Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(196,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.196");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.i (of order \(3\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 391.14 | ||
Character | \(\chi\) | \(=\) | 585.391 |
Dual form | 585.2.i.h.196.14 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26258 | + | 2.18685i | 0.892776 | + | 1.54633i | 0.836533 | + | 0.547917i | \(0.184579\pi\) |
0.0562438 | + | 0.998417i | \(0.482088\pi\) | |||||||
\(3\) | −0.259881 | − | 1.71244i | −0.150042 | − | 0.988680i | ||||
\(4\) | −2.18820 | + | 3.79007i | −1.09410 | + | 1.89504i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 3.41673 | − | 2.73041i | 1.39487 | − | 1.11469i | ||||
\(7\) | 0.799357 | + | 1.38453i | 0.302129 | + | 0.523302i | 0.976618 | − | 0.214983i | \(-0.0689695\pi\) |
−0.674489 | + | 0.738285i | \(0.735636\pi\) | |||||||
\(8\) | −6.00077 | −2.12159 | ||||||||
\(9\) | −2.86492 | + | 0.890062i | −0.954975 | + | 0.296687i | ||||
\(10\) | 2.52515 | 0.798524 | ||||||||
\(11\) | 2.68984 | + | 4.65893i | 0.811016 | + | 1.40472i | 0.912153 | + | 0.409849i | \(0.134419\pi\) |
−0.101137 | + | 0.994872i | \(0.532248\pi\) | |||||||
\(12\) | 7.05895 | + | 2.76220i | 2.03774 | + | 0.797379i | ||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | ||||
\(14\) | −2.01850 | + | 3.49614i | −0.539466 | + | 0.934383i | ||||
\(15\) | −1.61296 | − | 0.631158i | −0.416464 | − | 0.162964i | ||||
\(16\) | −3.20003 | − | 5.54262i | −0.800008 | − | 1.38565i | ||||
\(17\) | 3.08624 | 0.748524 | 0.374262 | − | 0.927323i | \(-0.377896\pi\) | ||||
0.374262 | + | 0.927323i | \(0.377896\pi\) | |||||||
\(18\) | −5.56361 | − | 5.14138i | −1.31136 | − | 1.21183i | ||||
\(19\) | 3.72202 | 0.853889 | 0.426944 | − | 0.904278i | \(-0.359590\pi\) | ||||
0.426944 | + | 0.904278i | \(0.359590\pi\) | |||||||
\(20\) | 2.18820 | + | 3.79007i | 0.489296 | + | 0.847486i | ||||
\(21\) | 2.16319 | − | 1.72867i | 0.472046 | − | 0.377226i | ||||
\(22\) | −6.79225 | + | 11.7645i | −1.44811 | + | 2.50820i | ||||
\(23\) | −0.847988 | + | 1.46876i | −0.176818 | + | 0.306257i | −0.940789 | − | 0.338993i | \(-0.889914\pi\) |
0.763971 | + | 0.645251i | \(0.223247\pi\) | |||||||
\(24\) | 1.55948 | + | 10.2760i | 0.318328 | + | 2.09757i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −2.52515 | −0.495223 | ||||||||
\(27\) | 2.26872 | + | 4.67471i | 0.436615 | + | 0.899648i | ||||
\(28\) | −6.99661 | −1.32223 | ||||||||
\(29\) | −0.320437 | − | 0.555014i | −0.0595037 | − | 0.103063i | 0.834739 | − | 0.550646i | \(-0.185618\pi\) |
−0.894243 | + | 0.447582i | \(0.852285\pi\) | |||||||
\(30\) | −0.656238 | − | 4.32418i | −0.119812 | − | 0.789484i | ||||
\(31\) | −2.79393 | + | 4.83923i | −0.501805 | + | 0.869152i | 0.498193 | + | 0.867066i | \(0.333997\pi\) |
−0.999998 | + | 0.00208580i | \(0.999336\pi\) | |||||||
\(32\) | 2.07980 | − | 3.60232i | 0.367660 | − | 0.636807i | ||||
\(33\) | 7.27912 | − | 5.81696i | 1.26713 | − | 1.01260i | ||||
\(34\) | 3.89662 | + | 6.74914i | 0.668264 | + | 1.15747i | ||||
\(35\) | 1.59871 | 0.270232 | ||||||||
\(36\) | 2.89563 | − | 12.8059i | 0.482604 | − | 2.13432i | ||||
\(37\) | 0.445044 | 0.0731647 | 0.0365824 | − | 0.999331i | \(-0.488353\pi\) | ||||
0.0365824 | + | 0.999331i | \(0.488353\pi\) | |||||||
\(38\) | 4.69933 | + | 8.13948i | 0.762332 | + | 1.32040i | ||||
\(39\) | 1.61296 | + | 0.631158i | 0.258280 | + | 0.101066i | ||||
\(40\) | −3.00038 | + | 5.19682i | −0.474402 | + | 0.821689i | ||||
\(41\) | 3.19674 | − | 5.53691i | 0.499246 | − | 0.864720i | −0.500753 | − | 0.865590i | \(-0.666944\pi\) |
1.00000 | 0.000870040i | \(0.000276942\pi\) | ||||||||
\(42\) | 6.51151 | + | 2.54798i | 1.00475 | + | 0.393163i | ||||
\(43\) | −2.82920 | − | 4.90031i | −0.431448 | − | 0.747290i | 0.565550 | − | 0.824714i | \(-0.308664\pi\) |
−0.996998 | + | 0.0774237i | \(0.975331\pi\) | |||||||
\(44\) | −23.5436 | −3.54933 | ||||||||
\(45\) | −0.661646 | + | 2.92613i | −0.0986324 | + | 0.436201i | ||||
\(46\) | −4.28260 | −0.631435 | ||||||||
\(47\) | −5.70445 | − | 9.88040i | −0.832080 | − | 1.44120i | −0.896386 | − | 0.443274i | \(-0.853817\pi\) |
0.0643062 | − | 0.997930i | \(-0.479517\pi\) | |||||||
\(48\) | −8.65979 | + | 6.92029i | −1.24993 | + | 0.998858i | ||||
\(49\) | 2.22206 | − | 3.84872i | 0.317437 | − | 0.549817i | ||||
\(50\) | 1.26258 | − | 2.18685i | 0.178555 | − | 0.309267i | ||||
\(51\) | −0.802054 | − | 5.28501i | −0.112310 | − | 0.740050i | ||||
\(52\) | −2.18820 | − | 3.79007i | −0.303449 | − | 0.525588i | ||||
\(53\) | −10.3086 | −1.41600 | −0.708000 | − | 0.706212i | \(-0.750402\pi\) | ||||
−0.708000 | + | 0.706212i | \(0.750402\pi\) | |||||||
\(54\) | −7.35844 | + | 10.8635i | −1.00136 | + | 1.47834i | ||||
\(55\) | 5.37967 | 0.725395 | ||||||||
\(56\) | −4.79676 | − | 8.30823i | −0.640993 | − | 1.11023i | ||||
\(57\) | −0.967280 | − | 6.37374i | −0.128119 | − | 0.844222i | ||||
\(58\) | 0.809153 | − | 1.40149i | 0.106247 | − | 0.184025i | ||||
\(59\) | 4.67420 | − | 8.09595i | 0.608529 | − | 1.05400i | −0.382954 | − | 0.923767i | \(-0.625093\pi\) |
0.991483 | − | 0.130236i | \(-0.0415734\pi\) | |||||||
\(60\) | 5.92161 | − | 4.73213i | 0.764477 | − | 0.610916i | ||||
\(61\) | 3.23867 | + | 5.60954i | 0.414669 | + | 0.718228i | 0.995394 | − | 0.0958721i | \(-0.0305640\pi\) |
−0.580724 | + | 0.814100i | \(0.697231\pi\) | |||||||
\(62\) | −14.1102 | −1.79200 | ||||||||
\(63\) | −3.52241 | − | 3.25509i | −0.443782 | − | 0.410102i | ||||
\(64\) | −2.29649 | −0.287062 | ||||||||
\(65\) | 0.500000 | + | 0.866025i | 0.0620174 | + | 0.107417i | ||||
\(66\) | 21.9112 | + | 8.57397i | 2.69709 | + | 1.05538i | ||||
\(67\) | 7.64188 | − | 13.2361i | 0.933604 | − | 1.61705i | 0.156498 | − | 0.987678i | \(-0.449979\pi\) |
0.777105 | − | 0.629371i | \(-0.216687\pi\) | |||||||
\(68\) | −6.75331 | + | 11.6971i | −0.818959 | + | 1.41848i | ||||
\(69\) | 2.73554 | + | 1.07043i | 0.329321 | + | 0.128865i | ||||
\(70\) | 2.01850 | + | 3.49614i | 0.241257 | + | 0.417869i | ||||
\(71\) | −5.56344 | −0.660258 | −0.330129 | − | 0.943936i | \(-0.607092\pi\) | ||||
−0.330129 | + | 0.943936i | \(0.607092\pi\) | |||||||
\(72\) | 17.1917 | − | 5.34105i | 2.02607 | − | 0.629449i | ||||
\(73\) | 11.7669 | 1.37721 | 0.688604 | − | 0.725138i | \(-0.258224\pi\) | ||||
0.688604 | + | 0.725138i | \(0.258224\pi\) | |||||||
\(74\) | 0.561902 | + | 0.973242i | 0.0653197 | + | 0.113137i | ||||
\(75\) | −1.35308 | + | 1.08128i | −0.156240 | + | 0.124856i | ||||
\(76\) | −8.14451 | + | 14.1067i | −0.934239 | + | 1.61815i | ||||
\(77\) | −4.30028 | + | 7.44830i | −0.490062 | + | 0.848813i | ||||
\(78\) | 0.656238 | + | 4.32418i | 0.0743044 | + | 0.489617i | ||||
\(79\) | 2.66045 | + | 4.60803i | 0.299324 | + | 0.518444i | 0.975981 | − | 0.217854i | \(-0.0699056\pi\) |
−0.676658 | + | 0.736298i | \(0.736572\pi\) | |||||||
\(80\) | −6.40006 | −0.715549 | ||||||||
\(81\) | 7.41558 | − | 5.09992i | 0.823953 | − | 0.566658i | ||||
\(82\) | 16.1445 | 1.78286 | ||||||||
\(83\) | 4.87457 | + | 8.44301i | 0.535054 | + | 0.926741i | 0.999161 | + | 0.0409616i | \(0.0130421\pi\) |
−0.464107 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(84\) | 1.81828 | + | 11.9813i | 0.198391 | + | 1.30727i | ||||
\(85\) | 1.54312 | − | 2.67276i | 0.167375 | − | 0.289902i | ||||
\(86\) | 7.14415 | − | 12.3740i | 0.770374 | − | 1.33433i | ||||
\(87\) | −0.867154 | + | 0.692968i | −0.0929687 | + | 0.0742940i | ||||
\(88\) | −16.1411 | − | 27.9572i | −1.72065 | − | 2.98025i | ||||
\(89\) | −15.7300 | −1.66737 | −0.833687 | − | 0.552237i | \(-0.813774\pi\) | ||||
−0.833687 | + | 0.552237i | \(0.813774\pi\) | |||||||
\(90\) | −7.23437 | + | 2.24754i | −0.762570 | + | 0.236912i | ||||
\(91\) | −1.59871 | −0.167591 | ||||||||
\(92\) | −3.71114 | − | 6.42787i | −0.386913 | − | 0.670152i | ||||
\(93\) | 9.01300 | + | 3.52683i | 0.934605 | + | 0.365715i | ||||
\(94\) | 14.4046 | − | 24.9495i | 1.48572 | − | 2.57335i | ||||
\(95\) | 1.86101 | − | 3.22336i | 0.190935 | − | 0.330710i | ||||
\(96\) | −6.70927 | − | 2.62537i | −0.684762 | − | 0.267951i | ||||
\(97\) | 0.456931 | + | 0.791428i | 0.0463943 | + | 0.0803573i | 0.888290 | − | 0.459283i | \(-0.151894\pi\) |
−0.841896 | + | 0.539640i | \(0.818560\pi\) | |||||||
\(98\) | 11.2221 | 1.13360 | ||||||||
\(99\) | −11.8529 | − | 10.9534i | −1.19126 | − | 1.10086i | ||||
\(100\) | 4.37640 | 0.437640 | ||||||||
\(101\) | −2.91268 | − | 5.04491i | −0.289823 | − | 0.501988i | 0.683945 | − | 0.729534i | \(-0.260263\pi\) |
−0.973767 | + | 0.227546i | \(0.926930\pi\) | |||||||
\(102\) | 10.5449 | − | 8.42670i | 1.04410 | − | 0.834368i | ||||
\(103\) | 8.54446 | − | 14.7994i | 0.841911 | − | 1.45823i | −0.0463665 | − | 0.998924i | \(-0.514764\pi\) |
0.888277 | − | 0.459308i | \(-0.151902\pi\) | |||||||
\(104\) | 3.00038 | − | 5.19682i | 0.294212 | − | 0.509590i | ||||
\(105\) | −0.415475 | − | 2.73771i | −0.0405462 | − | 0.267173i | ||||
\(106\) | −13.0154 | − | 22.5434i | −1.26417 | − | 2.18961i | ||||
\(107\) | 6.04979 | 0.584855 | 0.292428 | − | 0.956288i | \(-0.405537\pi\) | ||||
0.292428 | + | 0.956288i | \(0.405537\pi\) | |||||||
\(108\) | −22.6819 | − | 1.63059i | −2.18257 | − | 0.156904i | ||||
\(109\) | −3.64767 | −0.349383 | −0.174692 | − | 0.984623i | \(-0.555893\pi\) | ||||
−0.174692 | + | 0.984623i | \(0.555893\pi\) | |||||||
\(110\) | 6.79225 | + | 11.7645i | 0.647616 | + | 1.12170i | ||||
\(111\) | −0.115658 | − | 0.762112i | −0.0109778 | − | 0.0723365i | ||||
\(112\) | 5.11594 | − | 8.86106i | 0.483410 | − | 0.837291i | ||||
\(113\) | −6.16716 | + | 10.6818i | −0.580158 | + | 1.00486i | 0.415302 | + | 0.909683i | \(0.363676\pi\) |
−0.995460 | + | 0.0951792i | \(0.969658\pi\) | |||||||
\(114\) | 12.7171 | − | 10.1626i | 1.19107 | − | 0.951817i | ||||
\(115\) | 0.847988 | + | 1.46876i | 0.0790753 | + | 0.136962i | ||||
\(116\) | 2.80472 | 0.260412 | ||||||||
\(117\) | 0.661646 | − | 2.92613i | 0.0611692 | − | 0.270521i | ||||
\(118\) | 23.6061 | 2.17312 | ||||||||
\(119\) | 2.46701 | + | 4.27298i | 0.226150 | + | 0.391704i | ||||
\(120\) | 9.67900 | + | 3.78744i | 0.883568 | + | 0.345744i | ||||
\(121\) | −8.97044 | + | 15.5373i | −0.815495 | + | 1.41248i | ||||
\(122\) | −8.17814 | + | 14.1649i | −0.740414 | + | 1.28243i | ||||
\(123\) | −10.3124 | − | 4.03529i | −0.929839 | − | 0.363850i | ||||
\(124\) | −12.2274 | − | 21.1784i | −1.09805 | − | 1.90188i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.67106 | − | 11.8128i | 0.237957 | − | 1.05237i | ||||
\(127\) | 14.2039 | 1.26039 | 0.630197 | − | 0.776435i | \(-0.282974\pi\) | ||||
0.630197 | + | 0.776435i | \(0.282974\pi\) | |||||||
\(128\) | −7.05910 | − | 12.2267i | −0.623942 | − | 1.08070i | ||||
\(129\) | −7.65625 | + | 6.11833i | −0.674095 | + | 0.538689i | ||||
\(130\) | −1.26258 | + | 2.18685i | −0.110735 | + | 0.191799i | ||||
\(131\) | −9.34730 | + | 16.1900i | −0.816678 | + | 1.41453i | 0.0914393 | + | 0.995811i | \(0.470853\pi\) |
−0.908117 | + | 0.418717i | \(0.862480\pi\) | |||||||
\(132\) | 6.11852 | + | 40.3171i | 0.532549 | + | 3.50915i | ||||
\(133\) | 2.97522 | + | 5.15323i | 0.257984 | + | 0.446842i | ||||
\(134\) | 38.5938 | 3.33400 | ||||||||
\(135\) | 5.18278 | + | 0.372587i | 0.446062 | + | 0.0320672i | ||||
\(136\) | −18.5198 | −1.58806 | ||||||||
\(137\) | −6.92932 | − | 12.0019i | −0.592012 | − | 1.02539i | −0.993961 | − | 0.109732i | \(-0.965001\pi\) |
0.401950 | − | 0.915662i | \(-0.368333\pi\) | |||||||
\(138\) | 1.11297 | + | 7.33371i | 0.0947419 | + | 0.624287i | ||||
\(139\) | −3.26336 | + | 5.65230i | −0.276794 | + | 0.479422i | −0.970586 | − | 0.240754i | \(-0.922605\pi\) |
0.693792 | + | 0.720175i | \(0.255939\pi\) | |||||||
\(140\) | −3.49830 | + | 6.05924i | −0.295661 | + | 0.512099i | ||||
\(141\) | −15.4371 | + | 12.3363i | −1.30004 | + | 1.03890i | ||||
\(142\) | −7.02426 | − | 12.1664i | −0.589463 | − | 1.02098i | ||||
\(143\) | −5.37967 | −0.449871 | ||||||||
\(144\) | 14.1011 | + | 13.0310i | 1.17509 | + | 1.08591i | ||||
\(145\) | −0.640875 | −0.0532217 | ||||||||
\(146\) | 14.8566 | + | 25.7323i | 1.22954 | + | 2.12962i | ||||
\(147\) | −7.16818 | − | 2.80494i | −0.591221 | − | 0.231348i | ||||
\(148\) | −0.973844 | + | 1.68675i | −0.0800495 | + | 0.138650i | ||||
\(149\) | 5.88878 | − | 10.1997i | 0.482427 | − | 0.835589i | −0.517369 | − | 0.855762i | \(-0.673089\pi\) |
0.999796 | + | 0.0201737i | \(0.00642192\pi\) | |||||||
\(150\) | −4.07297 | − | 1.59377i | −0.332557 | − | 0.130131i | ||||
\(151\) | 4.79569 | + | 8.30638i | 0.390268 | + | 0.675964i | 0.992485 | − | 0.122369i | \(-0.0390491\pi\) |
−0.602217 | + | 0.798332i | \(0.705716\pi\) | |||||||
\(152\) | −22.3350 | −1.81160 | ||||||||
\(153\) | −8.84185 | + | 2.74695i | −0.714821 | + | 0.222077i | ||||
\(154\) | −21.7177 | −1.75006 | ||||||||
\(155\) | 2.79393 | + | 4.83923i | 0.224414 | + | 0.388697i | ||||
\(156\) | −5.92161 | + | 4.73213i | −0.474108 | + | 0.378874i | ||||
\(157\) | −3.96466 | + | 6.86698i | −0.316414 | + | 0.548045i | −0.979737 | − | 0.200288i | \(-0.935812\pi\) |
0.663323 | + | 0.748333i | \(0.269146\pi\) | |||||||
\(158\) | −6.71804 | + | 11.6360i | −0.534458 | + | 0.925709i | ||||
\(159\) | 2.67902 | + | 17.6530i | 0.212460 | + | 1.39997i | ||||
\(160\) | −2.07980 | − | 3.60232i | −0.164423 | − | 0.284789i | ||||
\(161\) | −2.71138 | −0.213687 | ||||||||
\(162\) | 20.5155 | + | 9.77770i | 1.61185 | + | 0.768209i | ||||
\(163\) | −2.74092 | −0.214685 | −0.107343 | − | 0.994222i | \(-0.534234\pi\) | ||||
−0.107343 | + | 0.994222i | \(0.534234\pi\) | |||||||
\(164\) | 13.9902 | + | 24.2317i | 1.09245 | + | 1.89218i | ||||
\(165\) | −1.39807 | − | 9.21239i | −0.108840 | − | 0.717183i | ||||
\(166\) | −12.3090 | + | 21.3199i | −0.955367 | + | 1.65474i | ||||
\(167\) | 8.88551 | − | 15.3902i | 0.687582 | − | 1.19093i | −0.285036 | − | 0.958517i | \(-0.592006\pi\) |
0.972618 | − | 0.232410i | \(-0.0746610\pi\) | |||||||
\(168\) | −12.9808 | + | 10.3733i | −1.00149 | + | 0.800319i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 7.79323 | 0.597714 | ||||||||
\(171\) | −10.6633 | + | 3.31282i | −0.815442 | + | 0.253338i | ||||
\(172\) | 24.7634 | 1.88819 | ||||||||
\(173\) | −5.28655 | − | 9.15657i | −0.401929 | − | 0.696161i | 0.592030 | − | 0.805916i | \(-0.298327\pi\) |
−0.993959 | + | 0.109755i | \(0.964993\pi\) | |||||||
\(174\) | −2.61026 | − | 1.02141i | −0.197884 | − | 0.0774327i | ||||
\(175\) | 0.799357 | − | 1.38453i | 0.0604257 | − | 0.104660i | ||||
\(176\) | 17.2151 | − | 29.8175i | 1.29764 | − | 2.24758i | ||||
\(177\) | −15.0786 | − | 5.90032i | −1.13338 | − | 0.443495i | ||||
\(178\) | −19.8603 | − | 34.3990i | −1.48859 | − | 2.57832i | ||||
\(179\) | 5.47435 | 0.409172 | 0.204586 | − | 0.978849i | \(-0.434415\pi\) | ||||
0.204586 | + | 0.978849i | \(0.434415\pi\) | |||||||
\(180\) | −9.64242 | − | 8.91064i | −0.718704 | − | 0.664160i | ||||
\(181\) | −1.35324 | −0.100585 | −0.0502927 | − | 0.998735i | \(-0.516015\pi\) | ||||
−0.0502927 | + | 0.998735i | \(0.516015\pi\) | |||||||
\(182\) | −2.01850 | − | 3.49614i | −0.149621 | − | 0.259151i | ||||
\(183\) | 8.76435 | − | 7.00385i | 0.647880 | − | 0.517739i | ||||
\(184\) | 5.08858 | − | 8.81368i | 0.375135 | − | 0.649753i | ||||
\(185\) | 0.222522 | − | 0.385419i | 0.0163601 | − | 0.0283366i | ||||
\(186\) | 3.66697 | + | 24.1630i | 0.268876 | + | 1.77171i | ||||
\(187\) | 8.30149 | + | 14.3786i | 0.607065 | + | 1.05147i | ||||
\(188\) | 49.9299 | 3.64151 | ||||||||
\(189\) | −4.65875 | + | 6.87786i | −0.338874 | + | 0.500291i | ||||
\(190\) | 9.39866 | 0.681850 | ||||||||
\(191\) | −1.83277 | − | 3.17445i | −0.132615 | − | 0.229695i | 0.792069 | − | 0.610431i | \(-0.209004\pi\) |
−0.924684 | + | 0.380736i | \(0.875671\pi\) | |||||||
\(192\) | 0.596814 | + | 3.93262i | 0.0430714 | + | 0.283812i | ||||
\(193\) | 4.37529 | − | 7.57823i | 0.314940 | − | 0.545493i | −0.664484 | − | 0.747302i | \(-0.731349\pi\) |
0.979425 | + | 0.201809i | \(0.0646821\pi\) | |||||||
\(194\) | −1.15382 | + | 1.99848i | −0.0828395 | + | 0.143482i | ||||
\(195\) | 1.35308 | − | 1.08128i | 0.0968960 | − | 0.0774324i | ||||
\(196\) | 9.72461 | + | 16.8435i | 0.694615 | + | 1.20311i | ||||
\(197\) | −9.50585 | −0.677264 | −0.338632 | − | 0.940919i | \(-0.609964\pi\) | ||||
−0.338632 | + | 0.940919i | \(0.609964\pi\) | |||||||
\(198\) | 8.98813 | − | 39.7500i | 0.638758 | − | 2.82491i | ||||
\(199\) | 25.5829 | 1.81353 | 0.906763 | − | 0.421640i | \(-0.138545\pi\) | ||||
0.906763 | + | 0.421640i | \(0.138545\pi\) | |||||||
\(200\) | 3.00038 | + | 5.19682i | 0.212159 | + | 0.367471i | ||||
\(201\) | −24.6521 | − | 9.64647i | −1.73882 | − | 0.680409i | ||||
\(202\) | 7.35497 | − | 12.7392i | 0.517494 | − | 0.896326i | ||||
\(203\) | 0.512288 | − | 0.887308i | 0.0359555 | − | 0.0622768i | ||||
\(204\) | 21.7856 | + | 8.52482i | 1.52530 | + | 0.596857i | ||||
\(205\) | −3.19674 | − | 5.53691i | −0.223270 | − | 0.386715i | ||||
\(206\) | 43.1521 | 3.00655 | ||||||||
\(207\) | 1.12214 | − | 4.96265i | 0.0779939 | − | 0.344928i | ||||
\(208\) | 6.40006 | 0.443765 | ||||||||
\(209\) | 10.0116 | + | 17.3406i | 0.692518 | + | 1.19948i | ||||
\(210\) | 5.46238 | − | 4.36514i | 0.376940 | − | 0.301224i | ||||
\(211\) | 2.59044 | − | 4.48678i | 0.178333 | − | 0.308882i | −0.762976 | − | 0.646426i | \(-0.776263\pi\) |
0.941310 | + | 0.337544i | \(0.109596\pi\) | |||||||
\(212\) | 22.5574 | − | 39.0705i | 1.54925 | − | 2.68337i | ||||
\(213\) | 1.44583 | + | 9.52707i | 0.0990666 | + | 0.652784i | ||||
\(214\) | 7.63832 | + | 13.2300i | 0.522145 | + | 0.904381i | ||||
\(215\) | −5.65839 | −0.385899 | ||||||||
\(216\) | −13.6141 | − | 28.0519i | −0.926319 | − | 1.90869i | ||||
\(217\) | −8.93340 | −0.606439 | ||||||||
\(218\) | −4.60546 | − | 7.97689i | −0.311921 | − | 0.540263i | ||||
\(219\) | −3.05798 | − | 20.1501i | −0.206639 | − | 1.36162i | ||||
\(220\) | −11.7718 | + | 20.3893i | −0.793654 | + | 1.37465i | ||||
\(221\) | −1.54312 | + | 2.67276i | −0.103802 | + | 0.179790i | ||||
\(222\) | 1.52059 | − | 1.21515i | 0.102056 | − | 0.0815556i | ||||
\(223\) | −7.52975 | − | 13.0419i | −0.504230 | − | 0.873351i | −0.999988 | − | 0.00489073i | \(-0.998443\pi\) |
0.495759 | − | 0.868460i | \(-0.334890\pi\) | |||||||
\(224\) | 6.65001 | 0.444323 | ||||||||
\(225\) | 2.20328 | + | 2.03607i | 0.146885 | + | 0.135738i | ||||
\(226\) | −31.1461 | −2.07180 | ||||||||
\(227\) | −10.8699 | − | 18.8272i | −0.721459 | − | 1.24960i | −0.960415 | − | 0.278573i | \(-0.910139\pi\) |
0.238956 | − | 0.971030i | \(-0.423195\pi\) | |||||||
\(228\) | 26.2735 | + | 10.2810i | 1.74001 | + | 0.680873i | ||||
\(229\) | −13.5876 | + | 23.5344i | −0.897892 | + | 1.55520i | −0.0677090 | + | 0.997705i | \(0.521569\pi\) |
−0.830183 | + | 0.557490i | \(0.811764\pi\) | |||||||
\(230\) | −2.14130 | + | 3.70884i | −0.141193 | + | 0.244554i | ||||
\(231\) | 13.8724 | + | 5.42831i | 0.912734 | + | 0.357157i | ||||
\(232\) | 1.92287 | + | 3.33051i | 0.126243 | + | 0.218659i | ||||
\(233\) | 24.1372 | 1.58128 | 0.790641 | − | 0.612280i | \(-0.209747\pi\) | ||||
0.790641 | + | 0.612280i | \(0.209747\pi\) | |||||||
\(234\) | 7.23437 | − | 2.24754i | 0.472926 | − | 0.146926i | ||||
\(235\) | −11.4089 | −0.744235 | ||||||||
\(236\) | 20.4562 | + | 35.4311i | 1.33158 | + | 2.30637i | ||||
\(237\) | 7.19959 | − | 5.75340i | 0.467664 | − | 0.373724i | ||||
\(238\) | −6.22957 | + | 10.7899i | −0.403803 | + | 0.699408i | ||||
\(239\) | −8.64007 | + | 14.9650i | −0.558879 | + | 0.968008i | 0.438711 | + | 0.898628i | \(0.355435\pi\) |
−0.997590 | + | 0.0693793i | \(0.977898\pi\) | |||||||
\(240\) | 1.66325 | + | 10.9597i | 0.107363 | + | 0.707449i | ||||
\(241\) | 8.28251 | + | 14.3457i | 0.533523 | + | 0.924090i | 0.999233 | + | 0.0391522i | \(0.0124657\pi\) |
−0.465710 | + | 0.884938i | \(0.654201\pi\) | |||||||
\(242\) | −45.3035 | −2.91222 | ||||||||
\(243\) | −10.6605 | − | 11.3734i | −0.683871 | − | 0.729603i | ||||
\(244\) | −28.3474 | −1.81476 | ||||||||
\(245\) | −2.22206 | − | 3.84872i | −0.141962 | − | 0.245885i | ||||
\(246\) | −4.19564 | − | 27.6465i | −0.267504 | − | 1.76268i | ||||
\(247\) | −1.86101 | + | 3.22336i | −0.118413 | + | 0.205097i | ||||
\(248\) | 16.7657 | − | 29.0391i | 1.06463 | − | 1.84399i | ||||
\(249\) | 13.1914 | − | 10.5416i | 0.835969 | − | 0.668047i | ||||
\(250\) | −1.26258 | − | 2.18685i | −0.0798524 | − | 0.138308i | ||||
\(251\) | 10.2182 | 0.644965 | 0.322482 | − | 0.946575i | \(-0.395483\pi\) | ||||
0.322482 | + | 0.946575i | \(0.395483\pi\) | |||||||
\(252\) | 20.0448 | − | 6.22741i | 1.26270 | − | 0.392290i | ||||
\(253\) | −9.12380 | −0.573608 | ||||||||
\(254\) | 17.9335 | + | 31.0618i | 1.12525 | + | 1.94899i | ||||
\(255\) | −4.97798 | − | 1.94791i | −0.311733 | − | 0.121983i | ||||
\(256\) | 15.5288 | − | 26.8967i | 0.970551 | − | 1.68104i | ||||
\(257\) | −14.2157 | + | 24.6224i | −0.886754 | + | 1.53590i | −0.0430639 | + | 0.999072i | \(0.513712\pi\) |
−0.843690 | + | 0.536831i | \(0.819621\pi\) | |||||||
\(258\) | −23.0465 | − | 9.01818i | −1.43481 | − | 0.561448i | ||||
\(259\) | 0.355749 | + | 0.616175i | 0.0221051 | + | 0.0382872i | ||||
\(260\) | −4.37640 | −0.271413 | ||||||||
\(261\) | 1.41203 | + | 1.30486i | 0.0874022 | + | 0.0807690i | ||||
\(262\) | −47.2067 | −2.91644 | ||||||||
\(263\) | −6.62365 | − | 11.4725i | −0.408432 | − | 0.707425i | 0.586282 | − | 0.810107i | \(-0.300591\pi\) |
−0.994714 | + | 0.102682i | \(0.967258\pi\) | |||||||
\(264\) | −43.6803 | + | 34.9062i | −2.68834 | + | 2.14833i | ||||
\(265\) | −5.15432 | + | 8.92754i | −0.316627 | + | 0.548415i | ||||
\(266\) | −7.51288 | + | 13.0127i | −0.460644 | + | 0.797859i | ||||
\(267\) | 4.08792 | + | 26.9367i | 0.250176 | + | 1.64850i | ||||
\(268\) | 33.4439 | + | 57.9265i | 2.04291 | + | 3.53842i | ||||
\(269\) | −20.2913 | −1.23718 | −0.618590 | − | 0.785714i | \(-0.712296\pi\) | ||||
−0.618590 | + | 0.785714i | \(0.712296\pi\) | |||||||
\(270\) | 5.72886 | + | 11.8044i | 0.348647 | + | 0.718390i | ||||
\(271\) | −7.28275 | −0.442396 | −0.221198 | − | 0.975229i | \(-0.570997\pi\) | ||||
−0.221198 | + | 0.975229i | \(0.570997\pi\) | |||||||
\(272\) | −9.87607 | − | 17.1059i | −0.598825 | − | 1.03719i | ||||
\(273\) | 0.415475 | + | 2.73771i | 0.0251457 | + | 0.165694i | ||||
\(274\) | 17.4976 | − | 30.3067i | 1.05707 | − | 1.83090i | ||||
\(275\) | 2.68984 | − | 4.65893i | 0.162203 | − | 0.280944i | ||||
\(276\) | −10.0429 | + | 8.02559i | −0.604513 | + | 0.483084i | ||||
\(277\) | −6.87279 | − | 11.9040i | −0.412946 | − | 0.715244i | 0.582264 | − | 0.813000i | \(-0.302167\pi\) |
−0.995210 | + | 0.0977558i | \(0.968834\pi\) | |||||||
\(278\) | −16.4809 | −0.988461 | ||||||||
\(279\) | 3.69719 | − | 16.3508i | 0.221345 | − | 0.978898i | ||||
\(280\) | −9.59351 | −0.573322 | ||||||||
\(281\) | 0.451460 | + | 0.781952i | 0.0269318 | + | 0.0466473i | 0.879177 | − | 0.476495i | \(-0.158093\pi\) |
−0.852245 | + | 0.523142i | \(0.824760\pi\) | |||||||
\(282\) | −46.4681 | − | 18.1832i | −2.76714 | − | 1.08279i | ||||
\(283\) | 13.9264 | − | 24.1212i | 0.827836 | − | 1.43385i | −0.0718962 | − | 0.997412i | \(-0.522905\pi\) |
0.899732 | − | 0.436442i | \(-0.143762\pi\) | |||||||
\(284\) | 12.1739 | − | 21.0858i | 0.722388 | − | 1.25121i | ||||
\(285\) | −6.00346 | − | 2.34918i | −0.355614 | − | 0.139153i | ||||
\(286\) | −6.79225 | − | 11.7645i | −0.401634 | − | 0.695651i | ||||
\(287\) | 10.2213 | 0.603346 | ||||||||
\(288\) | −2.75218 | + | 12.1715i | −0.162174 | + | 0.717214i | ||||
\(289\) | −7.47511 | −0.439713 | ||||||||
\(290\) | −0.809153 | − | 1.40149i | −0.0475151 | − | 0.0822986i | ||||
\(291\) | 1.23653 | − | 0.988146i | 0.0724866 | − | 0.0579261i | ||||
\(292\) | −25.7482 | + | 44.5973i | −1.50680 | + | 2.60986i | ||||
\(293\) | 1.62563 | − | 2.81568i | 0.0949706 | − | 0.164494i | −0.814626 | − | 0.579987i | \(-0.803058\pi\) |
0.909596 | + | 0.415493i | \(0.136391\pi\) | |||||||
\(294\) | −2.91640 | − | 19.2172i | −0.170088 | − | 1.12077i | ||||
\(295\) | −4.67420 | − | 8.09595i | −0.272142 | − | 0.471364i | ||||
\(296\) | −2.67060 | −0.155226 | ||||||||
\(297\) | −15.6767 | + | 23.1440i | −0.909653 | + | 1.34295i | ||||
\(298\) | 29.7401 | 1.72280 | ||||||||
\(299\) | −0.847988 | − | 1.46876i | −0.0490404 | − | 0.0849405i | ||||
\(300\) | −1.13734 | − | 7.49433i | −0.0656644 | − | 0.432686i | ||||
\(301\) | 4.52307 | − | 7.83419i | 0.260706 | − | 0.451555i | ||||
\(302\) | −12.1099 | + | 20.9749i | −0.696844 | + | 1.20697i | ||||
\(303\) | −7.88218 | + | 6.29888i | −0.452819 | + | 0.361861i | ||||
\(304\) | −11.9106 | − | 20.6297i | −0.683118 | − | 1.18319i | ||||
\(305\) | 6.47734 | 0.370891 | ||||||||
\(306\) | −17.1707 | − | 15.8675i | −0.981581 | − | 0.907087i | ||||
\(307\) | 23.0790 | 1.31719 | 0.658593 | − | 0.752499i | \(-0.271152\pi\) | ||||
0.658593 | + | 0.752499i | \(0.271152\pi\) | |||||||
\(308\) | −18.8197 | − | 32.5967i | −1.07235 | − | 1.85737i | ||||
\(309\) | −27.5637 | − | 10.7858i | −1.56805 | − | 0.613584i | ||||
\(310\) | −7.05511 | + | 12.2198i | −0.400703 | + | 0.694038i | ||||
\(311\) | −3.23713 | + | 5.60687i | −0.183561 | + | 0.317936i | −0.943091 | − | 0.332536i | \(-0.892096\pi\) |
0.759530 | + | 0.650472i | \(0.225429\pi\) | |||||||
\(312\) | −9.67900 | − | 3.78744i | −0.547965 | − | 0.214421i | ||||
\(313\) | −3.92191 | − | 6.79296i | −0.221680 | − | 0.383961i | 0.733638 | − | 0.679540i | \(-0.237821\pi\) |
−0.955318 | + | 0.295580i | \(0.904487\pi\) | |||||||
\(314\) | −20.0227 | −1.12995 | ||||||||
\(315\) | −4.58019 | + | 1.42295i | −0.258065 | + | 0.0801744i | ||||
\(316\) | −23.2864 | −1.30996 | ||||||||
\(317\) | 15.8696 | + | 27.4870i | 0.891326 | + | 1.54382i | 0.838287 | + | 0.545230i | \(0.183558\pi\) |
0.0530394 | + | 0.998592i | \(0.483109\pi\) | |||||||
\(318\) | −35.2219 | + | 28.1468i | −1.97514 | + | 1.57839i | ||||
\(319\) | 1.72385 | − | 2.98579i | 0.0965170 | − | 0.167172i | ||||
\(320\) | −1.14825 | + | 1.98882i | −0.0641889 | + | 0.111179i | ||||
\(321\) | −1.57222 | − | 10.3599i | −0.0877529 | − | 0.578234i | ||||
\(322\) | −3.42333 | − | 5.92938i | −0.190775 | − | 0.330431i | ||||
\(323\) | 11.4870 | 0.639156 | ||||||||
\(324\) | 3.10229 | + | 39.2652i | 0.172350 | + | 2.18140i | ||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −3.46062 | − | 5.99396i | −0.191666 | − | 0.331975i | ||||
\(327\) | 0.947958 | + | 6.24642i | 0.0524222 | + | 0.345428i | ||||
\(328\) | −19.1829 | + | 33.2257i | −1.05920 | + | 1.83458i | ||||
\(329\) | 9.11979 | − | 15.7959i | 0.502790 | − | 0.870858i | ||||
\(330\) | 18.3809 | − | 14.6887i | 1.01184 | − | 0.808587i | ||||
\(331\) | −9.05397 | − | 15.6819i | −0.497651 | − | 0.861958i | 0.502345 | − | 0.864667i | \(-0.332471\pi\) |
−0.999996 | + | 0.00270979i | \(0.999137\pi\) | |||||||
\(332\) | −42.6662 | −2.34161 | ||||||||
\(333\) | −1.27502 | + | 0.396116i | −0.0698704 | + | 0.0217070i | ||||
\(334\) | 44.8746 | 2.45543 | ||||||||
\(335\) | −7.64188 | − | 13.2361i | −0.417520 | − | 0.723166i | ||||
\(336\) | −16.5036 | − | 6.45793i | −0.900345 | − | 0.352309i | ||||
\(337\) | 7.48318 | − | 12.9613i | 0.407635 | − | 0.706044i | −0.586989 | − | 0.809595i | \(-0.699687\pi\) |
0.994624 | + | 0.103550i | \(0.0330203\pi\) | |||||||
\(338\) | 1.26258 | − | 2.18685i | 0.0686751 | − | 0.118949i | ||||
\(339\) | 19.8948 | + | 7.78491i | 1.08054 | + | 0.422818i | ||||
\(340\) | 6.75331 | + | 11.6971i | 0.366250 | + | 0.634363i | ||||
\(341\) | −30.0609 | −1.62789 | ||||||||
\(342\) | −20.7079 | − | 19.1363i | −1.11975 | − | 1.03477i | ||||
\(343\) | 18.2959 | 0.987884 | ||||||||
\(344\) | 16.9773 | + | 29.4056i | 0.915357 | + | 1.58545i | ||||
\(345\) | 2.29479 | − | 1.83383i | 0.123547 | − | 0.0987303i | ||||
\(346\) | 13.3493 | − | 23.1217i | 0.717665 | − | 1.24303i | ||||
\(347\) | −5.90574 | + | 10.2290i | −0.317037 | + | 0.549124i | −0.979868 | − | 0.199645i | \(-0.936021\pi\) |
0.662831 | + | 0.748769i | \(0.269355\pi\) | |||||||
\(348\) | −0.728893 | − | 4.80293i | −0.0390728 | − | 0.257464i | ||||
\(349\) | 11.6750 | + | 20.2217i | 0.624949 | + | 1.08244i | 0.988551 | + | 0.150889i | \(0.0482137\pi\) |
−0.363602 | + | 0.931555i | \(0.618453\pi\) | |||||||
\(350\) | 4.03700 | 0.215787 | ||||||||
\(351\) | −5.18278 | − | 0.372587i | −0.276636 | − | 0.0198872i | ||||
\(352\) | 22.3773 | 1.19271 | ||||||||
\(353\) | −6.78898 | − | 11.7589i | −0.361341 | − | 0.625861i | 0.626841 | − | 0.779147i | \(-0.284348\pi\) |
−0.988182 | + | 0.153286i | \(0.951014\pi\) | |||||||
\(354\) | −6.13478 | − | 40.4242i | −0.326060 | − | 2.14852i | ||||
\(355\) | −2.78172 | + | 4.81808i | −0.147638 | + | 0.255717i | ||||
\(356\) | 34.4203 | − | 59.6177i | 1.82427 | − | 3.15973i | ||||
\(357\) | 6.67612 | − | 5.33508i | 0.353337 | − | 0.282362i | ||||
\(358\) | 6.91178 | + | 11.9716i | 0.365299 | + | 0.632716i | ||||
\(359\) | −5.90809 | −0.311817 | −0.155908 | − | 0.987772i | \(-0.549830\pi\) | ||||
−0.155908 | + | 0.987772i | \(0.549830\pi\) | |||||||
\(360\) | 3.97038 | − | 17.5590i | 0.209258 | − | 0.925441i | ||||
\(361\) | −5.14660 | −0.270874 | ||||||||
\(362\) | −1.70857 | − | 2.95932i | −0.0898003 | − | 0.155539i | ||||
\(363\) | 28.9379 | + | 11.3235i | 1.51885 | + | 0.594332i | ||||
\(364\) | 3.49830 | − | 6.05924i | 0.183361 | − | 0.317590i | ||||
\(365\) | 5.88343 | − | 10.1904i | 0.307953 | − | 0.533390i | ||||
\(366\) | 26.3820 | + | 10.3234i | 1.37901 | + | 0.539613i | ||||
\(367\) | 1.22318 | + | 2.11861i | 0.0638494 | + | 0.110590i | 0.896183 | − | 0.443685i | \(-0.146329\pi\) |
−0.832334 | + | 0.554275i | \(0.812996\pi\) | |||||||
\(368\) | 10.8544 | 0.565823 | ||||||||
\(369\) | −4.23022 | + | 18.7081i | −0.220216 | + | 0.973906i | ||||
\(370\) | 1.12380 | 0.0584237 | ||||||||
\(371\) | −8.24028 | − | 14.2726i | −0.427814 | − | 0.740996i | ||||
\(372\) | −33.0892 | + | 26.4425i | −1.71559 | + | 1.37098i | ||||
\(373\) | 4.09993 | − | 7.10128i | 0.212286 | − | 0.367690i | −0.740143 | − | 0.672449i | \(-0.765242\pi\) |
0.952430 | + | 0.304759i | \(0.0985758\pi\) | |||||||
\(374\) | −20.9625 | + | 36.3082i | −1.08395 | + | 1.87745i | ||||
\(375\) | 0.259881 | + | 1.71244i | 0.0134202 | + | 0.0884302i | ||||
\(376\) | 34.2311 | + | 59.2900i | 1.76533 | + | 3.05765i | ||||
\(377\) | 0.640875 | 0.0330067 | ||||||||
\(378\) | −20.9229 | − | 1.50413i | −1.07616 | − | 0.0773643i | ||||
\(379\) | −0.155663 | −0.00799586 | −0.00399793 | − | 0.999992i | \(-0.501273\pi\) | ||||
−0.00399793 | + | 0.999992i | \(0.501273\pi\) | |||||||
\(380\) | 8.14451 | + | 14.1067i | 0.417805 | + | 0.723659i | ||||
\(381\) | −3.69133 | − | 24.3234i | −0.189112 | − | 1.24613i | ||||
\(382\) | 4.62802 | − | 8.01597i | 0.236790 | − | 0.410133i | ||||
\(383\) | −8.30317 | + | 14.3815i | −0.424272 | + | 0.734861i | −0.996352 | − | 0.0853368i | \(-0.972803\pi\) |
0.572080 | + | 0.820198i | \(0.306137\pi\) | |||||||
\(384\) | −19.1030 | + | 15.2658i | −0.974848 | + | 0.779030i | ||||
\(385\) | 4.30028 | + | 7.44830i | 0.219163 | + | 0.379601i | ||||
\(386\) | 22.0966 | 1.12469 | ||||||||
\(387\) | 12.4670 | + | 11.5209i | 0.633734 | + | 0.585638i | ||||
\(388\) | −3.99943 | −0.203040 | ||||||||
\(389\) | −10.4497 | − | 18.0994i | −0.529819 | − | 0.917674i | −0.999395 | − | 0.0347817i | \(-0.988926\pi\) |
0.469576 | − | 0.882892i | \(-0.344407\pi\) | |||||||
\(390\) | 4.07297 | + | 1.59377i | 0.206243 | + | 0.0807038i | ||||
\(391\) | −2.61710 | + | 4.53295i | −0.132352 | + | 0.229241i | ||||
\(392\) | −13.3341 | + | 23.0953i | −0.673471 | + | 1.16649i | ||||
\(393\) | 30.1536 | + | 11.7993i | 1.52105 | + | 0.595194i | ||||
\(394\) | −12.0019 | − | 20.7878i | −0.604645 | − | 1.04728i | ||||
\(395\) | 5.32090 | 0.267723 | ||||||||
\(396\) | 67.4506 | − | 20.9553i | 3.38952 | − | 1.05304i | ||||
\(397\) | −15.5139 | −0.778618 | −0.389309 | − | 0.921107i | \(-0.627286\pi\) | ||||
−0.389309 | + | 0.921107i | \(0.627286\pi\) | |||||||
\(398\) | 32.3004 | + | 55.9460i | 1.61907 | + | 2.80432i | ||||
\(399\) | 8.05141 | − | 6.43412i | 0.403075 | − | 0.322109i | ||||
\(400\) | −3.20003 | + | 5.54262i | −0.160002 | + | 0.277131i | ||||
\(401\) | −16.8282 | + | 29.1473i | −0.840360 | + | 1.45555i | 0.0492298 | + | 0.998787i | \(0.484323\pi\) |
−0.889590 | + | 0.456759i | \(0.849010\pi\) | |||||||
\(402\) | −10.0298 | − | 66.0897i | −0.500240 | − | 3.29626i | ||||
\(403\) | −2.79393 | − | 4.83923i | −0.139176 | − | 0.241059i | ||||
\(404\) | 25.4941 | 1.26838 | ||||||||
\(405\) | −0.708869 | − | 8.97204i | −0.0352240 | − | 0.445824i | ||||
\(406\) | 2.58721 | 0.128401 | ||||||||
\(407\) | 1.19709 | + | 2.07343i | 0.0593378 | + | 0.102776i | ||||
\(408\) | 4.81294 | + | 31.7141i | 0.238276 | + | 1.57008i | ||||
\(409\) | −10.0723 | + | 17.4458i | −0.498044 | + | 0.862638i | −0.999997 | − | 0.00225691i | \(-0.999282\pi\) |
0.501953 | + | 0.864895i | \(0.332615\pi\) | |||||||
\(410\) | 8.07225 | − | 13.9815i | 0.398660 | − | 0.690499i | ||||
\(411\) | −18.7518 | + | 14.9851i | −0.924960 | + | 0.739162i | ||||
\(412\) | 37.3940 | + | 64.7682i | 1.84227 | + | 3.19090i | ||||
\(413\) | 14.9454 | 0.735416 | ||||||||
\(414\) | 12.2693 | − | 3.81178i | 0.603005 | − | 0.187339i | ||||
\(415\) | 9.74915 | 0.478567 | ||||||||
\(416\) | 2.07980 | + | 3.60232i | 0.101971 | + | 0.176618i | ||||
\(417\) | 10.5273 | + | 4.11939i | 0.515525 | + | 0.201727i | ||||
\(418\) | −25.2809 | + | 43.7877i | −1.23653 | + | 2.14173i | ||||
\(419\) | 16.7215 | − | 28.9625i | 0.816898 | − | 1.41491i | −0.0910582 | − | 0.995846i | \(-0.529025\pi\) |
0.907957 | − | 0.419064i | \(-0.137642\pi\) | |||||||
\(420\) | 11.2852 | + | 4.41597i | 0.550664 | + | 0.215477i | ||||
\(421\) | −13.1682 | − | 22.8081i | −0.641781 | − | 1.11160i | −0.985035 | − | 0.172355i | \(-0.944862\pi\) |
0.343254 | − | 0.939243i | \(-0.388471\pi\) | |||||||
\(422\) | 13.0825 | 0.636847 | ||||||||
\(423\) | 25.1370 | + | 23.2293i | 1.22220 | + | 1.12945i | ||||
\(424\) | 61.8598 | 3.00418 | ||||||||
\(425\) | −1.54312 | − | 2.67276i | −0.0748524 | − | 0.129648i | ||||
\(426\) | −19.0088 | + | 15.1905i | −0.920978 | + | 0.735980i | ||||
\(427\) | −5.17771 | + | 8.96805i | −0.250567 | + | 0.433994i | ||||
\(428\) | −13.2381 | + | 22.9291i | −0.639890 | + | 1.10832i | ||||
\(429\) | 1.39807 | + | 9.21239i | 0.0674996 | + | 0.444778i | ||||
\(430\) | −7.14415 | − | 12.3740i | −0.344522 | − | 0.596729i | ||||
\(431\) | 10.7108 | 0.515922 | 0.257961 | − | 0.966155i | \(-0.416949\pi\) | ||||
0.257961 | + | 0.966155i | \(0.416949\pi\) | |||||||
\(432\) | 18.6502 | − | 27.5339i | 0.897306 | − | 1.32472i | ||||
\(433\) | −10.5665 | −0.507795 | −0.253898 | − | 0.967231i | \(-0.581713\pi\) | ||||
−0.253898 | + | 0.967231i | \(0.581713\pi\) | |||||||
\(434\) | −11.2791 | − | 19.5360i | −0.541414 | − | 0.937757i | ||||
\(435\) | 0.166551 | + | 1.09746i | 0.00798551 | + | 0.0526193i | ||||
\(436\) | 7.98182 | − | 13.8249i | 0.382260 | − | 0.662094i | ||||
\(437\) | −3.15623 | + | 5.46674i | −0.150983 | + | 0.261510i | ||||
\(438\) | 40.2042 | − | 32.1284i | 1.92103 | − | 1.53515i | ||||
\(439\) | 16.9499 | + | 29.3581i | 0.808975 | + | 1.40119i | 0.913574 | + | 0.406672i | \(0.133311\pi\) |
−0.104599 | + | 0.994514i | \(0.533356\pi\) | |||||||
\(440\) | −32.2822 | −1.53899 | ||||||||
\(441\) | −2.94043 | + | 13.0040i | −0.140020 | + | 0.619240i | ||||
\(442\) | −7.79323 | −0.370686 | ||||||||
\(443\) | −14.7155 | − | 25.4881i | −0.699157 | − | 1.21097i | −0.968759 | − | 0.248003i | \(-0.920226\pi\) |
0.269603 | − | 0.962972i | \(-0.413108\pi\) | |||||||
\(444\) | 3.14154 | + | 1.22930i | 0.149091 | + | 0.0583400i | ||||
\(445\) | −7.86499 | + | 13.6226i | −0.372836 | + | 0.645771i | ||||
\(446\) | 19.0138 | − | 32.9328i | 0.900328 | − | 1.55941i | ||||
\(447\) | −18.9967 | − | 7.43350i | −0.898514 | − | 0.351593i | ||||
\(448\) | −1.83572 | − | 3.17956i | −0.0867295 | − | 0.150220i | ||||
\(449\) | 37.6658 | 1.77756 | 0.888780 | − | 0.458335i | \(-0.151554\pi\) | ||||
0.888780 | + | 0.458335i | \(0.151554\pi\) | |||||||
\(450\) | −1.67076 | + | 7.38892i | −0.0787603 | + | 0.348317i | ||||
\(451\) | 34.3948 | 1.61959 | ||||||||
\(452\) | −26.9900 | − | 46.7480i | −1.26950 | − | 2.19884i | ||||
\(453\) | 12.9779 | − | 10.3710i | 0.609755 | − | 0.487273i | ||||
\(454\) | 27.4481 | − | 47.5415i | 1.28820 | − | 2.23123i | ||||
\(455\) | −0.799357 | + | 1.38453i | −0.0374744 | + | 0.0649076i | ||||
\(456\) | 5.80442 | + | 38.2473i | 0.271817 | + | 1.79110i | ||||
\(457\) | 15.9738 | + | 27.6674i | 0.747223 | + | 1.29423i | 0.949149 | + | 0.314827i | \(0.101947\pi\) |
−0.201926 | + | 0.979401i | \(0.564720\pi\) | |||||||
\(458\) | −68.6214 | −3.20647 | ||||||||
\(459\) | 7.00181 | + | 14.4273i | 0.326817 | + | 0.673408i | ||||
\(460\) | −7.42227 | −0.346065 | ||||||||
\(461\) | 7.01569 | + | 12.1515i | 0.326753 | + | 0.565953i | 0.981866 | − | 0.189578i | \(-0.0607121\pi\) |
−0.655112 | + | 0.755531i | \(0.727379\pi\) | |||||||
\(462\) | 5.64402 | + | 37.1904i | 0.262583 | + | 1.73025i | ||||
\(463\) | −20.4647 | + | 35.4460i | −0.951077 | + | 1.64731i | −0.207976 | + | 0.978134i | \(0.566688\pi\) |
−0.743101 | + | 0.669180i | \(0.766646\pi\) | |||||||
\(464\) | −2.05082 | + | 3.55212i | −0.0952069 | + | 0.164903i | ||||
\(465\) | 7.56083 | − | 6.04208i | 0.350625 | − | 0.280195i | ||||
\(466\) | 30.4751 | + | 52.7844i | 1.41173 | + | 2.44519i | ||||
\(467\) | −4.20484 | −0.194577 | −0.0972884 | − | 0.995256i | \(-0.531017\pi\) | ||||
−0.0972884 | + | 0.995256i | \(0.531017\pi\) | |||||||
\(468\) | 9.64242 | + | 8.91064i | 0.445721 | + | 0.411894i | ||||
\(469\) | 24.4343 | 1.12827 | ||||||||
\(470\) | −14.4046 | − | 24.9495i | −0.664435 | − | 1.15084i | ||||
\(471\) | 12.7897 | + | 5.00465i | 0.589316 | + | 0.230602i | ||||
\(472\) | −28.0488 | + | 48.5819i | −1.29105 | + | 2.23616i | ||||
\(473\) | 15.2201 | − | 26.3621i | 0.699823 | − | 1.21213i | ||||
\(474\) | 21.6718 | + | 8.48029i | 0.995421 | + | 0.389513i | ||||
\(475\) | −1.86101 | − | 3.22336i | −0.0853889 | − | 0.147898i | ||||
\(476\) | −21.5932 | −0.989724 | ||||||||
\(477\) | 29.5335 | − | 9.17533i | 1.35224 | − | 0.420109i | ||||
\(478\) | −43.6350 | −1.99582 | ||||||||
\(479\) | −13.2705 | − | 22.9851i | −0.606344 | − | 1.05022i | −0.991838 | − | 0.127507i | \(-0.959302\pi\) |
0.385494 | − | 0.922710i | \(-0.374031\pi\) | |||||||
\(480\) | −5.62827 | + | 4.49772i | −0.256894 | + | 0.205292i | ||||
\(481\) | −0.222522 | + | 0.385419i | −0.0101461 | + | 0.0175736i | ||||
\(482\) | −20.9146 | + | 36.2252i | −0.952634 | + | 1.65001i | ||||
\(483\) | 0.704636 | + | 4.64309i | 0.0320620 | + | 0.211268i | ||||
\(484\) | −39.2582 | − | 67.9972i | −1.78446 | − | 3.09078i | ||||
\(485\) | 0.913862 | 0.0414963 | ||||||||
\(486\) | 11.4122 | − | 37.6726i | 0.517667 | − | 1.70887i | ||||
\(487\) | 29.2682 | 1.32627 | 0.663135 | − | 0.748500i | \(-0.269225\pi\) | ||||
0.663135 | + | 0.748500i | \(0.269225\pi\) | |||||||
\(488\) | −19.4345 | − | 33.6616i | −0.879759 | − | 1.52379i | ||||
\(489\) | 0.712311 | + | 4.69366i | 0.0322118 | + | 0.212255i | ||||
\(490\) | 5.61103 | − | 9.71860i | 0.253481 | − | 0.439041i | ||||
\(491\) | −11.4610 | + | 19.8511i | −0.517229 | + | 0.895867i | 0.482570 | + | 0.875857i | \(0.339703\pi\) |
−0.999800 | + | 0.0200103i | \(0.993630\pi\) | |||||||
\(492\) | 37.8597 | − | 30.2548i | 1.70685 | − | 1.36399i | ||||
\(493\) | −0.988947 | − | 1.71291i | −0.0445399 | − | 0.0771454i | ||||
\(494\) | −9.39866 | −0.422866 | ||||||||
\(495\) | −15.4124 | + | 4.78824i | −0.692734 | + | 0.215215i | ||||
\(496\) | 35.7627 | 1.60579 | ||||||||
\(497\) | −4.44717 | − | 7.70273i | −0.199483 | − | 0.345514i | ||||
\(498\) | 39.7080 | + | 15.5379i | 1.77936 | + | 0.696271i | ||||
\(499\) | −2.93038 | + | 5.07556i | −0.131182 | + | 0.227213i | −0.924132 | − | 0.382072i | \(-0.875210\pi\) |
0.792951 | + | 0.609286i | \(0.208544\pi\) | |||||||
\(500\) | 2.18820 | − | 3.79007i | 0.0978592 | − | 0.169497i | ||||
\(501\) | −28.6640 | − | 11.2163i | −1.28061 | − | 0.501109i | ||||
\(502\) | 12.9012 | + | 22.3456i | 0.575809 | + | 0.997331i | ||||
\(503\) | 0.171544 | 0.00764877 | 0.00382439 | − | 0.999993i | \(-0.498783\pi\) | ||||
0.00382439 | + | 0.999993i | \(0.498783\pi\) | |||||||
\(504\) | 21.1372 | + | 19.5330i | 0.941525 | + | 0.870070i | ||||
\(505\) | −5.82536 | −0.259225 | ||||||||
\(506\) | −11.5195 | − | 19.9524i | −0.512104 | − | 0.886990i | ||||
\(507\) | −1.35308 | + | 1.08128i | −0.0600924 | + | 0.0480215i | ||||
\(508\) | −31.0810 | + | 53.8339i | −1.37900 | + | 2.38849i | ||||
\(509\) | 18.2170 | − | 31.5528i | 0.807454 | − | 1.39855i | −0.107167 | − | 0.994241i | \(-0.534178\pi\) |
0.914622 | − | 0.404311i | \(-0.132489\pi\) | |||||||
\(510\) | −2.02531 | − | 13.3455i | −0.0896823 | − | 0.590947i | ||||
\(511\) | 9.40593 | + | 16.2915i | 0.416094 | + | 0.720696i | ||||
\(512\) | 50.1889 | 2.21806 | ||||||||
\(513\) | 8.44421 | + | 17.3993i | 0.372821 | + | 0.768200i | ||||
\(514\) | −71.7939 | −3.16669 | ||||||||
\(515\) | −8.54446 | − | 14.7994i | −0.376514 | − | 0.652141i | ||||
\(516\) | −6.43552 | − | 42.4059i | −0.283308 | − | 1.86681i | ||||
\(517\) | 30.6881 | − | 53.1533i | 1.34966 | − | 2.33768i | ||||
\(518\) | −0.898320 | + | 1.55594i | −0.0394699 | + | 0.0683639i | ||||
\(519\) | −14.3062 | + | 11.4325i | −0.627974 | + | 0.501832i | ||||
\(520\) | −3.00038 | − | 5.19682i | −0.131576 | − | 0.227896i | ||||
\(521\) | 6.99027 | 0.306249 | 0.153125 | − | 0.988207i | \(-0.451066\pi\) | ||||
0.153125 | + | 0.988207i | \(0.451066\pi\) | |||||||
\(522\) | −1.07075 | + | 4.73537i | −0.0468653 | + | 0.207262i | ||||
\(523\) | 10.2358 | 0.447579 | 0.223790 | − | 0.974637i | \(-0.428157\pi\) | ||||
0.223790 | + | 0.974637i | \(0.428157\pi\) | |||||||
\(524\) | −40.9075 | − | 70.8539i | −1.78705 | − | 3.09527i | ||||
\(525\) | −2.57866 | − | 1.00904i | −0.112542 | − | 0.0440382i | ||||
\(526\) | 16.7257 | − | 28.9698i | 0.729277 | − | 1.26314i | ||||
\(527\) | −8.62275 | + | 14.9350i | −0.375613 | + | 0.650581i | ||||
\(528\) | −55.5346 | − | 21.7309i | −2.41683 | − | 0.945718i | ||||
\(529\) | 10.0618 | + | 17.4276i | 0.437471 | + | 0.757722i | ||||
\(530\) | −26.0309 | −1.13071 | ||||||||
\(531\) | −6.18533 | + | 27.3546i | −0.268420 | + | 1.18709i | ||||
\(532\) | −26.0415 | −1.12904 | ||||||||
\(533\) | 3.19674 | + | 5.53691i | 0.138466 | + | 0.239830i | ||||
\(534\) | −53.7451 | + | 42.9493i | −2.32578 | + | 1.85860i | ||||
\(535\) | 3.02489 | − | 5.23927i | 0.130778 | − | 0.226513i | ||||
\(536\) | −45.8571 | + | 79.4269i | −1.98073 | + | 3.43072i | ||||
\(537\) | −1.42268 | − | 9.37451i | −0.0613930 | − | 0.404540i | ||||
\(538\) | −25.6193 | − | 44.3739i | −1.10453 | − | 1.91309i | ||||
\(539\) | 23.9079 | 1.02979 | ||||||||
\(540\) | −12.7531 | + | 18.8278i | −0.548805 | + | 0.810220i | ||||
\(541\) | −14.1128 | −0.606755 | −0.303378 | − | 0.952870i | \(-0.598114\pi\) | ||||
−0.303378 | + | 0.952870i | \(0.598114\pi\) | |||||||
\(542\) | −9.19503 | − | 15.9263i | −0.394960 | − | 0.684092i | ||||
\(543\) | 0.351680 | + | 2.31734i | 0.0150920 | + | 0.0994467i | ||||
\(544\) | 6.41877 | − | 11.1176i | 0.275202 | − | 0.476665i | ||||
\(545\) | −1.82383 | + | 3.15897i | −0.0781244 | + | 0.135316i | ||||
\(546\) | −5.46238 | + | 4.36514i | −0.233768 | + | 0.186811i | ||||
\(547\) | 3.24835 | + | 5.62631i | 0.138890 | + | 0.240564i | 0.927077 | − | 0.374872i | \(-0.122313\pi\) |
−0.788187 | + | 0.615436i | \(0.788980\pi\) | |||||||
\(548\) | 60.6509 | 2.59088 | ||||||||
\(549\) | −14.2714 | − | 13.1883i | −0.609088 | − | 0.562863i | ||||
\(550\) | 13.5845 | 0.579245 | ||||||||
\(551\) | −1.19267 | − | 2.06577i | −0.0508096 | − | 0.0880047i | ||||
\(552\) | −16.4154 | − | 6.42340i | −0.698684 | − | 0.273398i | ||||
\(553\) | −4.25329 | + | 7.36692i | −0.180868 | + | 0.313273i | ||||
\(554\) | 17.3549 | − | 30.0595i | 0.737337 | − | 1.27711i | ||||
\(555\) | −0.717837 | − | 0.280893i | −0.0304705 | − | 0.0119232i | ||||
\(556\) | −14.2817 | − | 24.7367i | −0.605681 | − | 1.04907i | ||||
\(557\) | 13.7471 | 0.582483 | 0.291242 | − | 0.956650i | \(-0.405932\pi\) | ||||
0.291242 | + | 0.956650i | \(0.405932\pi\) | |||||||
\(558\) | 40.4247 | − | 12.5590i | 1.71131 | − | 0.531663i | ||||
\(559\) | 5.65839 | 0.239324 | ||||||||
\(560\) | −5.11594 | − | 8.86106i | −0.216188 | − | 0.374448i | ||||
\(561\) | 22.4651 | − | 17.9525i | 0.948479 | − | 0.757957i | ||||
\(562\) | −1.14001 | + | 1.97455i | −0.0480882 | + | 0.0832913i | ||||
\(563\) | −0.645415 | + | 1.11789i | −0.0272010 | + | 0.0471135i | −0.879305 | − | 0.476258i | \(-0.841993\pi\) |
0.852104 | + | 0.523372i | \(0.175326\pi\) | |||||||
\(564\) | −12.9758 | − | 85.5021i | −0.546380 | − | 3.60029i | ||||
\(565\) | 6.16716 | + | 10.6818i | 0.259454 | + | 0.449388i | ||||
\(566\) | 70.3324 | 2.95629 | ||||||||
\(567\) | 12.9887 | + | 6.19041i | 0.545473 | + | 0.259973i | ||||
\(568\) | 33.3849 | 1.40080 | ||||||||
\(569\) | −5.81243 | − | 10.0674i | −0.243670 | − | 0.422048i | 0.718087 | − | 0.695953i | \(-0.245018\pi\) |
−0.961757 | + | 0.273905i | \(0.911685\pi\) | |||||||
\(570\) | −2.44253 | − | 16.0947i | −0.102306 | − | 0.674132i | ||||
\(571\) | 8.88874 | − | 15.3958i | 0.371982 | − | 0.644292i | −0.617888 | − | 0.786266i | \(-0.712012\pi\) |
0.989870 | + | 0.141974i | \(0.0453449\pi\) | |||||||
\(572\) | 11.7718 | − | 20.3893i | 0.492203 | − | 0.852521i | ||||
\(573\) | −4.95976 | + | 3.96349i | −0.207197 | + | 0.165577i | ||||
\(574\) | 12.9052 | + | 22.3525i | 0.538653 | + | 0.932975i | ||||
\(575\) | 1.69598 | 0.0707271 | ||||||||
\(576\) | 6.57928 | − | 2.04402i | 0.274137 | − | 0.0851675i | ||||
\(577\) | −30.0210 | −1.24979 | −0.624896 | − | 0.780708i | \(-0.714859\pi\) | ||||
−0.624896 | + | 0.780708i | \(0.714859\pi\) | |||||||
\(578\) | −9.43790 | − | 16.3469i | −0.392565 | − | 0.679942i | ||||
\(579\) | −14.1143 | − | 5.52300i | −0.586572 | − | 0.229528i | ||||
\(580\) | 1.40236 | − | 2.42896i | 0.0582299 | − | 0.100857i | ||||
\(581\) | −7.79305 | + | 13.4980i | −0.323310 | + | 0.559990i | ||||
\(582\) | 3.72213 | + | 1.45649i | 0.154287 | + | 0.0603734i | ||||
\(583\) | −27.7286 | − | 48.0273i | −1.14840 | − | 1.98909i | ||||
\(584\) | −70.6103 | −2.92187 | ||||||||
\(585\) | −2.20328 | − | 2.03607i | −0.0910943 | − | 0.0841810i | ||||
\(586\) | 8.20995 | 0.339150 | ||||||||
\(587\) | 1.10857 | + | 1.92010i | 0.0457556 | + | 0.0792510i | 0.887996 | − | 0.459851i | \(-0.152097\pi\) |
−0.842241 | + | 0.539102i | \(0.818764\pi\) | |||||||
\(588\) | 26.3163 | − | 21.0301i | 1.08527 | − | 0.867268i | ||||
\(589\) | −10.3991 | + | 18.0117i | −0.428486 | + | 0.742159i | ||||
\(590\) | 11.8031 | − | 20.4435i | 0.485925 | − | 0.841646i | ||||
\(591\) | 2.47039 | + | 16.2782i | 0.101618 | + | 0.669597i | ||||
\(592\) | −1.42415 | − | 2.46671i | −0.0585323 | − | 0.101381i | ||||
\(593\) | 15.6211 | 0.641483 | 0.320742 | − | 0.947167i | \(-0.396068\pi\) | ||||
0.320742 | + | 0.947167i | \(0.396068\pi\) | |||||||
\(594\) | −70.4054 | − | 5.06141i | −2.88877 | − | 0.207672i | ||||
\(595\) | 4.93402 | 0.202275 | ||||||||
\(596\) | 25.7716 | + | 44.6378i | 1.05565 | + | 1.82843i | ||||
\(597\) | −6.64851 | − | 43.8093i | −0.272105 | − | 1.79300i | ||||
\(598\) | 2.14130 | − | 3.70884i | 0.0875643 | − | 0.151666i | ||||
\(599\) | −11.5585 | + | 20.0200i | −0.472269 | + | 0.817994i | −0.999496 | − | 0.0317303i | \(-0.989898\pi\) |
0.527227 | + | 0.849724i | \(0.323232\pi\) | |||||||
\(600\) | 8.11951 | − | 6.48854i | 0.331478 | − | 0.264894i | ||||
\(601\) | 1.70480 | + | 2.95280i | 0.0695402 | + | 0.120447i | 0.898699 | − | 0.438566i | \(-0.144513\pi\) |
−0.829159 | + | 0.559013i | \(0.811180\pi\) | |||||||
\(602\) | 22.8429 | 0.931007 | ||||||||
\(603\) | −10.1124 | + | 44.7222i | −0.411810 | + | 1.82123i | ||||
\(604\) | −41.9757 | −1.70797 | ||||||||
\(605\) | 8.97044 | + | 15.5373i | 0.364700 | + | 0.631679i | ||||
\(606\) | −23.7265 | − | 9.28430i | −0.963825 | − | 0.377149i | ||||
\(607\) | −10.5060 | + | 18.1970i | −0.426427 | + | 0.738593i | −0.996553 | − | 0.0829645i | \(-0.973561\pi\) |
0.570126 | + | 0.821558i | \(0.306895\pi\) | |||||||
\(608\) | 7.74105 | − | 13.4079i | 0.313941 | − | 0.543762i | ||||
\(609\) | −1.65260 | − | 0.646669i | −0.0669667 | − | 0.0262044i | ||||
\(610\) | 8.17814 | + | 14.1649i | 0.331123 | + | 0.573522i | ||||
\(611\) | 11.4089 | 0.461555 | ||||||||
\(612\) | 8.93660 | − | 39.5221i | 0.361241 | − | 1.59759i | ||||
\(613\) | 4.34045 | 0.175309 | 0.0876546 | − | 0.996151i | \(-0.472063\pi\) | ||||
0.0876546 | + | 0.996151i | \(0.472063\pi\) | |||||||
\(614\) | 29.1390 | + | 50.4702i | 1.17595 | + | 2.03681i | ||||
\(615\) | −8.65087 | + | 6.91317i | −0.348837 | + | 0.278766i | ||||
\(616\) | 25.8050 | − | 44.6955i | 1.03971 | − | 1.80083i | ||||
\(617\) | −12.3921 | + | 21.4637i | −0.498887 | + | 0.864098i | −0.999999 | − | 0.00128460i | \(-0.999591\pi\) |
0.501112 | + | 0.865382i | \(0.332924\pi\) | |||||||
\(618\) | −11.2144 | − | 73.8956i | −0.451110 | − | 2.97252i | ||||
\(619\) | −17.4471 | − | 30.2193i | −0.701258 | − | 1.21461i | −0.968025 | − | 0.250853i | \(-0.919289\pi\) |
0.266767 | − | 0.963761i | \(-0.414045\pi\) | |||||||
\(620\) | −24.4547 | −0.982126 | ||||||||
\(621\) | −8.78987 | − | 0.631899i | −0.352725 | − | 0.0253572i | ||||
\(622\) | −16.3485 | −0.655514 | ||||||||
\(623\) | −12.5739 | − | 21.7786i | −0.503761 | − | 0.872540i | ||||
\(624\) | −1.66325 | − | 10.9597i | −0.0665834 | − | 0.438741i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 9.90343 | − | 17.1533i | 0.395821 | − | 0.685582i | ||||
\(627\) | 27.0930 | − | 21.6508i | 1.08199 | − | 0.864650i | ||||
\(628\) | −17.3509 | − | 30.0527i | −0.692377 | − | 1.19923i | ||||
\(629\) | 1.37351 | 0.0547655 | ||||||||
\(630\) | −8.89463 | − | 8.21959i | −0.354370 | − | 0.327476i | ||||
\(631\) | −27.9002 | −1.11069 | −0.555344 | − | 0.831620i | \(-0.687414\pi\) | ||||
−0.555344 | + | 0.831620i | \(0.687414\pi\) | |||||||
\(632\) | −15.9647 | − | 27.6517i | −0.635043 | − | 1.09993i | ||||
\(633\) | −8.35656 | − | 3.26996i | −0.332143 | − | 0.129969i | ||||
\(634\) | −40.0732 | + | 69.4088i | −1.59151 | + | 2.75658i | ||||
\(635\) | 7.10196 | − | 12.3010i | 0.281833 | − | 0.488149i | ||||
\(636\) | −72.7682 | − | 28.4745i | −2.88545 | − | 1.12909i | ||||
\(637\) | 2.22206 | + | 3.84872i | 0.0880411 | + | 0.152492i | ||||
\(638\) | 8.70596 | 0.344672 | ||||||||
\(639\) | 15.9388 | − | 4.95180i | 0.630530 | − | 0.195890i | ||||
\(640\) | −14.1182 | −0.558071 | ||||||||
\(641\) | −1.63649 | − | 2.83448i | −0.0646374 | − | 0.111955i | 0.831896 | − | 0.554932i | \(-0.187256\pi\) |
−0.896533 | + | 0.442977i | \(0.853922\pi\) | |||||||
\(642\) | 20.6705 | − | 16.5184i | 0.815800 | − | 0.651929i | ||||
\(643\) | −17.2981 | + | 29.9612i | −0.682170 | + | 1.18155i | 0.292148 | + | 0.956373i | \(0.405630\pi\) |
−0.974317 | + | 0.225179i | \(0.927703\pi\) | |||||||
\(644\) | 5.93304 | − | 10.2763i | 0.233795 | − | 0.404944i | ||||
\(645\) | 1.47051 | + | 9.68967i | 0.0579011 | + | 0.381531i | ||||
\(646\) | 14.5033 | + | 25.1204i | 0.570623 | + | 0.988349i | ||||
\(647\) | 32.2974 | 1.26974 | 0.634871 | − | 0.772618i | \(-0.281053\pi\) | ||||
0.634871 | + | 0.772618i | \(0.281053\pi\) | |||||||
\(648\) | −44.4992 | + | 30.6034i | −1.74809 | + | 1.20222i | ||||
\(649\) | 50.2913 | 1.97411 | ||||||||
\(650\) | 1.26258 | + | 2.18685i | 0.0495223 | + | 0.0857752i | ||||
\(651\) | 2.32162 | + | 15.2979i | 0.0909914 | + | 0.599574i | ||||
\(652\) | 5.99767 | − | 10.3883i | 0.234887 | − | 0.406836i | ||||
\(653\) | −17.7871 | + | 30.8081i | −0.696062 | + | 1.20561i | 0.273760 | + | 0.961798i | \(0.411733\pi\) |
−0.969821 | + | 0.243816i | \(0.921601\pi\) | |||||||
\(654\) | −12.4631 | + | 9.95963i | −0.487346 | + | 0.389452i | ||||
\(655\) | 9.34730 | + | 16.1900i | 0.365229 | + | 0.632596i | ||||
\(656\) | −40.9186 | −1.59760 | ||||||||
\(657\) | −33.7112 | + | 10.4732i | −1.31520 | + | 0.408600i | ||||
\(658\) | 46.0577 | 1.79552 | ||||||||
\(659\) | 15.0300 | + | 26.0327i | 0.585484 | + | 1.01409i | 0.994815 | + | 0.101703i | \(0.0324290\pi\) |
−0.409330 | + | 0.912386i | \(0.634238\pi\) | |||||||
\(660\) | 37.9749 | + | 14.8597i | 1.47817 | + | 0.578414i | ||||
\(661\) | −2.58617 | + | 4.47938i | −0.100590 | + | 0.174228i | −0.911928 | − | 0.410350i | \(-0.865407\pi\) |
0.811338 | + | 0.584578i | \(0.198740\pi\) | |||||||
\(662\) | 22.8627 | − | 39.5993i | 0.888583 | − | 1.53907i | ||||
\(663\) | 4.97798 | + | 1.94791i | 0.193329 | + | 0.0756505i | ||||
\(664\) | −29.2512 | − | 50.6646i | −1.13517 | − | 1.96617i | ||||
\(665\) | 5.95044 | 0.230748 | ||||||||
\(666\) | −2.47605 | − | 2.28814i | −0.0959450 | − | 0.0886635i | ||||
\(667\) | 1.08691 | 0.0420853 | ||||||||
\(668\) | 38.8865 | + | 67.3535i | 1.50457 | + | 2.60598i | ||||
\(669\) | −20.3767 | + | 16.2836i | −0.787809 | + | 0.629561i | ||||
\(670\) | 19.2969 | − | 33.4232i | 0.745504 | − | 1.29125i | ||||
\(671\) | −17.4230 | + | 30.1775i | −0.672607 | + | 1.16499i | ||||
\(672\) | −1.72821 | − | 11.3878i | −0.0666672 | − | 0.439293i | ||||
\(673\) | −5.71413 | − | 9.89716i | −0.220263 | − | 0.381507i | 0.734624 | − | 0.678474i | \(-0.237358\pi\) |
−0.954888 | + | 0.296967i | \(0.904025\pi\) | |||||||
\(674\) | 37.7924 | 1.45571 | ||||||||
\(675\) | 2.91406 | − | 4.30212i | 0.112162 | − | 0.165589i | ||||
\(676\) | 4.37640 | 0.168323 | ||||||||
\(677\) | 4.25402 | + | 7.36818i | 0.163495 | + | 0.283182i | 0.936120 | − | 0.351681i | \(-0.114390\pi\) |
−0.772625 | + | 0.634863i | \(0.781056\pi\) | |||||||
\(678\) | 8.09426 | + | 53.3358i | 0.310858 | + | 2.04835i | ||||
\(679\) | −0.730502 | + | 1.26527i | −0.0280341 | + | 0.0485565i | ||||
\(680\) | −9.25991 | + | 16.0386i | −0.355101 | + | 0.615054i | ||||
\(681\) | −29.4156 | + | 23.5069i | −1.12721 | + | 0.900785i | ||||
\(682\) | −37.9542 | − | 65.7386i | −1.45334 | − | 2.51726i | ||||
\(683\) | −17.6393 | −0.674947 | −0.337474 | − | 0.941335i | \(-0.609572\pi\) | ||||
−0.337474 | + | 0.941335i | \(0.609572\pi\) | |||||||
\(684\) | 10.7776 | − | 47.6638i | 0.412090 | − | 1.82247i | ||||
\(685\) | −13.8586 | −0.529511 | ||||||||
\(686\) | 23.0999 | + | 40.0102i | 0.881959 | + | 1.52760i | ||||
\(687\) | 43.8324 | + | 17.1518i | 1.67231 | + | 0.654383i | ||||
\(688\) | −18.1070 | + | 31.3623i | −0.690324 | + | 1.19568i | ||||
\(689\) | 5.15432 | − | 8.92754i | 0.196364 | − | 0.340112i | ||||
\(690\) | 6.90766 | + | 2.70300i | 0.262970 | + | 0.102901i | ||||
\(691\) | −17.4651 | − | 30.2505i | −0.664404 | − | 1.15078i | −0.979447 | − | 0.201704i | \(-0.935352\pi\) |
0.315042 | − | 0.949078i | \(-0.397981\pi\) | |||||||
\(692\) | 46.2721 | 1.75900 | ||||||||
\(693\) | 5.69052 | − | 25.1663i | 0.216165 | − | 0.955990i | ||||
\(694\) | −29.8258 | −1.13217 | ||||||||
\(695\) | 3.26336 | + | 5.65230i | 0.123786 | + | 0.214404i | ||||
\(696\) | 5.20359 | − | 4.15834i | 0.197242 | − | 0.157622i | ||||
\(697\) | 9.86590 | − | 17.0882i | 0.373698 | − | 0.647263i | ||||
\(698\) | −29.4812 | + | 51.0629i | −1.11588 | + | 1.93276i | ||||
\(699\) | −6.27280 | − | 41.3336i | −0.237259 | − | 1.56338i | ||||
\(700\) | 3.49830 | + | 6.05924i | 0.132223 | + | 0.229018i | ||||
\(701\) | −49.5629 | −1.87197 | −0.935983 | − | 0.352045i | \(-0.885486\pi\) | ||||
−0.935983 | + | 0.352045i | \(0.885486\pi\) | |||||||
\(702\) | −5.72886 | − | 11.8044i | −0.216222 | − | 0.445527i | ||||
\(703\) | 1.65646 | 0.0624745 | ||||||||
\(704\) | −6.17719 | − | 10.6992i | −0.232812 | − | 0.403242i | ||||
\(705\) | 2.96495 | + | 19.5371i | 0.111667 | + | 0.735810i | ||||
\(706\) | 17.1432 | − | 29.6929i | 0.645194 | − | 1.11751i | ||||
\(707\) | 4.65655 | − | 8.06537i | 0.175127 | − | 0.303330i | ||||
\(708\) | 55.3576 | − | 44.2379i | 2.08047 | − | 1.66256i | ||||
\(709\) | −18.0806 | − | 31.3165i | −0.679031 | − | 1.17612i | −0.975273 | − | 0.221003i | \(-0.929067\pi\) |
0.296243 | − | 0.955113i | \(-0.404266\pi\) | |||||||
\(710\) | −14.0485 | −0.527232 | ||||||||
\(711\) | −11.7234 | − | 10.8337i | −0.439662 | − | 0.406295i | ||||
\(712\) | 94.3919 | 3.53749 | ||||||||
\(713\) | −4.73845 | − | 8.20723i | −0.177456 | − | 0.307363i | ||||
\(714\) | 20.0961 | + | 7.86370i | 0.752078 | + | 0.294291i | ||||
\(715\) | −2.68984 | + | 4.65893i | −0.100594 | + | 0.174234i | ||||
\(716\) | −11.9790 | + | 20.7482i | −0.447675 | + | 0.775395i | ||||
\(717\) | 27.8722 | + | 10.9065i | 1.04090 | + | 0.407311i | ||||
\(718\) | −7.45941 | − | 12.9201i | −0.278383 | − | 0.482173i | ||||
\(719\) | 21.1195 | 0.787624 | 0.393812 | − | 0.919191i | \(-0.371156\pi\) | ||||
0.393812 | + | 0.919191i | \(0.371156\pi\) | |||||||
\(720\) | 18.3357 | − | 5.69645i | 0.683331 | − | 0.212294i | ||||
\(721\) | 27.3203 | 1.01746 | ||||||||
\(722\) | −6.49798 | − | 11.2548i | −0.241830 | − | 0.418861i | ||||
\(723\) | 22.4138 | − | 17.9115i | 0.833578 | − | 0.666136i | ||||
\(724\) | 2.96115 | − | 5.12887i | 0.110050 | − | 0.190613i | ||||
\(725\) | −0.320437 | + | 0.555014i | −0.0119007 | + | 0.0206127i | ||||
\(726\) | 11.7735 | + | 77.5796i | 0.436955 | + | 2.87925i | ||||
\(727\) | 13.6302 | + | 23.6081i | 0.505515 | + | 0.875577i | 0.999980 | + | 0.00637961i | \(0.00203071\pi\) |
−0.494465 | + | 0.869198i | \(0.664636\pi\) | |||||||
\(728\) | 9.59351 | 0.355559 | ||||||||
\(729\) | −16.7058 | + | 21.2112i | −0.618734 | + | 0.785600i | ||||
\(730\) | 29.7131 | 1.09973 | ||||||||
\(731\) | −8.73158 | − | 15.1235i | −0.322949 | − | 0.559364i | ||||
\(732\) | 7.36695 | + | 48.5433i | 0.272290 | + | 1.79421i | ||||
\(733\) | 5.80668 | − | 10.0575i | 0.214474 | − | 0.371481i | −0.738635 | − | 0.674105i | \(-0.764529\pi\) |
0.953110 | + | 0.302624i | \(0.0978628\pi\) | |||||||
\(734\) | −3.08871 | + | 5.34981i | −0.114006 | + | 0.197465i | ||||
\(735\) | −6.01324 | + | 4.80535i | −0.221802 | + | 0.177248i | ||||
\(736\) | 3.52730 | + | 6.10945i | 0.130018 | + | 0.225197i | ||||
\(737\) | 82.2216 | 3.02867 | ||||||||
\(738\) | −46.2528 | + | 14.3696i | −1.70259 | + | 0.528952i | ||||
\(739\) | 42.9401 | 1.57958 | 0.789788 | − | 0.613380i | \(-0.210191\pi\) | ||||
0.789788 | + | 0.613380i | \(0.210191\pi\) | |||||||
\(740\) | 0.973844 | + | 1.68675i | 0.0357992 | + | 0.0620061i | ||||
\(741\) | 6.00346 | + | 2.34918i | 0.220543 | + | 0.0862993i | ||||
\(742\) | 20.8080 | − | 36.0405i | 0.763885 | − | 1.32309i | ||||
\(743\) | 17.3555 | − | 30.0606i | 0.636711 | − | 1.10282i | −0.349439 | − | 0.936959i | \(-0.613628\pi\) |
0.986150 | − | 0.165856i | \(-0.0530388\pi\) | |||||||
\(744\) | −54.0850 | − | 21.1637i | −1.98285 | − | 0.775898i | ||||
\(745\) | −5.88878 | − | 10.1997i | −0.215748 | − | 0.373687i | ||||
\(746\) | 20.7059 | 0.758096 | ||||||||
\(747\) | −21.4801 | − | 19.8499i | −0.785915 | − | 0.726270i | ||||
\(748\) | −72.6612 | −2.65676 | ||||||||
\(749\) | 4.83594 | + | 8.37609i | 0.176701 | + | 0.306056i | ||||
\(750\) | −3.41673 | + | 2.73041i | −0.124761 | + | 0.0997005i | ||||
\(751\) | −0.655127 | + | 1.13471i | −0.0239059 | + | 0.0414062i | −0.877731 | − | 0.479154i | \(-0.840944\pi\) |
0.853825 | + | 0.520560i | \(0.174277\pi\) | |||||||
\(752\) | −36.5089 | + | 63.2352i | −1.33134 | + | 2.30595i | ||||
\(753\) | −2.65550 | − | 17.4980i | −0.0967719 | − | 0.637663i | ||||
\(754\) | 0.809153 | + | 1.40149i | 0.0294676 | + | 0.0510394i | ||||
\(755\) | 9.59138 | 0.349066 | ||||||||
\(756\) | −15.8733 | − | 32.7071i | −0.577308 | − | 1.18955i | ||||
\(757\) | 1.73705 | 0.0631343 | 0.0315671 | − | 0.999502i | \(-0.489950\pi\) | ||||
0.0315671 | + | 0.999502i | \(0.489950\pi\) | |||||||
\(758\) | −0.196536 | − | 0.340411i | −0.00713852 | − | 0.0123643i | ||||
\(759\) | 2.37110 | + | 15.6240i | 0.0860655 | + | 0.567115i | ||||
\(760\) | −11.1675 | + | 19.3426i | −0.405087 | + | 0.701631i | ||||
\(761\) | 9.10484 | − | 15.7700i | 0.330050 | − | 0.571663i | −0.652471 | − | 0.757813i | \(-0.726268\pi\) |
0.982521 | + | 0.186150i | \(0.0596010\pi\) | |||||||
\(762\) | 48.5310 | − | 38.7825i | 1.75809 | − | 1.40494i | ||||
\(763\) | −2.91579 | − | 5.05029i | −0.105559 | − | 0.182833i | ||||
\(764\) | 16.0419 | 0.580374 | ||||||||
\(765\) | −2.04200 | + | 9.03074i | −0.0738286 | + | 0.326507i | ||||
\(766\) | −41.9336 | −1.51512 | ||||||||
\(767\) | 4.67420 | + | 8.09595i | 0.168776 | + | 0.292328i | ||||
\(768\) | −50.0947 | − | 19.6023i | −1.80764 | − | 0.707337i | ||||
\(769\) | −20.5593 | + | 35.6098i | −0.741388 | + | 1.28412i | 0.210475 | + | 0.977599i | \(0.432499\pi\) |
−0.951863 | + | 0.306523i | \(0.900834\pi\) | |||||||
\(770\) | −10.8589 | + | 18.8081i | −0.391326 | + | 0.677797i | ||||
\(771\) | 45.8589 | + | 17.9448i | 1.65157 | + | 0.646265i | ||||
\(772\) | 19.1480 | + | 33.1653i | 0.689152 | + | 1.19365i | ||||
\(773\) | 21.2243 | 0.763384 | 0.381692 | − | 0.924290i | \(-0.375342\pi\) | ||||
0.381692 | + | 0.924290i | \(0.375342\pi\) | |||||||
\(774\) | −9.45380 | + | 41.8094i | −0.339810 | + | 1.50281i | ||||
\(775\) | 5.58787 | 0.200722 | ||||||||
\(776\) | −2.74194 | − | 4.74918i | −0.0984298 | − | 0.170485i | ||||
\(777\) | 0.962712 | − | 0.769331i | 0.0345371 | − | 0.0275996i | ||||
\(778\) | 26.3870 | − | 45.7037i | 0.946020 | − | 1.63856i | ||||
\(779\) | 11.8983 | − | 20.6085i | 0.426301 | − | 0.738375i | ||||
\(780\) | 1.13734 | + | 7.49433i | 0.0407233 | + | 0.268340i | ||||
\(781\) | −14.9647 | − | 25.9197i | −0.535480 | − | 0.927479i | ||||
\(782\) | −13.2171 | −0.472644 | ||||||||
\(783\) | 1.86755 | − | 2.75712i | 0.0667407 | − | 0.0985315i | ||||
\(784\) | −28.4426 | −1.01581 | ||||||||
\(785\) | 3.96466 | + | 6.86698i | 0.141505 | + | 0.245093i | ||||
\(786\) | 12.2681 | + | 80.8389i | 0.437589 | + | 2.88343i | ||||
\(787\) | 4.82991 | − | 8.36565i | 0.172168 | − | 0.298203i | −0.767010 | − | 0.641636i | \(-0.778256\pi\) |
0.939177 | + | 0.343432i | \(0.111590\pi\) | |||||||
\(788\) | 20.8007 | − | 36.0279i | 0.740994 | − | 1.28344i | ||||
\(789\) | −17.9247 | + | 14.3241i | −0.638135 | + | 0.509952i | ||||
\(790\) | 6.71804 | + | 11.6360i | 0.239017 | + | 0.413990i | ||||
\(791\) | −19.7191 | −0.701129 | ||||||||
\(792\) | 71.1266 | + | 65.7286i | 2.52737 | + | 2.33557i | ||||
\(793\) | −6.47734 | −0.230017 | ||||||||
\(794\) | −19.5874 | − | 33.9264i | −0.695132 | − | 1.20400i | ||||
\(795\) | 16.6274 | + | 6.50638i | 0.589714 | + | 0.230758i | ||||
\(796\) | −55.9806 | + | 96.9612i | −1.98418 | + | 3.43670i | ||||
\(797\) | 17.9391 | − | 31.0714i | 0.635435 | − | 1.10061i | −0.350988 | − | 0.936380i | \(-0.614154\pi\) |
0.986423 | − | 0.164225i | \(-0.0525124\pi\) | |||||||
\(798\) | 24.2360 | + | 9.48364i | 0.857943 | + | 0.335717i | ||||
\(799\) | −17.6053 | − | 30.4933i | −0.622831 | − | 1.07878i | ||||
\(800\) | −4.15960 | −0.147064 | ||||||||
\(801\) | 45.0652 | − | 14.0006i | 1.59230 | − | 0.494689i | ||||
\(802\) | −84.9876 | −3.00102 | ||||||||
\(803\) | 31.6510 | + | 54.8211i | 1.11694 | + | 1.93459i | ||||
\(804\) | 90.5044 | − | 72.3247i | 3.19185 | − | 2.55070i | ||||
\(805\) | −1.35569 | + | 2.34813i | −0.0477818 | + | 0.0827606i | ||||
\(806\) | 7.05511 | − | 12.2198i | 0.248506 | − | 0.430424i | ||||
\(807\) | 5.27331 | + | 34.7476i | 0.185629 | + | 1.22318i | ||||
\(808\) | 17.4783 | + | 30.2734i | 0.614886 | + | 1.06501i | ||||
\(809\) | 35.0035 | 1.23066 | 0.615329 | − | 0.788270i | \(-0.289023\pi\) | ||||
0.615329 | + | 0.788270i | \(0.289023\pi\) | |||||||
\(810\) | 18.7255 | − | 12.8781i | 0.657946 | − | 0.452489i | ||||
\(811\) | 10.9673 | 0.385115 | 0.192558 | − | 0.981286i | \(-0.438322\pi\) | ||||
0.192558 | + | 0.981286i | \(0.438322\pi\) | |||||||
\(812\) | 2.24197 | + | 3.88321i | 0.0786779 | + | 0.136274i | ||||
\(813\) | 1.89265 | + | 12.4713i | 0.0663780 | + | 0.437388i | ||||
\(814\) | −3.02285 | + | 5.23572i | −0.105951 | + | 0.183512i | ||||
\(815\) | −1.37046 | + | 2.37370i | −0.0480051 | + | 0.0831472i | ||||
\(816\) | −26.7262 | + | 21.3577i | −0.935605 | + | 0.747669i | ||||
\(817\) | −10.5303 | − | 18.2390i | −0.368409 | − | 0.638103i | ||||
\(818\) | −50.8683 | −1.77857 | ||||||||
\(819\) | 4.58019 | − | 1.42295i | 0.160045 | − | 0.0497220i | ||||
\(820\) | 27.9804 | 0.977117 | ||||||||
\(821\) | −12.6573 | − | 21.9230i | −0.441741 | − | 0.765118i | 0.556077 | − | 0.831130i | \(-0.312306\pi\) |
−0.997819 | + | 0.0660120i | \(0.978972\pi\) | |||||||
\(822\) | −56.4458 | − | 22.0875i | −1.96877 | − | 0.770390i | ||||
\(823\) | −10.0481 | + | 17.4038i | −0.350254 | + | 0.606657i | −0.986294 | − | 0.164999i | \(-0.947238\pi\) |
0.636040 | + | 0.771656i | \(0.280571\pi\) | |||||||
\(824\) | −51.2733 | + | 88.8080i | −1.78619 | + | 3.09377i | ||||
\(825\) | −8.67720 | − | 3.39543i | −0.302101 | − | 0.118214i | ||||
\(826\) | 18.8697 | + | 32.6833i | 0.656562 | + | 1.13720i | ||||
\(827\) | −25.4134 | −0.883710 | −0.441855 | − | 0.897086i | \(-0.645679\pi\) | ||||
−0.441855 | + | 0.897086i | \(0.645679\pi\) | |||||||
\(828\) | 16.3533 | + | 15.1122i | 0.568317 | + | 0.525186i | ||||
\(829\) | −9.17826 | −0.318774 | −0.159387 | − | 0.987216i | \(-0.550952\pi\) | ||||
−0.159387 | + | 0.987216i | \(0.550952\pi\) | |||||||
\(830\) | 12.3090 | + | 21.3199i | 0.427253 | + | 0.740024i | ||||
\(831\) | −18.5989 | + | 14.8629i | −0.645188 | + | 0.515588i | ||||
\(832\) | 1.14825 | − | 1.98882i | 0.0398083 | − | 0.0689500i | ||||
\(833\) | 6.85780 | − | 11.8781i | 0.237609 | − | 0.411551i | ||||
\(834\) | 4.28308 | + | 28.2227i | 0.148311 | + | 0.977272i | ||||
\(835\) | −8.88551 | − | 15.3902i | −0.307496 | − | 0.532598i | ||||
\(836\) | −87.6296 | −3.03073 | ||||||||
\(837\) | −28.9607 | − | 2.08197i | −1.00103 | − | 0.0719633i | ||||
\(838\) | 84.4487 | 2.91723 | ||||||||
\(839\) | 0.0468293 | + | 0.0811108i | 0.00161673 | + | 0.00280025i | 0.866833 | − | 0.498599i | \(-0.166152\pi\) |
−0.865216 | + | 0.501399i | \(0.832819\pi\) | |||||||
\(840\) | 2.49317 | + | 16.4283i | 0.0860225 | + | 0.566832i | ||||
\(841\) | 14.2946 | − | 24.7590i | 0.492919 | − | 0.853760i | ||||
\(842\) | 33.2518 | − | 57.5939i | 1.14593 | − | 1.98482i | ||||
\(843\) | 1.22172 | − | 0.976314i | 0.0420783 | − | 0.0336260i | ||||
\(844\) | 11.3368 | + | 19.6359i | 0.390229 | + | 0.675896i | ||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | −19.0615 | + | 84.2995i | −0.655348 | + | 2.89828i | ||||
\(847\) | −28.6823 | −0.985537 | ||||||||
\(848\) | 32.9880 | + | 57.1368i | 1.13281 | + | 1.96209i | ||||
\(849\) | −44.9253 | − | 17.5795i | −1.54183 | − | 0.603326i | ||||
\(850\) | 3.89662 | − | 6.74914i | 0.133653 | − | 0.231493i | ||||
\(851\) | −0.377392 | + | 0.653662i | −0.0129368 | + | 0.0224072i | ||||
\(852\) | −39.2720 | − | 15.3673i | −1.34544 | − | 0.526476i | ||||
\(853\) | −11.8513 | − | 20.5270i | −0.405780 | − | 0.702832i | 0.588632 | − | 0.808401i | \(-0.299667\pi\) |
−0.994412 | + | 0.105570i | \(0.966333\pi\) | |||||||
\(854\) | −26.1490 | −0.894800 | ||||||||
\(855\) | −2.46266 | + | 10.8911i | −0.0842211 | + | 0.372468i | ||||
\(856\) | −36.3034 | −1.24082 | ||||||||
\(857\) | 6.30907 | + | 10.9276i | 0.215514 | + | 0.373281i | 0.953431 | − | 0.301610i | \(-0.0975241\pi\) |
−0.737918 | + | 0.674891i | \(0.764191\pi\) | |||||||
\(858\) | −18.3809 | + | 14.6887i | −0.627514 | + | 0.501464i | ||||
\(859\) | −0.261117 | + | 0.452268i | −0.00890921 | + | 0.0154312i | −0.870446 | − | 0.492265i | \(-0.836169\pi\) |
0.861536 | + | 0.507696i | \(0.169503\pi\) | |||||||
\(860\) | 12.3817 | − | 21.4457i | 0.422212 | − | 0.731293i | ||||
\(861\) | −2.65633 | − | 17.5035i | −0.0905274 | − | 0.596516i | ||||
\(862\) | 13.5232 | + | 23.4229i | 0.460603 | + | 0.797789i | ||||
\(863\) | −34.3229 | −1.16837 | −0.584183 | − | 0.811622i | \(-0.698585\pi\) | ||||
−0.584183 | + | 0.811622i | \(0.698585\pi\) | |||||||
\(864\) | 21.5583 | + | 1.54981i | 0.733428 | + | 0.0527258i | ||||
\(865\) | −10.5731 | −0.359496 | ||||||||
\(866\) | −13.3411 | − | 23.1074i | −0.453348 | − | 0.785221i | ||||
\(867\) | 1.94264 | + | 12.8007i | 0.0659754 | + | 0.434735i | ||||
\(868\) | 19.5481 | − | 33.8582i | 0.663504 | − | 1.14922i | ||||
\(869\) | −14.3123 | + | 24.7897i | −0.485513 | + | 0.840933i | ||||
\(870\) | −2.18970 | + | 1.74985i | −0.0742377 | + | 0.0593255i | ||||
\(871\) | 7.64188 | + | 13.2361i | 0.258935 | + | 0.448489i | ||||
\(872\) | 21.8888 | 0.741249 | ||||||||
\(873\) | −2.01349 | − | 1.86068i | −0.0681464 | − | 0.0629746i | ||||
\(874\) | −15.9399 | −0.539175 | ||||||||
\(875\) | −0.799357 | − | 1.38453i | −0.0270232 | − | 0.0468055i | ||||
\(876\) | 83.0618 | + | 32.5024i | 2.80640 | + | 1.09816i | ||||
\(877\) | 2.26797 | − | 3.92824i | 0.0765839 | − | 0.132647i | −0.825190 | − | 0.564855i | \(-0.808932\pi\) |
0.901774 | + | 0.432208i | \(0.142265\pi\) | |||||||
\(878\) | −42.8011 | + | 74.1337i | −1.44447 | + | 2.50189i | ||||
\(879\) | −5.24417 | − | 2.05207i | −0.176881 | − | 0.0692145i | ||||
\(880\) | −17.2151 | − | 29.8175i | −0.580322 | − | 1.00515i | ||||
\(881\) | 36.4784 | 1.22899 | 0.614494 | − | 0.788922i | \(-0.289360\pi\) | ||||
0.614494 | + | 0.788922i | \(0.289360\pi\) | |||||||
\(882\) | −32.1504 | + | 9.98833i | −1.08256 | + | 0.336325i | ||||
\(883\) | −15.3187 | −0.515515 | −0.257757 | − | 0.966210i | \(-0.582983\pi\) | ||||
−0.257757 | + | 0.966210i | \(0.582983\pi\) | |||||||
\(884\) | −6.75331 | − | 11.6971i | −0.227138 | − | 0.393415i | ||||
\(885\) | −12.6491 | + | 10.1083i | −0.425196 | + | 0.339786i | ||||
\(886\) | 37.1590 | − | 64.3613i | 1.24838 | − | 2.16226i | ||||
\(887\) | 10.4154 | − | 18.0400i | 0.349715 | − | 0.605725i | −0.636483 | − | 0.771290i | \(-0.719612\pi\) |
0.986199 | + | 0.165566i | \(0.0529450\pi\) | |||||||
\(888\) | 0.694038 | + | 4.57326i | 0.0232904 | + | 0.153468i | ||||
\(889\) | 11.3540 | + | 19.6657i | 0.380801 | + | 0.659567i | ||||
\(890\) | −39.7206 | −1.33144 | ||||||||
\(891\) | 43.7069 | + | 20.8307i | 1.46424 | + | 0.697856i | ||||
\(892\) | 65.9064 | 2.20671 | ||||||||
\(893\) | −21.2321 | − | 36.7750i | −0.710504 | − | 1.23063i | ||||
\(894\) | −7.72888 | − | 50.9283i | −0.258492 | − | 1.70330i | ||||
\(895\) | 2.73717 | − | 4.74092i | 0.0914936 | − | 0.158472i | ||||
\(896\) | 11.2855 | − | 19.5470i | 0.377022 | − | 0.653020i | ||||
\(897\) | −2.29479 | + | 1.83383i | −0.0766208 | + | 0.0612299i | ||||
\(898\) | 47.5560 | + | 82.3693i | 1.58696 | + | 2.74870i | ||||
\(899\) | 3.58112 | 0.119437 | ||||||||
\(900\) | −12.5380 | + | 3.89526i | −0.417935 | + | 0.129842i | ||||
\(901\) | −31.8149 | −1.05991 | ||||||||
\(902\) | 43.4261 | + | 75.2161i | 1.44593 | + | 2.50442i | ||||
\(903\) | −14.5911 | − | 5.70955i | −0.485560 | − | 0.190002i | ||||
\(904\) | 37.0077 | − | 64.0992i | 1.23086 | − | 2.13191i | ||||
\(905\) | −0.676619 | + | 1.17194i | −0.0224916 | + | 0.0389566i | ||||
\(906\) | 39.0654 | + | 15.2865i | 1.29786 | + | 0.507859i | ||||
\(907\) | −5.91025 | − | 10.2369i | −0.196247 | − | 0.339909i | 0.751062 | − | 0.660232i | \(-0.229542\pi\) |
−0.947308 | + | 0.320323i | \(0.896209\pi\) | |||||||
\(908\) | 95.1418 | 3.15739 | ||||||||
\(909\) | 12.8349 | + | 11.8608i | 0.425707 | + | 0.393399i | ||||
\(910\) | −4.03700 | −0.133825 | ||||||||
\(911\) | −2.86152 | − | 4.95631i | −0.0948065 | − | 0.164210i | 0.814721 | − | 0.579853i | \(-0.196890\pi\) |
−0.909528 | + | 0.415643i | \(0.863557\pi\) | |||||||
\(912\) | −32.2319 | + | 25.7574i | −1.06730 | + | 0.852914i | ||||
\(913\) | −26.2236 | + | 45.4206i | −0.867875 | + | 1.50320i | ||||
\(914\) | −40.3363 | + | 69.8645i | −1.33421 | + | 2.31091i | ||||
\(915\) | −1.68334 | − | 11.0921i | −0.0556494 | − | 0.366693i | ||||
\(916\) | −59.4647 | − | 102.996i | −1.96477 | − | 3.40308i | ||||
\(917\) | −29.8873 | −0.986966 | ||||||||
\(918\) | −22.7099 | + | 33.5274i | −0.749540 | + | 1.10657i | ||||
\(919\) | 16.2414 | 0.535754 | 0.267877 | − | 0.963453i | \(-0.413678\pi\) | ||||
0.267877 | + | 0.963453i | \(0.413678\pi\) | |||||||
\(920\) | −5.08858 | − | 8.81368i | −0.167766 | − | 0.290579i | ||||
\(921\) | −5.99778 | − | 39.5214i | −0.197634 | − | 1.30228i | ||||
\(922\) | −17.7157 | + | 30.6845i | −0.583435 | + | 1.01054i | ||||
\(923\) | 2.78172 | − | 4.81808i | 0.0915614 | − | 0.158589i | ||||
\(924\) | −50.9292 | + | 40.6990i | −1.67545 | + | 1.33890i | ||||
\(925\) | −0.222522 | − | 0.385419i | −0.00731647 | − | 0.0126725i | ||||
\(926\) | −103.353 | −3.39640 | ||||||||
\(927\) | −11.3068 | + | 50.0044i | −0.371365 | + | 1.64236i | ||||
\(928\) | −2.66578 | −0.0875087 | ||||||||
\(929\) | 2.98637 | + | 5.17255i | 0.0979797 | + | 0.169706i | 0.910848 | − | 0.412741i | \(-0.135429\pi\) |
−0.812869 | + | 0.582447i | \(0.802095\pi\) | |||||||
\(930\) | 22.7592 | + | 8.90578i | 0.746304 | + | 0.292032i | ||||
\(931\) | 8.27053 | − | 14.3250i | 0.271056 | − | 0.469482i | ||||
\(932\) | −52.8171 | + | 91.4818i | −1.73008 | + | 2.99659i | ||||
\(933\) | 10.4427 | + | 4.08628i | 0.341879 | + | 0.133779i | ||||
\(934\) | −5.30893 | − | 9.19534i | −0.173714 | − | 0.300881i | ||||
\(935\) | 16.6030 | 0.542975 | ||||||||
\(936\) | −3.97038 | + | 17.5590i | −0.129776 | + | 0.573934i | ||||
\(937\) | −36.1153 | −1.17984 | −0.589918 | − | 0.807463i | \(-0.700840\pi\) | ||||
−0.589918 | + | 0.807463i | \(0.700840\pi\) | |||||||
\(938\) | 30.8502 | + | 53.4342i | 1.00730 | + | 1.74469i | ||||
\(939\) | −10.6133 | + | 8.48141i | −0.346353 | + | 0.276780i | ||||
\(940\) | 24.9650 | − | 43.2406i | 0.814267 | − | 1.41035i | ||||
\(941\) | −3.01318 | + | 5.21898i | −0.0982268 | + | 0.170134i | −0.910951 | − | 0.412515i | \(-0.864650\pi\) |
0.812724 | + | 0.582649i | \(0.197984\pi\) | |||||||
\(942\) | 5.20352 | + | 34.2878i | 0.169540 | + | 1.11716i | ||||
\(943\) | 5.42159 | + | 9.39047i | 0.176551 | + | 0.305796i | ||||
\(944\) | −59.8303 | −1.94731 | ||||||||
\(945\) | 3.62703 | + | 7.47352i | 0.117987 | + | 0.243114i | ||||
\(946\) | 76.8664 | 2.49914 | ||||||||
\(947\) | −12.9752 | − | 22.4737i | −0.421638 | − | 0.730298i | 0.574462 | − | 0.818531i | \(-0.305211\pi\) |
−0.996100 | + | 0.0882332i | \(0.971878\pi\) | |||||||
\(948\) | 6.05167 | + | 39.8766i | 0.196549 | + | 1.29513i | ||||
\(949\) | −5.88343 | + | 10.1904i | −0.190984 | + | 0.330795i | ||||
\(950\) | 4.69933 | − | 8.13948i | 0.152466 | − | 0.264079i | ||||
\(951\) | 42.9457 | − | 34.3191i | 1.39261 | − | 1.11287i | ||||
\(952\) | −14.8039 | − | 25.6412i | −0.479799 | − | 0.831036i | ||||
\(953\) | −46.4390 | −1.50431 | −0.752153 | − | 0.658988i | \(-0.770985\pi\) | ||||
−0.752153 | + | 0.658988i | \(0.770985\pi\) | |||||||
\(954\) | 57.3533 | + | 53.0006i | 1.85688 | + | 1.71596i | ||||
\(955\) | −3.66554 | −0.118614 | ||||||||
\(956\) | −37.8124 | − | 65.4929i | −1.22294 | − | 2.11819i | ||||
\(957\) | −5.56100 | − | 2.17604i | −0.179761 | − | 0.0703415i | ||||
\(958\) | 33.5100 | − | 58.0410i | 1.08266 | − | 1.87522i | ||||
\(959\) | 11.0780 | − | 19.1877i | 0.357727 | − | 0.619602i | ||||
\(960\) | 3.70415 | + | 1.44945i | 0.119551 | + | 0.0467808i | ||||
\(961\) | −0.112129 | − | 0.194212i | −0.00361705 | − | 0.00626492i | ||||
\(962\) | −1.12380 | −0.0362329 | ||||||||
\(963\) | −17.3322 | + | 5.38468i | −0.558522 | + | 0.173519i | ||||
\(964\) | −72.4951 | −2.33491 | ||||||||
\(965\) | −4.37529 | − | 7.57823i | −0.140846 | − | 0.243952i | ||||
\(966\) | −9.26406 | + | 7.40318i | −0.298066 | + | 0.238194i | ||||
\(967\) | −13.7469 | + | 23.8104i | −0.442072 | + | 0.765691i | −0.997843 | − | 0.0656445i | \(-0.979090\pi\) |
0.555771 | + | 0.831335i | \(0.312423\pi\) | |||||||
\(968\) | 53.8295 | − | 93.2355i | 1.73015 | − | 2.99670i | ||||
\(969\) | −2.98526 | − | 19.6709i | −0.0959003 | − | 0.631920i | ||||
\(970\) | 1.15382 | + | 1.99848i | 0.0370470 | + | 0.0641672i | ||||
\(971\) | −8.04171 | −0.258071 | −0.129035 | − | 0.991640i | \(-0.541188\pi\) | ||||
−0.129035 | + | 0.991640i | \(0.541188\pi\) | |||||||
\(972\) | 66.4332 | − | 15.5168i | 2.13085 | − | 0.497701i | ||||
\(973\) | −10.4343 | −0.334510 | ||||||||
\(974\) | 36.9534 | + | 64.0051i | 1.18406 | + | 2.05086i | ||||
\(975\) | −0.259881 | − | 1.71244i | −0.00832284 | − | 0.0548421i | ||||
\(976\) | 20.7277 | − | 35.9014i | 0.663477 | − | 1.14918i | ||||
\(977\) | 5.27839 | − | 9.14245i | 0.168871 | − | 0.292493i | −0.769152 | − | 0.639065i | \(-0.779321\pi\) |
0.938023 | + | 0.346573i | \(0.112655\pi\) | |||||||
\(978\) | −9.36498 | + | 7.48383i | −0.299459 | + | 0.239306i | ||||
\(979\) | −42.3111 | − | 73.2849i | −1.35227 | − | 2.34220i | ||||
\(980\) | 19.4492 | 0.621282 | ||||||||
\(981\) | 10.4503 | − | 3.24665i | 0.333652 | − | 0.103658i | ||||
\(982\) | −57.8817 | −1.84708 | ||||||||
\(983\) | 6.03646 | + | 10.4555i | 0.192533 | + | 0.333477i | 0.946089 | − | 0.323906i | \(-0.104996\pi\) |
−0.753556 | + | 0.657384i | \(0.771663\pi\) | |||||||
\(984\) | 61.8824 | + | 24.2149i | 1.97274 | + | 0.771942i | ||||
\(985\) | −4.75293 | + | 8.23231i | −0.151441 | + | 0.262303i | ||||
\(986\) | 2.49724 | − | 4.32535i | 0.0795284 | − | 0.137747i | ||||
\(987\) | −29.4197 | − | 11.5121i | −0.936439 | − | 0.366433i | ||||
\(988\) | −8.14451 | − | 14.1067i | −0.259111 | − | 0.448794i | ||||
\(989\) | 9.59650 | 0.305151 | ||||||||
\(990\) | −29.9304 | − | 27.6589i | −0.951251 | − | 0.879059i | ||||
\(991\) | 15.6841 | 0.498222 | 0.249111 | − | 0.968475i | \(-0.419862\pi\) | ||||
0.249111 | + | 0.968475i | \(0.419862\pi\) | |||||||
\(992\) | 11.6217 | + | 20.1293i | 0.368988 | + | 0.639106i | ||||
\(993\) | −24.5015 | + | 19.5799i | −0.777531 | + | 0.621348i | ||||
\(994\) | 11.2298 | − | 19.4506i | 0.356187 | − | 0.616934i | ||||
\(995\) | 12.7915 | − | 22.1555i | 0.405517 | − | 0.702376i | ||||
\(996\) | 11.0881 | + | 73.0634i | 0.351340 | + | 2.31510i | ||||
\(997\) | 0.939391 | + | 1.62707i | 0.0297508 | + | 0.0515299i | 0.880517 | − | 0.474014i | \(-0.157195\pi\) |
−0.850767 | + | 0.525544i | \(0.823862\pi\) | |||||||
\(998\) | −14.7993 | −0.468464 | ||||||||
\(999\) | 1.00968 | + | 2.08045i | 0.0319448 | + | 0.0658225i |
(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 | 585.2.i.h.391.14 | yes | 30 | |
3.2 | odd | 2 | 1755.2.i.h.1171.2 | 30 | |||
9.2 | odd | 6 | 1755.2.i.h.586.2 | 30 | |||
9.4 | even | 3 | 5265.2.a.bk.1.2 | 15 | |||
9.5 | odd | 6 | 5265.2.a.bl.1.14 | 15 | |||
9.7 | even | 3 | inner | 585.2.i.h.196.14 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.h.196.14 | ✓ | 30 | 9.7 | even | 3 | inner | |
585.2.i.h.391.14 | yes | 30 | 1.1 | even | 1 | trivial | |
1755.2.i.h.586.2 | 30 | 9.2 | odd | 6 | |||
1755.2.i.h.1171.2 | 30 | 3.2 | odd | 2 | |||
5265.2.a.bk.1.2 | 15 | 9.4 | even | 3 | |||
5265.2.a.bl.1.14 | 15 | 9.5 | odd | 6 |