003 | + | 1.47225i | 0.881204 | + | 0.472735i | \(0.156733\pi\) |
−0.0312013 | + | 0.999513i | \(0.509933\pi\) | |||||||
\(332\) | −1.70784 | + | 2.95806i | −0.0937296 | + | 0.162344i | ||||
\(333\) | −9.63054 | − | 4.35119i | −0.527750 | − | 0.238444i | ||||
\(334\) | −2.92544 | + | 1.68901i | −0.160073 | + | 0.0924183i | ||||
\(335\) | −10.6197 | −0.580216 | ||||||||
\(336\) | 4.51940 | + | 0.758320i | 0.246553 | + | 0.0413697i | ||||
\(337\) | 8.74219 | 0.476217 | 0.238109 | − | 0.971239i | \(-0.423473\pi\) | ||||
0.238109 | + | 0.971239i | \(0.423473\pi\) | |||||||
\(338\) | 1.66729 | − | 0.962611i | 0.0906887 | − | 0.0523591i | ||||
\(339\) | −23.0451 | + | 7.41804i | −1.25164 | + | 0.402892i | ||||
\(340\) | 0.890781 | − | 1.54288i | 0.0483094 | − | 0.0836743i | ||||
\(341\) | −2.80223 | − | 4.85360i | −0.151749 | − | 0.262837i | ||||
\(342\) | 0.809711 | + | 8.13238i | 0.0437842 | + | 0.439749i | ||||
\(343\) | 18.3447 | − | 2.54418i | 0.990519 | − | 0.137373i | ||||
\(344\) | − | 9.85086i | − | 0.531123i | ||||||
\(345\) | 2.14256 | − | 9.94587i | 0.115352 | − | 0.535467i | ||||
\(346\) | 8.82057 | + | 5.09256i | 0.474197 | + | 0.273778i | ||||
\(347\) | 1.10854 | + | 0.640018i | 0.0595098 | + | 0.0343580i | 0.529460 | − | 0.848335i | \(-0.322395\pi\) |
−0.469950 | + | 0.882693i | \(0.655728\pi\) | |||||||
\(348\) | 2.64681 | − | 12.2866i | 0.141884 | − | 0.658631i | ||||
\(349\) | 13.1540i | 0.704117i | 0.935978 | + | 0.352058i | \(0.114518\pi\) | ||||
−0.935978 | + | 0.352058i | \(0.885482\pi\) | |||||||
\(350\) | 9.58370 | − | 6.13657i | 0.512271 | − | 0.328013i | ||||
\(351\) | 11.9325 | − | 16.1430i | 0.636912 | − | 0.861648i | ||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | −7.51019 | + | 13.0080i | −0.399727 | + | 0.692347i | −0.993692 | − | 0.112143i | \(-0.964228\pi\) |
0.593965 | + | 0.804491i | \(0.297562\pi\) | |||||||
\(354\) | 11.9005 | − | 3.83068i | 0.632504 | − | 0.203598i | ||||
\(355\) | −1.92888 | + | 1.11364i | −0.102374 | + | 0.0591059i | ||||
\(356\) | 0.711503 | 0.0377096 | ||||||||
\(357\) | −3.41637 | − | 9.14968i | −0.180813 | − | 0.484253i | ||||
\(358\) | 19.0577 | 1.00723 | ||||||||
\(359\) | −27.0726 | + | 15.6304i | −1.42884 | + | 0.824940i | −0.997029 | − | 0.0770249i | \(-0.975458\pi\) |
−0.431809 | + | 0.901965i | \(0.642125\pi\) | |||||||
\(360\) | −1.03253 | + | 2.28532i | −0.0544193 | + | 0.120447i | ||||
\(361\) | −5.78937 | + | 10.0275i | −0.304704 | + | 0.527763i | ||||
\(362\) | 10.6998 | + | 18.5327i | 0.562371 | + | 0.974056i | ||||
\(363\) | 1.16249 | − | 1.28398i | 0.0610150 | − | 0.0673917i | ||||
\(364\) | 0.469366 | + | 10.2106i | 0.0246014 | + | 0.535181i | ||||
\(365\) | − | 10.3847i | − | 0.543562i | ||||||
\(366\) | −4.52921 | − | 0.975693i | −0.236746 | − | 0.0510003i | ||||
\(367\) | −8.94931 | − | 5.16689i | −0.467150 | − | 0.269709i | 0.247896 | − | 0.968787i | \(-0.420261\pi\) |
−0.715046 | + | 0.699077i | \(0.753594\pi\) | |||||||
\(368\) | 6.08555 | + | 3.51349i | 0.317231 | + | 0.183154i | ||||
\(369\) | −2.03686 | + | 1.46288i | −0.106035 | + | 0.0761544i | ||||
\(370\) | 2.94462i | 0.153084i | ||||||||
\(371\) | 1.01904 | + | 22.1683i | 0.0529061 | + | 1.15092i | ||||
\(372\) | 7.19603 | + | 6.51513i | 0.373097 | + | 0.337794i | ||||
\(373\) | −6.99037 | − | 12.1077i | −0.361947 | − | 0.626911i | 0.626334 | − | 0.779555i | \(-0.284555\pi\) |
−0.988281 | + | 0.152644i | \(0.951221\pi\) | |||||||
\(374\) | 1.06563 | − | 1.84573i | 0.0551026 | − | 0.0954405i | ||||
\(375\) | 4.12636 | + | 12.8191i | 0.213084 | + | 0.661973i | ||||
\(376\) | 10.1202 | − | 5.84290i | 0.521909 | − | 0.301324i | ||||
\(377\) | 28.0338 | 1.44381 | ||||||||
\(378\) | 6.06129 | + | 12.3394i | 0.311759 | + | 0.634670i | ||||
\(379\) | −2.40372 | −0.123471 | −0.0617353 | − | 0.998093i | \(-0.519663\pi\) | ||||
−0.0617353 | + | 0.998093i | \(0.519663\pi\) | |||||||
\(380\) | 1.97212 | − | 1.13860i | 0.101167 | − | 0.0584090i | ||||
\(381\) | 5.53672 | + | 17.2005i | 0.283655 | + | 0.881209i | ||||
\(382\) | 4.44785 | − | 7.70390i | 0.227572 | − | 0.394166i | ||||
\(383\) | −11.4425 | − | 19.8189i | −0.584683 | − | 1.01270i | −0.994915 | − | 0.100720i | \(-0.967886\pi\) |
0.410232 | − | 0.911981i | \(-0.365448\pi\) | |||||||
\(384\) | −1.28398 | − | 1.16249i | −0.0655230 | − | 0.0593231i | ||||
\(385\) | −1.86253 | + | 1.19260i | −0.0949232 | + | 0.0607805i | ||||
\(386\) | 6.15351i | 0.313206i | ||||||||
\(387\) | 24.0034 | − | 17.2393i | 1.22016 | − | 0.876322i | ||||
\(388\) | −8.52699 | − | 4.92306i | −0.432892 | − | 0.249930i | ||||
\(389\) | 15.3333 | + | 8.85268i | 0.777428 | + | 0.448849i | 0.835518 | − | 0.549463i | \(-0.185168\pi\) |
−0.0580897 | + | 0.998311i | \(0.518501\pi\) | |||||||
\(390\) | −5.46807 | − | 1.17794i | −0.276886 | − | 0.0596475i | ||||
\(391\) | − | 14.9764i | − | 0.757388i | ||||||
\(392\) | −6.35771 | − | 2.92908i | −0.321113 | − | 0.147941i | ||||
\(393\) | 12.0961 | − | 13.3603i | 0.610170 | − | 0.673939i | ||||
\(394\) | 9.73707 | + | 16.8651i | 0.490547 | + | 0.849652i | ||||
\(395\) | 2.34953 | − | 4.06951i | 0.118218 | − | 0.204759i | ||||
\(396\) | −1.23521 | + | 2.73391i | −0.0620717 | + | 0.137384i | ||||
\(397\) | −31.0739 | + | 17.9405i | −1.55955 | + | 0.900408i | −0.562254 | + | 0.826965i | \(0.690066\pi\) |
−0.997299 | + | 0.0734435i | \(0.976601\pi\) | |||||||
\(398\) | 13.2726 | 0.665293 | ||||||||
\(399\) | 2.06581 | − | 12.3117i | 0.103420 | − | 0.616358i | ||||
\(400\) | −4.30124 | −0.215062 | ||||||||
\(401\) | 22.4661 | − | 12.9708i | 1.12191 | − | 0.647733i | 0.180019 | − | 0.983663i | \(-0.442384\pi\) |
0.941887 | + | 0.335931i | \(0.109051\pi\) | |||||||
\(402\) | 20.9460 | − | 6.74236i | 1.04469 | − | 0.336279i | ||||
\(403\) | −10.8259 | + | 18.7510i | −0.539276 | + | 0.934054i | ||||
\(404\) | −3.31704 | − | 5.74529i | −0.165029 | − | 0.285839i | ||||
\(405\) | −7.37555 | + | 1.48342i | −0.366494 | + | 0.0737117i | ||||
\(406\) | −8.82570 | + | 17.0498i | −0.438012 | + | 0.846165i | ||||
\(407\) | 3.52263i | 0.174610i | ||||||||
\(408\) | −0.777390 | + | 3.60868i | −0.0384865 | + | 0.178656i | ||||
\(409\) | 8.55454 | + | 4.93897i | 0.422995 | + | 0.244216i | 0.696358 | − | 0.717695i | \(-0.254803\pi\) |
−0.273363 | + | 0.961911i | \(0.588136\pi\) | |||||||
\(410\) | 0.605141 | + | 0.349379i | 0.0298858 | + | 0.0172546i | ||||
\(411\) | 2.36666 | − | 10.9861i | 0.116739 | − | 0.541905i | ||||
\(412\) | − | 15.2569i | − | 0.751651i | ||||||
\(413\) | −19.0767 | + | 0.876927i | −0.938703 | + | 0.0431508i | ||||
\(414\) | 2.08863 | + | 20.9772i | 0.102650 | + | 1.03098i | ||||
\(415\) | 1.42761 | + | 2.47269i | 0.0700785 | + | 0.121380i | ||||
\(416\) | 1.93166 | − | 3.34573i | 0.0947074 | − | 0.164038i | ||||
\(417\) | −24.8008 | + | 7.98319i | −1.21450 | + | 0.390939i | ||||
\(418\) | 2.35922 | − | 1.36210i | 0.115393 | − | 0.0666224i | ||||
\(419\) | 7.14212 | 0.348916 | 0.174458 | − | 0.984665i | \(-0.444183\pi\) | ||||
0.174458 | + | 0.984665i | \(0.444183\pi\) | |||||||
\(420\) | 2.43789 | − | 2.95476i | 0.118957 | − | 0.144178i | ||||
\(421\) | 2.83262 | 0.138053 | 0.0690267 | − | 0.997615i | \(-0.478011\pi\) | ||||
0.0690267 | + | 0.997615i | \(0.478011\pi\) | |||||||
\(422\) | 14.5566 | − | 8.40427i | 0.708606 | − | 0.409114i | ||||
\(423\) | 31.9479 | + | 14.4344i | 1.55336 | + | 0.701826i | ||||
\(424\) | 4.19384 | − | 7.26395i | 0.203671 | − | 0.352769i | ||||
\(425\) | 4.58355 | + | 7.93894i | 0.222335 | + | 0.385095i | ||||
\(426\) | 3.09743 | − | 3.42114i | 0.150071 | − | 0.165755i | ||||
\(427\) | 6.28506 | + | 3.25342i | 0.304155 | + | 0.157444i | ||||
\(428\) | − | 3.72505i | − | 0.180057i | ||||||
\(429\) | −6.54140 | − | 1.40916i | −0.315822 | − | 0.0680351i | ||||
\(430\) | −7.13129 | − | 4.11725i | −0.343901 | − | 0.198551i | ||||
\(431\) | 22.0931 | + | 12.7555i | 1.06419 | + | 0.614410i | 0.926588 | − | 0.376078i | \(-0.122728\pi\) |
0.137601 | + | 0.990488i | \(0.456061\pi\) | |||||||
\(432\) | 0.585609 | − | 5.16305i | 0.0281752 | − | 0.248407i | ||||
\(433\) | 17.6085i | 0.846213i | 0.906080 | + | 0.423106i | \(0.139060\pi\) | ||||
−0.906080 | + | 0.423106i | \(0.860940\pi\) | |||||||
\(434\) | −7.99585 | − | 12.4874i | −0.383813 | − | 0.599415i | ||||
\(435\) | −7.78832 | − | 7.05138i | −0.373421 | − | 0.338088i | ||||
\(436\) | 9.01132 | + | 15.6081i | 0.431564 | + | 0.747491i | ||||
\(437\) | 9.57145 | − | 16.5782i | 0.457865 | − | 0.793045i | ||||
\(438\) | 6.59319 | + | 20.4826i | 0.315035 | + | 0.978695i | ||||
\(439\) | 20.3880 | − | 11.7710i | 0.973068 | − | 0.561801i | 0.0728977 | − | 0.997339i | \(-0.476775\pi\) |
0.900170 | + | 0.435538i | \(0.143442\pi\) | |||||||
\(440\) | 0.835917 | 0.0398508 | ||||||||
\(441\) | −3.98896 | − | 20.6177i | −0.189950 | − | 0.981794i | ||||
\(442\) | −8.23376 | −0.391640 | ||||||||
\(443\) | −8.86868 | + | 5.12033i | −0.421363 | + | 0.243274i | −0.695661 | − | 0.718371i | \(-0.744888\pi\) |
0.274297 | + | 0.961645i | \(0.411555\pi\) | |||||||
\(444\) | −1.86952 | − | 5.80789i | −0.0887235 | − | 0.275630i | ||||
\(445\) | 0.297379 | − | 0.515075i | 0.0140971 | − | 0.0244169i | ||||
\(446\) | −2.99814 | − | 5.19292i | −0.141966 | − | 0.245892i | ||||
\(447\) | 6.23779 | + | 5.64756i | 0.295037 | + | 0.267120i | ||||
\(448\) | 1.42670 | + | 2.22812i | 0.0674051 | + | 0.105269i | ||||
\(449\) | − | 17.4205i | − | 0.822123i | −0.911608 | − | 0.411061i | \(-0.865158\pi\) | ||
0.911608 | − | 0.411061i | \(-0.134842\pi\) | |||||||
\(450\) | −7.52729 | − | 10.4807i | −0.354840 | − | 0.494067i | ||||
\(451\) | 0.723925 | + | 0.417958i | 0.0340883 | + | 0.0196809i | ||||
\(452\) | −12.1048 | − | 6.98869i | −0.569360 | − | 0.328720i | ||||
\(453\) | −28.6277 | − | 6.16704i | −1.34505 | − | 0.289753i | ||||
\(454\) | − | 7.42326i | − | 0.348391i | ||||||
\(455\) | 7.58788 | + | 3.92782i | 0.355725 | + | 0.184139i | ||||
\(456\) | −3.16686 | + | 3.49783i | −0.148302 | + | 0.163801i | ||||
\(457\) | −3.44330 | − | 5.96396i | −0.161071 | − | 0.278982i | 0.774182 | − | 0.632963i | \(-0.218161\pi\) |
−0.935253 | + | 0.353980i | \(0.884828\pi\) | |||||||
\(458\) | 5.84744 | − | 10.1281i | 0.273233 | − | 0.473253i | ||||
\(459\) | −10.1536 | + | 4.42104i | −0.473931 | + | 0.206356i | ||||
\(460\) | 5.08701 | − | 2.93699i | 0.237183 | − | 0.136938i | ||||
\(461\) | 6.62247 | 0.308439 | 0.154220 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154220 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(462\) | 2.91642 | − | 3.53475i | 0.135684 | − | 0.164452i | ||||
\(463\) | 21.3829 | 0.993749 | 0.496874 | − | 0.867822i | \(-0.334481\pi\) | ||||
0.496874 | + | 0.867822i | \(0.334481\pi\) | |||||||
\(464\) | 6.28423 | − | 3.62820i | 0.291738 | − | 0.168435i | ||||
\(465\) | 7.72411 | − | 2.48633i | 0.358197 | − | 0.115301i | ||||
\(466\) | 6.98286 | − | 12.0947i | 0.323475 | − | 0.560275i | ||||
\(467\) | −12.4871 | − | 21.6284i | −0.577836 | − | 1.00084i | −0.995727 | − | 0.0923444i | \(-0.970564\pi\) |
0.417891 | − | 0.908497i | \(-0.362769\pi\) | |||||||
\(468\) | 11.5329 | − | 1.14829i | 0.533110 | − | 0.0530798i | ||||
\(469\) | −33.5768 | + | 1.54348i | −1.55043 | + | 0.0712711i | ||||
\(470\) | − | 9.76835i | − | 0.450581i | ||||||
\(471\) | 1.38389 | − | 6.42406i | 0.0637661 | − | 0.296005i | ||||
\(472\) | 6.25091 | + | 3.60897i | 0.287722 | + | 0.166116i | ||||
\(473\) | −8.53109 | − | 4.92543i | −0.392260 | − | 0.226471i | ||||
\(474\) | −2.05045 | + | 9.51828i | −0.0941803 | + | 0.437189i | ||||
\(475\) | 11.7174i | 0.537633i | ||||||||
\(476\) | 2.59218 | − | 5.00766i | 0.118813 | − | 0.229526i | ||||
\(477\) | 25.0392 | − | 2.49307i | 1.14647 | − | 0.114150i | ||||
\(478\) | 4.62673 | + | 8.01372i | 0.211622 | + | 0.366539i | ||||
\(479\) | −14.4998 | + | 25.1144i | −0.662512 | + | 1.14750i | 0.317442 | + | 0.948278i | \(0.397176\pi\) |
−0.979954 | + | 0.199226i | \(0.936157\pi\) | |||||||
\(480\) | −1.37821 | + | 0.443635i | −0.0629063 | + | 0.0202491i | ||||
\(481\) | 11.7858 | − | 6.80452i | 0.537385 | − | 0.310259i | ||||
\(482\) | 4.75945 | 0.216787 | ||||||||
\(483\) | 5.32870 | − | 31.7577i | 0.242464 | − | 1.44503i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −7.12785 | + | 4.11527i | −0.323659 | + | 0.186865i | ||||
\(486\) | 13.6055 | − | 7.60853i | 0.617159 | − | 0.345130i | ||||
\(487\) | −7.81129 | + | 13.5296i | −0.353963 | + | 0.613082i | −0.986940 | − | 0.161088i | \(-0.948500\pi\) |
0.632977 | + | 0.774171i | \(0.281833\pi\) | |||||||
\(488\) | −1.33746 | − | 2.31656i | −0.0605441 | − | 0.104866i | ||||
\(489\) | 7.26025 | − | 8.01903i | 0.328320 | − | 0.362633i | ||||
\(490\) | −4.77769 | + | 3.37828i | −0.215834 | + | 0.152615i | ||||
\(491\) | − | 32.5285i | − | 1.46799i | −0.679154 | − | 0.733996i | \(-0.737653\pi\) | ||
0.679154 | − | 0.733996i | \(-0.262347\pi\) | |||||||
\(492\) | −1.41538 | − | 0.304905i | −0.0638103 | − | 0.0137462i | ||||
\(493\) | −13.3934 | − | 7.73266i | −0.603207 | − | 0.348262i | ||||
\(494\) | −9.11443 | − | 5.26222i | −0.410078 | − | 0.236759i | ||||
\(495\) | 1.46288 | + | 2.03686i | 0.0657515 | + | 0.0915501i | ||||
\(496\) | 5.60445i | 0.251647i | ||||||||
\(497\) | −5.93678 | + | 3.80140i | −0.266301 | + | 0.170516i | ||||
\(498\) | −4.38567 | − | 3.97069i | −0.196526 | − | 0.177931i | ||||
\(499\) | 7.65028 | + | 13.2507i | 0.342473 | + | 0.593181i | 0.984891 | − | 0.173173i | \(-0.0554020\pi\) |
−0.642418 | + | 0.766354i | \(0.722069\pi\) | |||||||
\(500\) | −3.88753 | + | 6.73341i | −0.173856 | + | 0.301127i | ||||
\(501\) | −1.79277 | − | 5.56946i | −0.0800950 | − | 0.248825i | ||||
\(502\) | 17.4906 | − | 10.0982i | 0.780642 | − | 0.450704i | ||||
\(503\) | 31.3069 | 1.39590 | 0.697952 | − | 0.716145i | \(-0.254095\pi\) | ||||
0.697952 | + | 0.716145i | \(0.254095\pi\) | |||||||
\(504\) | −2.93247 | + | 7.37568i | −0.130622 | + | 0.328539i | ||||
\(505\) | −5.54554 | −0.246773 | ||||||||
\(506\) | 6.08555 | − | 3.51349i | 0.270536 | − | 0.156194i | ||||
\(507\) | 1.02175 | + | 3.17419i | 0.0453774 | + | 0.140971i | ||||
\(508\) | −5.21626 | + | 9.03483i | −0.231434 | + | 0.400856i | ||||
\(509\) | −13.5445 | − | 23.4597i | −0.600348 | − | 1.03983i | −0.992768 | − | 0.120048i | \(-0.961695\pi\) |
0.392420 | − | 0.919786i | \(-0.371638\pi\) | |||||||
\(510\) | 2.28750 | + | 2.07105i | 0.101292 | + | 0.0917076i | ||||
\(511\) | −1.50933 | − | 32.8339i | −0.0667687 | − | 1.45249i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −14.0652 | − | 1.59532i | −0.620992 | − | 0.0704349i | ||||
\(514\) | −24.5429 | − | 14.1698i | −1.08254 | − | 0.625005i | ||||
\(515\) | −11.0448 | − | 6.37673i | −0.486693 | − | 0.280992i | ||||
\(516\) | 16.6796 | + | 3.59315i | 0.734276 | + | 0.158180i | ||||
\(517\) | − | 11.6858i | − | 0.513941i | ||||||
\(518\) | 0.427974 | + | 9.31017i | 0.0188041 | + | 0.409065i | ||||
\(519\) | −11.8401 | + | 13.0775i | −0.519723 | + | 0.574040i | ||||
\(520\) | −1.61471 | − | 2.79675i | −0.0708096 | − | 0.122646i | ||||
\(521\) | 7.87689 | − | 13.6432i | 0.345093 | − | 0.597718i | −0.640278 | − | 0.768143i | \(-0.721181\pi\) |
0.985371 | + | 0.170425i | \(0.0545142\pi\) | |||||||
\(522\) | 19.8383 | + | 8.96319i | 0.868300 | + | 0.392308i | ||||
\(523\) | 15.4013 | − | 8.89196i | 0.673453 | − | 0.388818i | −0.123931 | − | 0.992291i | \(-0.539550\pi\) |
0.797384 | + | 0.603473i | \(0.206217\pi\) | |||||||
\(524\) | 10.4054 | 0.454561 | ||||||||
\(525\) | 6.89478 | + | 18.4655i | 0.300913 | + | 0.805903i | ||||
\(526\) | 19.1404 | 0.834563 | ||||||||
\(527\) | 10.3443 | − | 5.97229i | 0.450605 | − | 0.260157i | ||||
\(528\) | −1.64874 | + | 0.530717i | −0.0717521 | + | 0.0230965i | ||||
\(529\) | 13.1893 | − | 22.8445i | 0.573447 | − | 0.993239i | ||||
\(530\) | −3.50570 | − | 6.07206i | −0.152278 | − | 0.263753i | ||||
\(531\) | 2.14538 | + | 21.5473i | 0.0931016 | + | 0.935071i | ||||
\(532\) | 6.06985 | − | 3.88660i | 0.263161 | − | 0.168506i | ||||
\(533\) | − | 3.22941i | − | 0.139881i | ||||||
\(534\) | −0.259524 | + | 1.20472i | −0.0112307 | + | 0.0521335i | ||||
\(535\) | −2.69666 | − | 1.55692i | −0.116587 | − | 0.0673114i | ||||
\(536\) | 11.0022 | + | 6.35213i | 0.475223 | + | 0.274370i | ||||
\(537\) | −6.95137 | + | 32.2686i | −0.299974 | + | 1.39249i | ||||
\(538\) | − | 8.48869i | − | 0.365973i | ||||||
\(539\) | −5.71551 | + | 4.04140i | −0.246184 | + | 0.174076i | ||||
\(540\) | −3.49290 | − | 2.58188i | −0.150311 | − | 0.111106i | ||||
\(541\) | 17.3541 | + | 30.0582i | 0.746111 | + | 1.29230i | 0.949674 | + | 0.313241i | \(0.101415\pi\) |
−0.203563 | + | 0.979062i | \(0.565252\pi\) | |||||||
\(542\) | −7.68275 | + | 13.3069i | −0.330002 | + | 0.571581i | ||||
\(543\) | −35.2825 | + | 11.3572i | −1.51412 | + | 0.487383i | ||||
\(544\) | −1.84573 | + | 1.06563i | −0.0791351 | + | 0.0456887i | ||||
\(545\) | 15.0654 | 0.645332 | ||||||||
\(546\) | −17.4599 | − | 2.92963i | −0.747213 | − | 0.125377i | ||||
\(547\) | −9.06564 | −0.387619 | −0.193809 | − | 0.981039i | \(-0.562084\pi\) | ||||
−0.193809 | + | 0.981039i | \(0.562084\pi\) | |||||||
\(548\) | 5.61907 | − | 3.24417i | 0.240035 | − | 0.138584i | ||||
\(549\) | 3.30410 | − | 7.31301i | 0.141016 | − | 0.312111i | ||||
\(550\) | −2.15062 | + | 3.72499i | −0.0917028 | + | 0.158834i | ||||
\(551\) | −9.88393 | − | 17.1195i | −0.421070 | − | 0.729314i | ||||
\(552\) | −8.16881 | + | 9.02254i | −0.347688 | + | 0.384025i | ||||
\(553\) | 6.83716 | − | 13.2082i | 0.290746 | − | 0.561672i | ||||
\(554\) | 20.3017i | 0.862535i | ||||||||
\(555\) | −4.98586 | − | 1.07407i | −0.211638 | − | 0.0455916i | ||||
\(556\) | −13.0270 | − | 7.52113i | −0.552467 | − | 0.318967i | ||||
\(557\) | −5.76379 | − | 3.32773i | −0.244220 | − | 0.141000i | 0.372895 | − | 0.927874i | \(-0.378365\pi\) |
−0.617115 | + | 0.786873i | \(0.711699\pi\) | |||||||
\(558\) | −13.6563 | + | 9.80795i | −0.578115 | + | 0.415204i | ||||
\(559\) | 38.0570i | 1.60964i | ||||||||
\(560\) | 2.20930 | − | 0.101558i | 0.0933598 | − | 0.00429161i | ||||
\(561\) | 2.73651 | + | 2.47758i | 0.115536 | + | 0.104603i | ||||
\(562\) | −5.86598 | − | 10.1602i | −0.247441 | − | 0.428581i | ||||
\(563\) | −20.7720 | + | 35.9782i | −0.875435 | + | 1.51630i | −0.0191372 | + | 0.999817i | \(0.506092\pi\) |
−0.856298 | + | 0.516482i | \(0.827241\pi\) | |||||||
\(564\) | 6.20185 | + | 19.2668i | 0.261145 | + | 0.811279i | ||||
\(565\) | −10.1186 | + | 5.84197i | −0.425692 | + | 0.245773i | ||||
\(566\) | −14.2630 | −0.599519 | ||||||||
\(567\) | −23.1041 | + | 5.76217i | −0.970279 | + | 0.241988i | ||||
\(568\) | 2.66448 | 0.111799 | ||||||||
\(569\) | 19.0011 | − | 10.9703i | 0.796566 | − | 0.459898i | −0.0457028 | − | 0.998955i | \(-0.514553\pi\) |
0.842269 | + | 0.539057i | \(0.181219\pi\) | |||||||
\(570\) | 1.20855 | + | 3.75451i | 0.0506206 | + | 0.157259i | ||||
\(571\) | −12.8656 | + | 22.2839i | −0.538409 | + | 0.932551i | 0.460581 | + | 0.887618i | \(0.347641\pi\) |
−0.998990 | + | 0.0449337i | \(0.985692\pi\) | |||||||
\(572\) | −1.93166 | − | 3.34573i | −0.0807667 | − | 0.139892i | ||||
\(573\) | 11.4219 | + | 10.3412i | 0.477158 | + | 0.432009i | ||||
\(574\) | 1.96408 | + | 1.01670i | 0.0819793 | + | 0.0424361i | ||||
\(575\) | 30.2248i | 1.26046i | ||||||||
\(576\) | 2.43668 | − | 1.75003i | 0.101528 | − | 0.0729178i | ||||
\(577\) | 9.60562 | + | 5.54581i | 0.399887 | + | 0.230875i | 0.686435 | − | 0.727191i | \(-0.259175\pi\) |
−0.286548 | + | 0.958066i | \(0.592508\pi\) | |||||||
\(578\) | −10.7887 | − | 6.22885i | −0.448750 | − | 0.259086i | ||||
\(579\) | −10.4192 | − | 2.24452i | −0.433006 | − | 0.0932792i | ||||
\(580\) | − | 6.06575i | − | 0.251866i | ||||||
\(581\) | 4.87312 | + | 7.61054i | 0.202171 | + | 0.315738i | ||||
\(582\) | 11.4460 | − | 12.6423i | 0.474453 | − | 0.524038i | ||||
\(583\) | −4.19384 | − | 7.26395i | −0.173691 | − | 0.300842i | ||||
\(584\) | −6.21158 | + | 10.7588i | −0.257037 | + | 0.445201i | ||||
\(585\) | 3.98901 | − | 8.82892i | 0.164925 | − | 0.365031i | ||||
\(586\) | 5.58919 | − | 3.22692i | 0.230887 | − | 0.133303i | ||||
\(587\) | −39.3634 | −1.62470 | −0.812351 | − | 0.583169i | \(-0.801813\pi\) | ||||
−0.812351 | + | 0.583169i | \(0.801813\pi\) | |||||||
\(588\) | 7.27854 | − | 9.69654i | 0.300162 | − | 0.399878i | ||||
\(589\) | 15.2676 | 0.629092 | ||||||||
\(590\) | 5.22524 | − | 3.01680i | 0.215120 | − | 0.124200i | ||||
\(591\) | −32.1078 | + | 10.3353i | −1.32074 | + | 0.425136i | ||||
\(592\) | 1.76131 | − | 3.05069i | 0.0723896 | − | 0.125382i | ||||
\(593\) | 4.17903 | + | 7.23829i | 0.171612 | + | 0.297241i | 0.938984 | − | 0.343962i | \(-0.111769\pi\) |
−0.767371 | + | 0.641203i | \(0.778436\pi\) | |||||||
\(594\) | −4.17853 | − | 3.08868i | −0.171447 | − | 0.126730i | ||||
\(595\) | −2.54175 | − | 3.96954i | −0.104201 | − | 0.162735i | ||||
\(596\) | 4.85815i | 0.198998i | ||||||||
\(597\) | −4.84123 | + | 22.4732i | −0.198138 | + | 0.919767i | ||||
\(598\) | −23.5104 | − | 13.5737i | −0.961412 | − | 0.555072i | ||||
\(599\) | 10.5034 | + | 6.06417i | 0.429159 | + | 0.247775i | 0.698988 | − | 0.715133i | \(-0.253634\pi\) |
−0.269829 | + | 0.962908i | \(0.586967\pi\) | |||||||
\(600\) | 1.56890 | − | 7.28290i | 0.0640500 | − | 0.297323i | ||||
\(601\) | − | 41.6196i | − | 1.69770i | −0.528634 | − | 0.848850i | \(-0.677295\pi\) | ||
0.528634 | − | 0.848850i | \(-0.322705\pi\) | |||||||
\(602\) | −23.1457 | − | 11.9812i | −0.943350 | − | 0.488319i | ||||
\(603\) | 3.77607 | + | 37.9252i | 0.153774 | + | 1.54443i | ||||
\(604\) | −8.45368 | − | 14.6422i | −0.343975 | − | 0.595783i | ||||
\(605\) | 0.417958 | − | 0.723925i | 0.0169924 | − | 0.0294317i | ||||
\(606\) | 10.9379 | − | 3.52082i | 0.444321 | − | 0.143024i | ||||
\(607\) | −18.6709 | + | 10.7797i | −0.757830 | + | 0.437533i | −0.828516 | − | 0.559965i | \(-0.810814\pi\) |
0.0706862 | + | 0.997499i | \(0.477481\pi\) | |||||||
\(608\) | −2.72420 | −0.110481 | ||||||||
\(609\) | −25.6496 | − | 21.1627i | −1.03937 | − | 0.857557i | ||||
\(610\) | −2.23602 | −0.0905337 | ||||||||
\(611\) | −39.0975 | + | 22.5730i | −1.58172 | + | 0.913204i | ||||
\(612\) | −5.82669 | − | 2.63257i | −0.235530 | − | 0.106415i | ||||
\(613\) | 2.42873 | − | 4.20669i | 0.0980955 | − | 0.169906i | −0.812801 | − | 0.582542i | \(-0.802058\pi\) |
0.910896 | + | 0.412635i | \(0.135392\pi\) | |||||||
\(614\) | −5.81835 | − | 10.0777i | −0.234809 | − | 0.406702i | ||||
\(615\) | −0.812299 | + | 0.897193i | −0.0327551 | + | 0.0361783i | ||||
\(616\) | 2.64296 | − | 0.121493i | 0.106488 | − | 0.00489509i | ||||
\(617\) | 20.6685i | 0.832084i | 0.909345 | + | 0.416042i | \(0.136583\pi\) | ||||
−0.909345 | + | 0.416042i | \(0.863417\pi\) | |||||||
\(618\) | 25.8330 | + | 5.56501i | 1.03916 | + | 0.223858i | ||||
\(619\) | −15.9542 | − | 9.21116i | −0.641253 | − | 0.370228i | 0.143844 | − | 0.989600i | \(-0.454054\pi\) |
−0.785097 | + | 0.619373i | \(0.787387\pi\) | |||||||
\(620\) | 4.05721 | + | 2.34243i | 0.162941 | + | 0.0940742i | ||||
\(621\) | −36.2807 | − | 4.11507i | −1.45589 | − | 0.165132i | ||||
\(622\) | 28.6538i | 1.14891i | ||||||||
\(623\) | 0.865376 | − | 1.67176i | 0.0346706 | − | 0.0669777i | ||||
\(624\) | 4.96044 | + | 4.49107i | 0.198576 | + | 0.179787i | ||||
\(625\) | −7.50345 | − | 12.9964i | −0.300138 | − | 0.519854i | ||||
\(626\) | −11.2144 | + | 19.4240i | −0.448219 | + | 0.776338i | ||||
\(627\) | 1.44578 | + | 4.49149i | 0.0577388 | + | 0.179373i | ||||
\(628\) | 3.28571 | − | 1.89701i | 0.131114 | − | 0.0756989i | ||||
\(629\) | −7.50766 | −0.299350 | ||||||||
\(630\) | 4.11379 | + | 5.20561i | 0.163897 | + | 0.207397i | ||||
\(631\) | −21.1539 | −0.842125 | −0.421063 | − | 0.907032i | \(-0.638343\pi\) | ||||
−0.421063 | + | 0.907032i | \(0.638343\pi\) | |||||||
\(632\) | −4.86831 | + | 2.81072i | −0.193651 | + | 0.111805i | ||||
\(633\) | 8.92059 | + | 27.7129i | 0.354561 | + | 1.10149i | ||||
\(634\) | −5.26659 | + | 9.12201i | −0.209163 | + | 0.362281i | ||||
\(635\) | 4.36036 | + | 7.55237i | 0.173036 | + | 0.299707i | ||||
\(636\) | 10.7697 | + | 9.75061i | 0.427045 | + | 0.386637i | ||||
\(637\) | 24.5619 | + | 11.3160i | 0.973176 | + | 0.448354i | ||||
\(638\) | − | 7.25640i | − | 0.287284i | ||||||
\(639\) | 4.66291 | + | 6.49247i | 0.184462 | + | 0.256838i | ||||
\(640\) | −0.723925 | − | 0.417958i | −0.0286157 | − | 0.0165213i | ||||
\(641\) | 29.6480 | + | 17.1173i | 1.17102 | + | 0.676091i | 0.953921 | − | 0.300058i | \(-0.0970059\pi\) |
0.217103 | + | 0.976149i | \(0.430339\pi\) | |||||||
\(642\) | 6.30729 | + | 1.35873i | 0.248929 | + | 0.0536248i | ||||
\(643\) | − | 37.5930i | − | 1.48252i | −0.671215 | − | 0.741262i | \(-0.734227\pi\) | ||
0.671215 | − | 0.741262i | \(-0.265773\pi\) | |||||||
\(644\) | 15.6570 | − | 10.0254i | 0.616972 | − | 0.395055i | ||||
\(645\) | 9.57253 | − | 10.5730i | 0.376918 | − | 0.416310i | ||||
\(646\) | 2.90300 | + | 5.02814i | 0.114217 | + | 0.197829i | ||||
\(647\) | 20.3948 | − | 35.3248i | 0.801802 | − | 1.38876i | −0.116628 | − | 0.993176i | \(-0.537208\pi\) |
0.918429 | − | 0.395585i | \(-0.129458\pi\) | |||||||
\(648\) | 8.52851 | + | 2.87481i | 0.335032 | + | 0.112933i | ||||
\(649\) | 6.25091 | − | 3.60897i | 0.245370 | − | 0.141664i | ||||
\(650\) | 16.6171 | 0.651775 | ||||||||
\(651\) | 24.0603 | − | 8.98380i | 0.942998 | − | 0.352103i | ||||
\(652\) | 6.24543 | 0.244590 | ||||||||
\(653\) | 36.7047 | − | 21.1915i | 1.43637 | − | 0.829286i | 0.438771 | − | 0.898599i | \(-0.355414\pi\) |
0.997595 | + | 0.0693127i | \(0.0220806\pi\) | |||||||
\(654\) | −29.7146 | + | 9.56492i | −1.16193 | + | 0.374018i | ||||
\(655\) | 4.34901 | − | 7.53271i | 0.169930 | − | 0.294327i | ||||
\(656\) | −0.417958 | − | 0.723925i | −0.0163185 | − | 0.0282645i | ||||
\(657\) | −37.0861 | + | 3.69253i | −1.44687 | + | 0.144059i | ||||
\(658\) | −1.41974 | − | 30.8851i | −0.0553472 | − | 1.20403i | ||||
\(659\) | 44.3754i | 1.72862i | 0.502961 | + | 0.864309i | \(0.332244\pi\) | ||||
−0.502961 | + | 0.864309i | \(0.667756\pi\) | |||||||
\(660\) | −0.304905 | + | 1.41538i | −0.0118684 | + | 0.0550936i | ||||
\(661\) | −15.0119 | − | 8.66712i | −0.583895 | − | 0.337112i | 0.178785 | − | 0.983888i | \(-0.442783\pi\) |
−0.762680 | + | 0.646776i | \(0.776117\pi\) | |||||||
\(662\) | −26.7852 | − | 15.4645i | −1.04104 | − | 0.601043i | ||||
\(663\) | 3.00330 | − | 13.9415i | 0.116639 | − | 0.541442i | ||||
\(664\) | − | 3.41567i | − | 0.132554i | ||||||
\(665\) | −0.276664 | − | 6.01856i | −0.0107286 | − | 0.233390i | ||||
\(666\) | 10.5159 | − | 1.04703i | 0.407482 | − | 0.0405715i | ||||
\(667\) | −25.4953 | − | 44.1592i | −0.987182 | − | 1.70985i | ||||
\(668\) | 1.68901 | − | 2.92544i | 0.0653496 | − | 0.113189i | ||||
\(669\) | 9.88629 | − | 3.18232i | 0.382226 | − | 0.123036i | ||||
\(670\) | 9.19693 | − | 5.30985i | 0.355308 | − | 0.205137i | ||||
\(671\) | −2.67493 | −0.103264 | ||||||||
\(672\) | −4.29307 | + | 1.60297i | −0.165609 | + | 0.0618361i | ||||
\(673\) | 8.22070 | 0.316885 | 0.158442 | − | 0.987368i | \(-0.449353\pi\) | ||||
0.158442 | + | 0.987368i | \(0.449353\pi\) | |||||||
\(674\) | −7.57096 | + | 4.37109i | −0.291622 | + | 0.168368i | ||||
\(675\) | 20.4917 | − | 8.92237i | 0.788726 | − | 0.343422i | ||||
\(676\) | −0.962611 | + | 1.66729i | −0.0370235 | + | 0.0641266i | ||||
\(677\) | −9.52599 | − | 16.4995i | −0.366113 | − | 0.634127i | 0.622841 | − | 0.782349i | \(-0.285978\pi\) |
−0.988954 | + | 0.148222i | \(0.952645\pi\) | |||||||
\(678\) | 16.2486 | − | 17.9467i | 0.624023 | − | 0.689240i | ||||
\(679\) | −21.9384 | + | 14.0474i | −0.841917 | + | 0.539090i | ||||
\(680\) | 1.78156i | 0.0683198i | ||||||||
\(681\) | 12.5691 | + | 2.70767i | 0.481650 | + | 0.103758i | ||||
\(682\) | 4.85360 | + | 2.80223i | 0.185854 | + | 0.107303i | ||||
\(683\) | 41.1088 | + | 23.7342i | 1.57299 | + | 0.908164i | 0.995800 | + | 0.0915501i | \(0.0291822\pi\) |
0.577185 | + | 0.816613i | \(0.304151\pi\) | |||||||
\(684\) | −4.76742 | − | 6.63799i | −0.182287 | − | 0.253810i | ||||
\(685\) | − | 5.42372i | − | 0.207230i | ||||||
\(686\) | −14.6149 | + | 11.3757i | −0.557998 | + | 0.434325i | ||||
\(687\) | 15.0160 | + | 13.5952i | 0.572897 | + | 0.518689i | ||||
\(688\) | 4.92543 | + | 8.53109i | 0.187780 | + | 0.325245i | ||||
\(689\) | −16.2021 | + | 28.0629i | −0.617253 | + | 1.06911i | ||||
\(690\) | 3.11742 | + | 9.68465i | 0.118678 | + | 0.368688i | ||||
\(691\) | 18.7810 | − | 10.8432i | 0.714464 | − | 0.412496i | −0.0982480 | − | 0.995162i | \(-0.531324\pi\) |
0.812712 | + | 0.582666i | \(0.197991\pi\) | |||||||
\(692\) | −10.1851 | −0.387180 | ||||||||
\(693\) | 4.92129 | + | 6.22743i | 0.186944 | + | 0.236560i | ||||
\(694\) | −1.28004 | −0.0485895 | ||||||||
\(695\) | −10.8895 | + | 6.28704i | −0.413061 | + | 0.238481i | ||||
\(696\) | 3.85110 | + | 11.9639i | 0.145975 | + | 0.453491i | ||||
\(697\) | −0.890781 | + | 1.54288i | −0.0337407 | + | 0.0584407i | ||||
\(698\) | −6.57699 | − | 11.3917i | −0.248943 | − | 0.431182i | ||||
\(699\) | 17.9318 | + | 16.2350i | 0.678241 | + | 0.614065i | ||||
\(700\) | −5.23145 | + | 10.1063i | −0.197730 | + | 0.381981i | ||||
\(701\) | − | 51.9746i | − | 1.96305i | −0.191328 | − | 0.981526i | \(-0.561280\pi\) | ||
0.191328 | − | 0.981526i | \(-0.438720\pi\) | |||||||
\(702\) | −2.26240 | + | 19.9465i | −0.0853886 | + | 0.752832i | ||||
\(703\) | −8.31067 | − | 4.79817i | −0.313443 | − | 0.180966i | ||||
\(704\) | −0.866025 | − | 0.500000i | −0.0326396 | − | 0.0188445i | ||||
\(705\) | 16.5399 | + | 3.56305i | 0.622927 | + | 0.134192i | ||||
\(706\) | − | 15.0204i | − | 0.565299i | ||||||
\(707\) | −17.5336 | + | 0.805994i | −0.659420 | + | 0.0303125i | ||||
\(708\) | −8.39078 | + | 9.26771i | −0.315345 | + | 0.348302i | ||||
\(709\) | 9.83314 | + | 17.0315i | 0.369291 | + | 0.639632i | 0.989455 | − | 0.144841i | \(-0.0462671\pi\) |
−0.620163 | + | 0.784473i | \(0.712934\pi\) | |||||||
\(710\) | 1.11364 | − | 1.92888i | 0.0417942 | − | 0.0723896i | ||||
\(711\) | −15.3685 | − | 6.94368i | −0.576364 | − | 0.260408i | ||||
\(712\) | −0.616180 | + | 0.355752i | −0.0230923 | + | 0.0133324i | ||||
\(713\) | 39.3824 | 1.47488 | ||||||||
\(714\) | 7.53350 | + | 6.21567i | 0.281934 | + | 0.232616i | ||||
\(715\) | −3.22941 | −0.120773 | ||||||||
\(716\) | −16.5044 | + | 9.52883i | −0.616799 | + | 0.356109i | ||||
\(717\) | −15.2565 | + | 4.91097i | −0.569765 | + | 0.183403i | ||||
\(718\) | 15.6304 | − | 27.0726i | 0.583321 | − | 1.01034i | ||||
\(719\) | 7.00169 | + | 12.1273i | 0.261119 | + | 0.452271i | 0.966540 | − | 0.256518i | \(-0.0825752\pi\) |
−0.705421 | + | 0.708789i | \(0.749242\pi\) | |||||||
\(720\) | −0.248459 | − | 2.49541i | −0.00925952 | − | 0.0929985i | ||||
\(721\) | −35.8478 | − | 18.5564i | −1.33504 | − | 0.691075i | ||||
\(722\) | − | 11.5787i | − | 0.430916i | ||||||
\(723\) | −1.73603 | + | 8.05874i | −0.0645638 | + | 0.299708i | ||||
\(724\) | −18.5327 | − | 10.6998i | −0.688761 | − | 0.397657i | ||||
\(725\) | 27.0300 | + | 15.6058i | 1.00387 | + | 0.579584i | ||||
\(726\) | −0.364755 | + | 1.69321i | −0.0135373 | + | 0.0628408i | ||||
\(727\) | − | 11.1514i | − | 0.413582i | −0.978385 | − | 0.206791i | \(-0.933698\pi\) | ||
0.978385 | − | 0.206791i | \(-0.0663020\pi\) | |||||||
\(728\) | −5.51178 | − | 8.60795i | −0.204280 | − | 0.319032i | ||||
\(729\) | 7.92015 | + | 25.8122i | 0.293339 | + | 0.956008i | ||||
\(730\) | 5.19237 | + | 8.99345i | 0.192178 | + | 0.332862i | ||||
\(731\) | 10.4974 | − | 18.1820i | 0.388260 | − | 0.672487i | ||||
\(732\) | 4.41026 | − | 1.41963i | 0.163008 | − | 0.0524710i | ||||
\(733\) | 9.63547 | − | 5.56304i | 0.355894 | − | 0.205476i | −0.311384 | − | 0.950284i | \(-0.600793\pi\) |
0.667278 | + | 0.744809i | \(0.267459\pi\) | |||||||
\(734\) | 10.3338 | 0.381427 | ||||||||
\(735\) | −3.97744 | − | 9.32187i | −0.146710 | − | 0.343842i | ||||
\(736\) | −7.02699 | −0.259018 | ||||||||
\(737\) | 11.0022 | − | 6.35213i | 0.405271 | − | 0.233984i | ||||
\(738\) | 1.03253 | − | 2.28532i | 0.0380081 | − | 0.0841238i | ||||
\(739\) | −19.4856 | + | 33.7501i | −0.716790 | + | 1.24152i | 0.245476 | + | 0.969403i | \(0.421056\pi\) |
−0.962265 | + | 0.272113i | \(0.912277\pi\) | |||||||
\(740\) | −1.47231 | − | 2.55012i | −0.0541233 | − | 0.0937443i | ||||
\(741\) | 12.2346 | − | 13.5132i | 0.449448 | − | 0.496420i | ||||
\(742\) | −11.9667 | − | 18.6888i | −0.439311 | − | 0.686088i | ||||
\(743\) | − | 6.23560i | − | 0.228762i | −0.993437 | − | 0.114381i | \(-0.963512\pi\) | ||
0.993437 | − | 0.114381i | \(-0.0364884\pi\) | |||||||
\(744\) | −9.48951 | − | 2.04425i | −0.347902 | − | 0.0749459i | ||||
\(745\) | 3.51694 | + | 2.03051i | 0.128851 | + | 0.0743920i | ||||
\(746\) | 12.1077 | + | 6.99037i | 0.443293 | + | 0.255936i | ||||
\(747\) | 8.32289 | − | 5.97752i | 0.304519 | − | 0.218706i | ||||
\(748\) | 2.13127i | 0.0779268i | ||||||||
\(749\) | −8.75245 | − | 4.53065i | −0.319808 | − | 0.165546i | ||||
\(750\) | −9.98306 | − | 9.03845i | −0.364530 | − | 0.330037i | ||||
\(751\) | 10.7770 | + | 18.6663i | 0.393257 | + | 0.681142i | 0.992877 | − | 0.119143i | \(-0.0380148\pi\) |
−0.599620 | + | 0.800285i | \(0.704681\pi\) | |||||||
\(752\) | −5.84290 | + | 10.1202i | −0.213069 | + | 0.369045i | ||||
\(753\) | 10.7186 | + | 33.2985i | 0.390606 | + | 1.21347i | ||||
\(754\) | −24.2780 | + | 14.0169i | −0.884151 | + | 0.510465i | ||||
\(755\) | −14.1332 | −0.514358 | ||||||||
\(756\) | −11.4189 | − | 7.65559i | −0.415302 | − | 0.278431i | ||||
\(757\) | −33.0536 | −1.20135 | −0.600676 | − | 0.799492i | \(-0.705102\pi\) | ||||
−0.600676 | + | 0.799492i | \(0.705102\pi\) | |||||||
\(758\) | 2.08168 | − | 1.20186i | 0.0756100 | − | 0.0436535i | ||||
\(759\) | 3.72934 | + | 11.5857i | 0.135367 | + | 0.420533i | ||||
\(760\) | −1.13860 | + | 1.97212i | −0.0413014 | + | 0.0715362i | ||||
\(761\) | −14.3382 | − | 24.8345i | −0.519759 | − | 0.900249i | −0.999736 | − | 0.0229682i | \(-0.992688\pi\) |
0.479977 | − | 0.877281i | \(-0.340645\pi\) | |||||||
\(762\) | −13.3952 | − | 12.1277i | −0.485257 | − | 0.439341i | ||||
\(763\) | 47.6331 | − | 2.18962i | 1.72443 | − | 0.0792696i | ||||
\(764\) | 8.89570i | 0.321835i | ||||||||
\(765\) | −4.34109 | + | 3.11778i | −0.156953 | + | 0.112724i | ||||
\(766\) | 19.8189 | + | 11.4425i | 0.716088 | + | 0.413433i | ||||
\(767\) | −24.1493 | − | 13.9426i | −0.871979 | − | 0.503437i | ||||
\(768\) | 1.69321 | + | 0.364755i | 0.0610984 | + | 0.0131620i | ||||
\(769\) | − | 41.1250i | − | 1.48301i | −0.670950 | − | 0.741503i | \(-0.734114\pi\) | ||
0.670950 | − | 0.741503i | \(-0.265886\pi\) | |||||||
\(770\) | 1.01670 | − | 1.96408i | 0.0366392 | − | 0.0707807i | ||||
\(771\) | 32.9446 | − | 36.3877i | 1.18647 | − | 1.31047i | ||||
\(772\) | −3.07676 | − | 5.32910i | −0.110735 | − | 0.191798i | ||||
\(773\) | −4.24621 | + | 7.35464i | −0.152725 | + | 0.264528i | −0.932228 | − | 0.361870i | \(-0.882138\pi\) |
0.779503 | + | 0.626398i | \(0.215472\pi\) | |||||||
\(774\) | −12.1679 | + | 26.9313i | −0.437366 | + | 0.968027i | ||||
\(775\) | −20.8765 | + | 12.0531i | −0.749906 | + | 0.432959i | ||||
\(776\) | 9.84612 | 0.353455 | ||||||||
\(777\) | −15.9202 | − | 2.67128i | −0.571132 | − | 0.0958316i | ||||
\(778\) | −17.7054 | −0.634768 | ||||||||
\(779\) | −1.97212 | + | 1.13860i | −0.0706584 | + | 0.0407946i | ||||
\(780\) | 5.32446 | − | 1.71390i | 0.190646 | − | 0.0613676i | ||||
\(781\) | 1.33224 | − | 2.30750i | 0.0476712 | − | 0.0825690i | ||||
\(782\) | 7.48819 | + | 12.9699i | 0.267777 | + | 0.463804i | ||||
\(783\) | −22.4127 | + | 30.3211i | −0.800964 | + | 1.08359i | ||||
\(784\) | 6.97048 | − | 0.642202i | 0.248946 | − | 0.0229358i | ||||
\(785\) | − | 3.17148i | − | 0.113195i | ||||||
\(786\) | −3.79541 | + | 17.6185i | −0.135378 | + | 0.628430i | ||||
\(787\) | −39.8454 | − | 23.0048i | −1.42034 | − | 0.820032i | −0.424009 | − | 0.905658i | \(-0.639378\pi\) |
−0.996327 | + | 0.0856262i | \(0.972711\pi\) | |||||||
\(788\) | −16.8651 | − | 9.73707i | −0.600795 | − | 0.346869i | ||||
\(789\) | −6.98157 | + | 32.4087i | −0.248550 | + | 1.15378i | ||||
\(790\) | 4.69906i | 0.167185i | ||||||||
\(791\) | −31.1433 | + | 19.9415i | −1.10733 | + | 0.709037i | ||||
\(792\) | −0.297229 | − | 2.98524i | −0.0105616 | − | 0.106076i | ||||
\(793\) | 5.16705 | + | 8.94959i | 0.183487 | + | 0.317809i | ||||
\(794\) | 17.9405 | − | 31.0739i | 0.636685 | − | 1.10277i | ||||
\(795\) | 11.5600 | − | 3.72107i | 0.409990 | − | 0.131973i | ||||
\(796\) | −11.4944 | + | 6.63628i | −0.407407 | + | 0.235217i | ||||
\(797\) | −29.2744 | −1.03695 | −0.518476 | − | 0.855092i | \(-0.673500\pi\) | ||||
−0.518476 | + | 0.855092i | \(0.673500\pi\) | |||||||
\(798\) | 4.36682 | + | 11.6952i | 0.154584 | + | 0.414005i | ||||
\(799\) | 24.9055 | 0.881095 | ||||||||
\(800\) | 3.72499 | − | 2.15062i | 0.131698 | − | 0.0760359i | ||||
\(801\) | −1.94518 | − | 0.878857i | −0.0687297 | − | 0.0310529i | ||||
\(802\) | −12.9708 | + | 22.4661i | −0.458016 | + | 0.793307i | ||||
\(803\) | 6.21158 | + | 10.7588i | 0.219202 | + | 0.379669i | ||||
\(804\) | −14.7686 | + | 16.3121i | −0.520848 | + | 0.575282i | ||||
\(805\) | −0.713646 | − | 15.5247i | −0.0251527 | − | 0.547173i | ||||
\(806\) | − | 21.6518i | − | 0.762652i | ||||||
\(807\) | 14.3731 | + | 3.09629i | 0.505958 | + | 0.108995i | ||||
\(808\) | 5.74529 | + | 3.31704i | 0.202118 | + | 0.116693i | ||||
\(809\) | 37.5875 | + | 21.7011i | 1.32151 | + | 0.762972i | 0.983969 | − | 0.178341i | \(-0.0570729\pi\) |
0.337537 | + | 0.941312i | \(0.390406\pi\) | |||||||
\(810\) | 5.64571 | − | 4.97246i | 0.198370 | − | 0.174714i | ||||
\(811\) | 3.75467i | 0.131844i | 0.997825 | + | 0.0659221i | \(0.0209989\pi\) | ||||
−0.997825 | + | 0.0659221i | \(0.979001\pi\) | |||||||
\(812\) | −0.881601 | − | 19.1784i | −0.0309381 | − | 0.673029i | ||||
\(813\) | −19.7291 | − | 17.8623i | −0.691928 | − | 0.626457i | ||||
\(814\) | −1.76131 | − | 3.05069i | −0.0617340 | − | 0.106926i | ||||
\(815\) | 2.61033 | − | 4.52122i | 0.0914358 | − | 0.158371i | ||||
\(816\) | −1.13110 | − | 3.51390i | −0.0395964 | − | 0.123011i | ||||
\(817\) | 23.2404 | − | 13.4178i | 0.813078 | − | 0.469431i | ||||
\(818\) | −9.87793 | −0.345374 | ||||||||
\(819\) | 11.3290 | − | 28.4946i | 0.395869 | − | 0.995682i | ||||
\(820\) | −0.698757 | −0.0244017 | ||||||||
\(821\) | 35.4502 | − | 20.4672i | 1.23722 | − | 0.714310i | 0.268696 | − | 0.963225i | \(-0.413407\pi\) |
0.968525 | + | 0.248915i | \(0.0800741\pi\) | |||||||
\(822\) | 3.44348 | + | 10.6976i | 0.120105 | + | 0.373121i | ||||
\(823\) | 14.6468 | − | 25.3690i | 0.510556 | − | 0.884309i | −0.489369 | − | 0.872077i | \(-0.662773\pi\) |
0.999925 | − | 0.0122325i | \(-0.00389383\pi\) | |||||||
\(824\) | 7.62843 | + | 13.2128i | 0.265749 | + | 0.460291i | ||||
\(825\) | −5.52273 | − | 5.00016i | −0.192277 | − | 0.174083i | ||||
\(826\) | 16.0825 | − | 10.2978i | 0.559580 | − | 0.358306i | ||||
\(827\) | 41.9854i | 1.45998i | 0.683460 | + | 0.729988i | \(0.260474\pi\) | ||||
−0.683460 | + | 0.729988i | \(0.739526\pi\) | |||||||
\(828\) | −12.2974 | − | 17.1225i | −0.427365 | − | 0.595048i | ||||
\(829\) | −33.3726 | − | 19.2677i | −1.15908 | − | 0.669195i | −0.207996 | − | 0.978130i | \(-0.566694\pi\) |
−0.951083 | + | 0.308935i | \(0.900027\pi\) | |||||||
\(830\) | −2.47269 | − | 1.42761i | −0.0858283 | − | 0.0495530i | ||||
\(831\) | −34.3749 | − | 7.40513i | −1.19245 | − | 0.256881i | ||||
\(832\) | 3.86332i | 0.133936i | ||||||||
\(833\) | −8.61331 | − | 12.1813i | −0.298433 | − | 0.422056i | ||||
\(834\) | 17.4865 | − | 19.3140i | 0.605508 | − | 0.668790i | ||||
\(835\) | −1.41187 | − | 2.44543i | −0.0488597 | − | 0.0846275i | ||||
\(836\) | −1.36210 | + | 2.35922i | −0.0471092 | + | 0.0815955i | ||||
\(837\) | −11.6257 | − | 26.7004i | −0.401844 | − | 0.922900i | ||||
\(838\) | −6.18526 | + | 3.57106i | −0.213666 | + | 0.123360i | ||||
\(839\) | 19.4169 | 0.670345 | 0.335172 | − | 0.942157i | \(-0.391205\pi\) | ||||
0.335172 | + | 0.942157i | \(0.391205\pi\) | |||||||
\(840\) | −0.633892 | + | 3.77784i | −0.0218714 | + | 0.130348i | ||||
\(841\) | −23.6553 | −0.815701 | ||||||||
\(842\) | −2.45312 | + | 1.41631i | −0.0845401 | + | 0.0488092i | ||||
\(843\) | 19.3429 | − | 6.22635i | 0.666206 | − | 0.214447i | ||||
\(844\) | −8.40427 | + | 14.5566i | −0.289287 | + | 0.501060i | ||||
\(845\) | 0.804663 | + | 1.39372i | 0.0276812 | + | 0.0479453i | ||||
\(846\) | −34.8849 | + | 3.47336i | −1.19937 | + | 0.119417i | ||||
\(847\) | 1.21626 | − | 2.34962i | 0.0417913 | − | 0.0807338i | ||||
\(848\) | 8.38769i | 0.288034i | ||||||||
\(849\) | 5.20250 | − | 24.1503i | 0.178549 | − | 0.828835i | ||||
\(850\) | −7.93894 | − | 4.58355i | −0.272303 | − | 0.157214i | ||||
\(851\) | −21.4371 | − | 12.3767i | −0.734855 | − | 0.424269i | ||||
\(852\) | −0.971880 | + | 4.51151i | −0.0332961 | + | 0.154562i | ||||
\(853\) | 44.3922i | 1.51996i | 0.649946 | + | 0.759980i | \(0.274791\pi\) | ||||
−0.649946 | + | 0.759980i | \(0.725209\pi\) | |||||||
\(854\) | −7.06973 | + | 0.324985i | −0.241921 | + | 0.0111207i | ||||
\(855\) | −6.79800 | + | 0.676851i | −0.232487 | + | 0.0231478i | ||||
\(856\) | 1.86253 | + | 3.22599i | 0.0636599 | + | 0.110262i | ||||
\(857\) | −19.3914 | + | 33.5868i | −0.662396 | + | 1.14730i | 0.317588 | + | 0.948229i | \(0.397127\pi\) |
−0.979984 | + | 0.199075i | \(0.936206\pi\) | |||||||
\(858\) | 6.36960 | − | 2.05033i | 0.217455 | − | 0.0699971i | ||||
\(859\) | 23.2887 | − | 13.4458i | 0.794601 | − | 0.458763i | −0.0469785 | − | 0.998896i | \(-0.514959\pi\) |
0.841580 | + | 0.540133i | \(0.181626\pi\) | |||||||
\(860\) | 8.23450 | 0.280794 | ||||||||
\(861\) | −2.43789 | + | 2.95476i | −0.0830830 | + | 0.100698i | ||||
\(862\) | −25.5110 | −0.868907 | ||||||||
\(863\) | −25.5304 | + | 14.7400i | −0.869063 | + | 0.501754i | −0.867037 | − | 0.498244i | \(-0.833978\pi\) |
−0.00202656 | + | 0.999998i | \(0.500645\pi\) | |||||||
\(864\) | 2.07437 | + | 4.76414i | 0.0705715 | + | 0.162079i | ||||
\(865\) | −4.25696 | + | 7.37326i | −0.144741 | + | 0.250698i | ||||
\(866\) | −8.80427 | − | 15.2494i | −0.299181 | − | 0.518197i | ||||
\(867\) | 14.4820 | − | 15.9955i | 0.491833 | − | 0.543235i | ||||
\(868\) | 13.1683 | + | 6.81650i | 0.446962 | + | 0.231367i | ||||
\(869\) | 5.62145i | 0.190694i | ||||||||
\(870\) | 10.2706 | + | 2.21251i | 0.348205 | + | 0.0750111i | ||||
\(871\) | −42.5050 | − | 24.5403i | −1.44023 | − | 0.831516i | ||||
\(872\) | −15.6081 | − | 9.01132i | −0.528556 | − | 0.305162i | ||||
\(873\) | 17.2310 | + | 23.9918i | 0.583180 | + | 0.812000i | ||||
\(874\) | 19.1429i | 0.647518i | ||||||||
\(875\) | 11.0927 | + | 17.3238i | 0.375000 | + | 0.585652i | ||||
\(876\) | −15.9511 | − | 14.4418i | −0.538939 | − | 0.487944i | ||||
\(877\) | −6.00638 | − | 10.4034i | −0.202821 | − | 0.351296i | 0.746615 | − | 0.665256i | \(-0.231678\pi\) |
−0.949436 | + | 0.313960i | \(0.898344\pi\) | |||||||
\(878\) | −11.7710 | + | 20.3880i | −0.397253 | + | 0.688063i | ||||
\(879\) | 3.42517 | + | 10.6407i | 0.115528 | + | 0.358902i | ||||
\(880\) | −0.723925 | + | 0.417958i | −0.0244035 | + | 0.0140894i | ||||
\(881\) | 15.9253 | 0.536538 | 0.268269 | − | 0.963344i | \(-0.413548\pi\) | ||||
0.268269 | + | 0.963344i | \(0.413548\pi\) | |||||||
\(882\) | 13.7634 | + | 15.8609i | 0.463437 | + | 0.534066i | ||||
\(883\) | 29.0733 | 0.978396 | 0.489198 | − | 0.872173i | \(-0.337290\pi\) | ||||
0.489198 | + | 0.872173i | \(0.337290\pi\) | |||||||
\(884\) | 7.13065 | − | 4.11688i | 0.239830 | − | 0.138466i | ||||
\(885\) | 3.20213 | + | 9.94782i | 0.107638 | + | 0.334392i | ||||
\(886\) | 5.12033 | − | 8.86868i | 0.172021 | − | 0.297949i | ||||
\(887\) | −2.94979 | − | 5.10919i | −0.0990443 | − | 0.171550i | 0.812245 | − | 0.583316i | \(-0.198245\pi\) |
−0.911289 | + | 0.411767i | \(0.864912\pi\) | |||||||
\(888\) | 4.52300 | + | 4.09502i | 0.151782 | + | 0.137420i | ||||
\(889\) | 14.8840 | + | 23.2450i | 0.499195 | + | 0.779611i | ||||
\(890\) | 0.594758i | 0.0199363i | ||||||||
\(891\) | 6.75391 | − | 5.94850i | 0.226264 | − | 0.199282i | ||||
\(892\) | 5.19292 | + | 2.99814i | 0.173872 | + | 0.100385i | ||||
\(893\) | 27.5694 | + | 15.9172i | 0.922575 | + | 0.532649i | ||||
\(894\) | −8.22586 | − | 1.77203i | −0.275114 | − | 0.0592657i | ||||
\(895\) | 15.9306i | 0.532502i | ||||||||
\(896\) | −2.34962 | − | 1.21626i | −0.0784952 | − | 0.0406325i | ||||
\(897\) | 31.5587 | − | 34.8569i | 1.05371 | − | 1.16384i | ||||
\(898\) | 8.71024 | + | 15.0866i | 0.290664 | + | 0.503445i | ||||
\(899\) | 20.3341 | − | 35.2197i | 0.678179 | − | 1.17464i | ||||
\(900\) | 11.7592 | + | 5.31295i | 0.391973 | + | 0.177098i | ||||
\(901\) | 15.4814 | − | 8.93820i | 0.515761 | − | 0.297775i | ||||
\(902\) | −0.835917 | −0.0278330 | ||||||||
\(903\) | 28.7293 | − | 34.8203i | 0.956050 | − | 1.15875i | ||||
\(904\) | 13.9774 | 0.464881 | ||||||||
\(905\) | −15.4918 | + | 8.94418i | −0.514964 | + | 0.297315i | ||||
\(906\) | 27.8758 | − | 8.97303i | 0.926112 | − | 0.298109i | ||||
\(907\) | 9.72266 | − | 16.8401i | 0.322836 | − | 0.559168i | −0.658236 | − | 0.752811i | \(-0.728697\pi\) |
0.981072 | + | 0.193644i | \(0.0620306\pi\) | |||||||
\(908\) | 3.71163 | + | 6.42873i | 0.123175 | + | 0.213345i | ||||
\(909\) | 1.97184 | + | 19.8043i | 0.0654019 | + | 0.656868i | ||||
\(910\) | −8.53521 | + | 0.392351i | −0.282939 | + | 0.0130063i | ||||
\(911\) | − | 14.8351i | − | 0.491510i | −0.969332 | − | 0.245755i | \(-0.920964\pi\) | ||
0.969332 | − | 0.245755i | \(-0.0790359\pi\) | |||||||
\(912\) | 0.993664 | − | 4.61263i | 0.0329035 | − | 0.152740i | ||||
\(913\) | −2.95806 | − | 1.70784i | −0.0978974 | − | 0.0565211i | ||||
\(914\) | 5.96396 | + | 3.44330i | 0.197270 | + | 0.113894i | ||||
\(915\) | 0.815598 | − | 3.78604i | 0.0269628 | − | 0.125163i | ||||
\(916\) | 11.6949i | 0.386410i | ||||||||
\(917\) | 12.6557 | − | 24.4486i | 0.417927 | − | 0.807365i | ||||
\(918\) | 6.58279 | − | 8.90555i | 0.217265 | − | 0.293927i | ||||
\(919\) | 18.3711 | + | 31.8197i | 0.606007 | + | 1.04964i | 0.991891 | + | 0.127088i | \(0.0405630\pi\) |
−0.385884 | + | 0.922547i | \(0.626104\pi\) | |||||||
\(920\) | −2.93699 | + | 5.08701i | −0.0968297 | + | 0.167714i | ||||
\(921\) | 19.1859 | − | 6.17579i | 0.632196 | − | 0.203499i | ||||
\(922\) | −5.73523 | + | 3.31124i | −0.188880 | + | 0.109050i | ||||
\(923\) | −10.2937 | −0.338822 | ||||||||
\(924\) | −0.758320 | + | 4.51940i | −0.0249469 | + | 0.148677i | ||||
\(925\) | 15.1517 | 0.498184 | ||||||||
\(926\) | −18.5182 | + | 10.6915i | −0.608544 | + | 0.351343i | ||||
\(927\) | −18.8454 | + | 41.7108i | −0.618966 | + | 1.36996i | ||||
\(928\) | −3.62820 | + | 6.28423i | −0.119101 | + | 0.206290i | ||||
\(929\) | −10.2616 | − | 17.7737i | −0.336674 | − | 0.583136i | 0.647131 | − | 0.762379i | \(-0.275969\pi\) |
−0.983805 | + | 0.179243i | \(0.942635\pi\) | |||||||
\(930\) | −5.44610 | + | 6.01528i | −0.178585 | + | 0.197249i | ||||
\(931\) | −1.74948 | − | 18.9890i | −0.0573370 | − | 0.622338i | ||||
\(932\) | 13.9657i | 0.457462i | ||||||||
\(933\) | −48.5169 | − | 10.4516i | −1.58837 | − | 0.342171i | ||||
\(934\) | 21.6284 | + | 12.4871i | 0.707702 | + | 0.408592i | ||||
\(935\) | 1.54288 | + | 0.890781i | 0.0504575 | + | 0.0291317i | ||||
\(936\) | −9.41366 | + | 6.76091i | −0.307695 | + | 0.220987i | ||||
\(937\) | − | 36.6682i | − | 1.19790i | −0.800788 | − | 0.598948i | \(-0.795586\pi\) | ||
0.800788 | − | 0.598948i | \(-0.204414\pi\) | |||||||
\(938\) | 28.3066 | − | 18.1251i | 0.924245 | − | 0.591806i | ||||
\(939\) | −28.7983 | − | 26.0734i | −0.939798 | − | 0.850872i | ||||
\(940\) | 4.88418 | + | 8.45964i | 0.159304 | + | 0.275923i | ||||
\(941\) | 4.81705 | − | 8.34338i | 0.157031 | − | 0.271987i | −0.776765 | − | 0.629790i | \(-0.783141\pi\) |
0.933797 | + | 0.357804i | \(0.116474\pi\) | |||||||
\(942\) | 2.01355 | + | 6.25534i | 0.0656050 | + | 0.203810i | ||||
\(943\) | −5.08701 | + | 2.93699i | −0.165656 | + | 0.0956415i | ||||
\(944\) | −7.21793 | −0.234924 | ||||||||
\(945\) | −10.3147 | + | 5.06673i | −0.335538 | + | 0.164821i | ||||
\(946\) | 9.85086 | 0.320279 | ||||||||
\(947\) | −9.23315 | + | 5.33076i | −0.300037 | + | 0.173227i | −0.642460 | − | 0.766320i | \(-0.722086\pi\) |
0.342422 | + | 0.939546i | \(0.388753\pi\) | |||||||
\(948\) | −2.98340 | − | 9.26829i | −0.0968962 | − | 0.301020i | ||||
\(949\) | 23.9973 | − | 41.5646i | 0.778986 | − | 1.34924i | ||||
\(950\) | −5.85872 | − | 10.1476i | −0.190082 | − | 0.329232i | ||||
\(951\) | −13.5244 | − | 12.2447i | −0.438560 | − | 0.397063i | ||||
\(952\) | 0.258934 | + | 5.63285i | 0.00839209 | + | 0.182562i | ||||
\(953\) | − | 20.5160i | − | 0.664579i | −0.943177 | − | 0.332290i | \(-0.892179\pi\) | ||
0.943177 | − | 0.332290i | \(-0.107821\pi\) | |||||||
\(954\) | −20.4381 | + | 14.6787i | −0.661708 | + | 0.475240i | ||||
\(955\) | 6.43982 | + | 3.71803i | 0.208388 | + | 0.120313i | ||||
\(956\) | −8.01372 | − | 4.62673i | −0.259182 | − | 0.149639i | ||||
\(957\) | 12.2866 | + | 2.64681i | 0.397169 | + | 0.0855591i | ||||
\(958\) | − | 28.9996i | − | 0.936933i | ||||||
\(959\) | −0.788288 | − | 17.1484i | −0.0254551 | − | 0.553752i | ||||
\(960\) | 0.971746 | − | 1.07330i | 0.0313630 | − | 0.0346407i | ||||
\(961\) | 0.204948 | + | 0.354981i | 0.00661124 | + | 0.0114510i | ||||
\(962\) | −6.80452 | + | 11.7858i | −0.219386 | + | 0.379988i | ||||
\(963\) | −4.60123 | + | 10.1840i | −0.148273 | + | 0.328173i | ||||
\(964\) | −4.12181 | + | 2.37973i | −0.132754 | + | 0.0766458i | ||||
\(965\) | −5.14382 | −0.165586 | ||||||||
\(966\) | 11.2641 | + | 30.1674i | 0.362416 | + | 0.970619i | ||||
\(967\) | 38.6686 | 1.24350 | 0.621749 | − | 0.783217i | \(-0.286423\pi\) | ||||
0.621749 | + | 0.783217i | \(0.286423\pi\) | |||||||
\(968\) | −0.866025 | + | 0.500000i | −0.0278351 | + | 0.0160706i | ||||
\(969\) | −9.57256 | + | 3.08134i | −0.307515 | + | 0.0989869i | ||||
\(970\) | 4.11527 | − | 7.12785i | 0.132133 | − | 0.228862i | ||||
\(971\) | 24.3770 | + | 42.2221i | 0.782294 | + | 1.35497i | 0.930602 | + | 0.366032i | \(0.119284\pi\) |
−0.148309 | + | 0.988941i | \(0.547383\pi\) | |||||||
\(972\) | −7.97846 | + | 13.3919i | −0.255909 | + | 0.429547i | ||||
\(973\) | −33.5160 | + | 21.4607i | −1.07448 | + | 0.688000i | ||||
\(974\) | − | 15.6226i | − | 0.500580i | ||||||
\(975\) | −6.06116 | + | 28.1362i | −0.194112 | + | 0.901078i | ||||
\(976\) | 2.31656 | + | 1.33746i | 0.0741511 | + | 0.0428112i | ||||
\(977\) | 14.6963 | + | 8.48489i | 0.470175 | + | 0.271456i | 0.716313 | − | 0.697779i | \(-0.245828\pi\) |
−0.246138 | + | 0.969235i | \(0.579162\pi\) | |||||||
\(978\) | −2.27805 | + | 10.5748i | −0.0728440 | + | 0.338145i | ||||
\(979\) | 0.711503i | 0.0227397i | ||||||||
\(980\) | 2.44846 | − | 5.31452i | 0.0782133 | − | 0.169766i | ||||
\(981\) | −5.35686 | − | 53.8019i | −0.171031 | − | 1.71776i | ||||
\(982\) | 16.2643 | + | 28.1705i | 0.519014 | + | 0.898958i | ||||
\(983\) | −11.3004 | + | 19.5728i | −0.360426 | + | 0.624276i | −0.988031 | − | 0.154256i | \(-0.950702\pi\) |
0.627605 | + | 0.778532i | \(0.284035\pi\) | |||||||
\(984\) | 1.37821 | − | 0.443635i | 0.0439357 | − | 0.0141426i | ||||
\(985\) | −14.0978 | + | 8.13939i | −0.449194 | + | 0.259342i | ||||
\(986\) | 15.4653 | 0.492516 | ||||||||
\(987\) | 52.8127 | + | 8.86157i | 1.68105 | + | 0.282067i | ||||
\(988\) | 10.5244 | 0.334827 | ||||||||
\(989\) | 59.9479 | − | 34.6109i | 1.90623 | − | 1.10056i | ||||
\(990\) | −2.28532 | − | 1.03253i | −0.0726322 | − | 0.0328161i | ||||
\(991\) | 3.09848 | − | 5.36672i | 0.0984264 | − | 0.170479i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911033 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(992\) | −2.80223 | − | 4.85360i | −0.0889708 | − | 0.154102i | ||||
\(993\) | 35.9546 | − | 39.7122i | 1.14098 | − | 1.26023i | ||||
\(994\) | 3.24071 | − | 6.26050i | 0.102789 | − | 0.198571i | ||||
\(995\) | 11.0948i | 0.351727i | ||||||||
\(996\) | 5.78344 | + | 1.24588i | 0.183255 | + | 0.0394773i | ||||
\(997\) | −36.9714 | − | 21.3455i | −1.17090 | − | 0.676017i | −0.217005 | − | 0.976170i | \(-0.569629\pi\) |
−0.953891 | + | 0.300153i | \(0.902962\pi\) | |||||||
\(998\) | −13.2507 | − | 7.65028i | −0.419443 | − | 0.242165i | ||||
\(999\) | −2.06288 | + | 18.1875i | −0.0652668 | + | 0.575427i |
(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 | 462.2.k.g.353.3 | yes | 20 | |
3.2 | odd | 2 | inner | 462.2.k.g.353.6 | yes | 20 | |
7.5 | odd | 6 | inner | 462.2.k.g.89.6 | yes | 20 | |
21.5 | even | 6 | inner | 462.2.k.g.89.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.k.g.89.3 | ✓ | 20 | 21.5 | even | 6 | inner | |
462.2.k.g.89.6 | yes | 20 | 7.5 | odd | 6 | inner | |
462.2.k.g.353.3 | yes | 20 | 1.1 | even | 1 | trivial | |
462.2.k.g.353.6 | yes | 20 | 3.2 | odd | 2 | inner |