Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(69,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.69");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.g (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.49320251780\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 137.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 187.137 |
Dual form | 187.2.g.c.86.1 |
$q$-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 \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.690983 | + | 2.12663i | 0.488599 | + | 1.50375i | 0.826700 | + | 0.562643i | \(0.190215\pi\) |
−0.338101 | + | 0.941110i | \(0.609785\pi\) | |||||||
\(3\) | 0.309017 | + | 0.224514i | 0.178411 | + | 0.129623i | 0.673407 | − | 0.739272i | \(-0.264830\pi\) |
−0.494996 | + | 0.868895i | \(0.664830\pi\) | |||||||
\(4\) | −2.42705 | + | 1.76336i | −1.21353 | + | 0.881678i | ||||
\(5\) | −0.618034 | + | 1.90211i | −0.276393 | + | 0.850651i | 0.712454 | + | 0.701719i | \(0.247584\pi\) |
−0.988847 | + | 0.148932i | \(0.952416\pi\) | |||||||
\(6\) | −0.263932 | + | 0.812299i | −0.107750 | + | 0.331620i | ||||
\(7\) | −0.500000 | + | 0.363271i | −0.188982 | + | 0.137304i | −0.678253 | − | 0.734828i | \(-0.737263\pi\) |
0.489271 | + | 0.872132i | \(0.337263\pi\) | |||||||
\(8\) | −1.80902 | − | 1.31433i | −0.639584 | − | 0.464685i | ||||
\(9\) | −0.881966 | − | 2.71441i | −0.293989 | − | 0.904804i | ||||
\(10\) | −4.47214 | −1.41421 | ||||||||
\(11\) | 3.23607 | + | 0.726543i | 0.975711 | + | 0.219061i | ||||
\(12\) | −1.14590 | −0.330792 | ||||||||
\(13\) | −0.500000 | − | 1.53884i | −0.138675 | − | 0.426798i | 0.857468 | − | 0.514536i | \(-0.172036\pi\) |
−0.996144 | + | 0.0877386i | \(0.972036\pi\) | |||||||
\(14\) | −1.11803 | − | 0.812299i | −0.298807 | − | 0.217096i | ||||
\(15\) | −0.618034 | + | 0.449028i | −0.159576 | + | 0.115939i | ||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | −0.309017 | + | 0.951057i | −0.0749476 | + | 0.230665i | ||||
\(18\) | 5.16312 | − | 3.75123i | 1.21696 | − | 0.884172i | ||||
\(19\) | 0.618034 | + | 0.449028i | 0.141787 | + | 0.103014i | 0.656418 | − | 0.754398i | \(-0.272071\pi\) |
−0.514631 | + | 0.857412i | \(0.672071\pi\) | |||||||
\(20\) | −1.85410 | − | 5.70634i | −0.414590 | − | 1.27598i | ||||
\(21\) | −0.236068 | −0.0515143 | ||||||||
\(22\) | 0.690983 | + | 7.38394i | 0.147318 | + | 1.57426i | ||||
\(23\) | 2.85410 | 0.595121 | 0.297561 | − | 0.954703i | \(-0.403827\pi\) | ||||
0.297561 | + | 0.954703i | \(0.403827\pi\) | |||||||
\(24\) | −0.263932 | − | 0.812299i | −0.0538749 | − | 0.165810i | ||||
\(25\) | 0.809017 | + | 0.587785i | 0.161803 | + | 0.117557i | ||||
\(26\) | 2.92705 | − | 2.12663i | 0.574042 | − | 0.417066i | ||||
\(27\) | 0.690983 | − | 2.12663i | 0.132980 | − | 0.409270i | ||||
\(28\) | 0.572949 | − | 1.76336i | 0.108277 | − | 0.333243i | ||||
\(29\) | 6.23607 | − | 4.53077i | 1.15801 | − | 0.841343i | 0.168484 | − | 0.985704i | \(-0.446113\pi\) |
0.989525 | + | 0.144362i | \(0.0461129\pi\) | |||||||
\(30\) | −1.38197 | − | 1.00406i | −0.252311 | − | 0.183315i | ||||
\(31\) | −2.00000 | − | 6.15537i | −0.359211 | − | 1.10554i | −0.953528 | − | 0.301306i | \(-0.902578\pi\) |
0.594317 | − | 0.804231i | \(-0.297422\pi\) | |||||||
\(32\) | −6.70820 | −1.18585 | ||||||||
\(33\) | 0.836881 | + | 0.951057i | 0.145682 | + | 0.165558i | ||||
\(34\) | −2.23607 | −0.383482 | ||||||||
\(35\) | −0.381966 | − | 1.17557i | −0.0645640 | − | 0.198708i | ||||
\(36\) | 6.92705 | + | 5.03280i | 1.15451 | + | 0.838800i | ||||
\(37\) | −2.00000 | + | 1.45309i | −0.328798 | + | 0.238886i | −0.739920 | − | 0.672694i | \(-0.765137\pi\) |
0.411122 | + | 0.911580i | \(0.365137\pi\) | |||||||
\(38\) | −0.527864 | + | 1.62460i | −0.0856309 | + | 0.263545i | ||||
\(39\) | 0.190983 | − | 0.587785i | 0.0305818 | − | 0.0941210i | ||||
\(40\) | 3.61803 | − | 2.62866i | 0.572061 | − | 0.415627i | ||||
\(41\) | 5.61803 | + | 4.08174i | 0.877390 | + | 0.637461i | 0.932560 | − | 0.361016i | \(-0.117570\pi\) |
−0.0551700 | + | 0.998477i | \(0.517570\pi\) | |||||||
\(42\) | −0.163119 | − | 0.502029i | −0.0251698 | − | 0.0774647i | ||||
\(43\) | 2.76393 | 0.421496 | 0.210748 | − | 0.977540i | \(-0.432410\pi\) | ||||
0.210748 | + | 0.977540i | \(0.432410\pi\) | |||||||
\(44\) | −9.13525 | + | 3.94298i | −1.37719 | + | 0.594427i | ||||
\(45\) | 5.70820 | 0.850929 | ||||||||
\(46\) | 1.97214 | + | 6.06961i | 0.290776 | + | 0.894915i | ||||
\(47\) | −7.23607 | − | 5.25731i | −1.05549 | − | 0.766858i | −0.0822405 | − | 0.996613i | \(-0.526208\pi\) |
−0.973249 | + | 0.229755i | \(0.926208\pi\) | |||||||
\(48\) | −0.309017 | + | 0.224514i | −0.0446028 | + | 0.0324058i | ||||
\(49\) | −2.04508 | + | 6.29412i | −0.292155 | + | 0.899161i | ||||
\(50\) | −0.690983 | + | 2.12663i | −0.0977198 | + | 0.300750i | ||||
\(51\) | −0.309017 | + | 0.224514i | −0.0432710 | + | 0.0314382i | ||||
\(52\) | 3.92705 | + | 2.85317i | 0.544584 | + | 0.395663i | ||||
\(53\) | −1.33688 | − | 4.11450i | −0.183635 | − | 0.565170i | 0.816287 | − | 0.577646i | \(-0.196029\pi\) |
−0.999922 | + | 0.0124763i | \(0.996029\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | −3.38197 | + | 5.70634i | −0.456024 | + | 0.769443i | ||||
\(56\) | 1.38197 | 0.184673 | ||||||||
\(57\) | 0.0901699 | + | 0.277515i | 0.0119433 | + | 0.0367577i | ||||
\(58\) | 13.9443 | + | 10.1311i | 1.83097 | + | 1.33028i | ||||
\(59\) | −0.236068 | + | 0.171513i | −0.0307334 | + | 0.0223291i | −0.603046 | − | 0.797706i | \(-0.706046\pi\) |
0.572312 | + | 0.820036i | \(0.306046\pi\) | |||||||
\(60\) | 0.708204 | − | 2.17963i | 0.0914287 | − | 0.281389i | ||||
\(61\) | 0.236068 | − | 0.726543i | 0.0302254 | − | 0.0930242i | −0.934806 | − | 0.355159i | \(-0.884427\pi\) |
0.965031 | + | 0.262135i | \(0.0844266\pi\) | |||||||
\(62\) | 11.7082 | − | 8.50651i | 1.48694 | − | 1.08033i | ||||
\(63\) | 1.42705 | + | 1.03681i | 0.179792 | + | 0.130626i | ||||
\(64\) | −4.01722 | − | 12.3637i | −0.502153 | − | 1.54547i | ||||
\(65\) | 3.23607 | 0.401385 | ||||||||
\(66\) | −1.44427 | + | 2.43690i | −0.177778 | + | 0.299961i | ||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | −0.927051 | − | 2.85317i | −0.112421 | − | 0.345998i | ||||
\(69\) | 0.881966 | + | 0.640786i | 0.106176 | + | 0.0771415i | ||||
\(70\) | 2.23607 | − | 1.62460i | 0.267261 | − | 0.194177i | ||||
\(71\) | 3.23607 | − | 9.95959i | 0.384051 | − | 1.18199i | −0.553116 | − | 0.833104i | \(-0.686561\pi\) |
0.937167 | − | 0.348882i | \(-0.113439\pi\) | |||||||
\(72\) | −1.97214 | + | 6.06961i | −0.232418 | + | 0.715310i | ||||
\(73\) | −3.85410 | + | 2.80017i | −0.451089 | + | 0.327735i | −0.790025 | − | 0.613074i | \(-0.789933\pi\) |
0.338937 | + | 0.940809i | \(0.389933\pi\) | |||||||
\(74\) | −4.47214 | − | 3.24920i | −0.519875 | − | 0.377711i | ||||
\(75\) | 0.118034 | + | 0.363271i | 0.0136294 | + | 0.0419470i | ||||
\(76\) | −2.29180 | −0.262887 | ||||||||
\(77\) | −1.88197 | + | 0.812299i | −0.214470 | + | 0.0925701i | ||||
\(78\) | 1.38197 | 0.156477 | ||||||||
\(79\) | −2.95492 | − | 9.09429i | −0.332454 | − | 1.02319i | −0.967963 | − | 0.251094i | \(-0.919210\pi\) |
0.635509 | − | 0.772094i | \(-0.280790\pi\) | |||||||
\(80\) | −1.61803 | − | 1.17557i | −0.180902 | − | 0.131433i | ||||
\(81\) | −6.23607 | + | 4.53077i | −0.692896 | + | 0.503419i | ||||
\(82\) | −4.79837 | + | 14.7679i | −0.529892 | + | 1.63084i | ||||
\(83\) | 2.38197 | − | 7.33094i | 0.261455 | − | 0.804675i | −0.731034 | − | 0.682341i | \(-0.760962\pi\) |
0.992489 | − | 0.122334i | \(-0.0390380\pi\) | |||||||
\(84\) | 0.572949 | − | 0.416272i | 0.0625139 | − | 0.0454190i | ||||
\(85\) | −1.61803 | − | 1.17557i | −0.175500 | − | 0.127509i | ||||
\(86\) | 1.90983 | + | 5.87785i | 0.205942 | + | 0.633825i | ||||
\(87\) | 2.94427 | 0.315659 | ||||||||
\(88\) | −4.89919 | − | 5.56758i | −0.522255 | − | 0.593506i | ||||
\(89\) | −9.79837 | −1.03863 | −0.519313 | − | 0.854584i | \(-0.673812\pi\) | ||||
−0.519313 | + | 0.854584i | \(0.673812\pi\) | |||||||
\(90\) | 3.94427 | + | 12.1392i | 0.415763 | + | 1.27959i | ||||
\(91\) | 0.809017 | + | 0.587785i | 0.0848080 | + | 0.0616166i | ||||
\(92\) | −6.92705 | + | 5.03280i | −0.722195 | + | 0.524705i | ||||
\(93\) | 0.763932 | − | 2.35114i | 0.0792161 | − | 0.243802i | ||||
\(94\) | 6.18034 | − | 19.0211i | 0.637453 | − | 1.96188i | ||||
\(95\) | −1.23607 | + | 0.898056i | −0.126818 | + | 0.0921386i | ||||
\(96\) | −2.07295 | − | 1.50609i | −0.211569 | − | 0.153714i | ||||
\(97\) | 1.85410 | + | 5.70634i | 0.188256 | + | 0.579391i | 0.999989 | − | 0.00463676i | \(-0.00147593\pi\) |
−0.811734 | + | 0.584028i | \(0.801476\pi\) | |||||||
\(98\) | −14.7984 | −1.49486 | ||||||||
\(99\) | −0.881966 | − | 9.42481i | −0.0886409 | − | 0.947229i | ||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | −4.28115 | − | 13.1760i | −0.425991 | − | 1.31106i | −0.902043 | − | 0.431647i | \(-0.857933\pi\) |
0.476052 | − | 0.879417i | \(-0.342067\pi\) | |||||||
\(102\) | −0.690983 | − | 0.502029i | −0.0684175 | − | 0.0497082i | ||||
\(103\) | −11.4721 | + | 8.33499i | −1.13038 | + | 0.821271i | −0.985751 | − | 0.168214i | \(-0.946200\pi\) |
−0.144633 | + | 0.989485i | \(0.546200\pi\) | |||||||
\(104\) | −1.11803 | + | 3.44095i | −0.109632 | + | 0.337413i | ||||
\(105\) | 0.145898 | − | 0.449028i | 0.0142382 | − | 0.0438206i | ||||
\(106\) | 7.82624 | − | 5.68609i | 0.760151 | − | 0.552282i | ||||
\(107\) | −2.73607 | − | 1.98787i | −0.264506 | − | 0.192175i | 0.447625 | − | 0.894221i | \(-0.352270\pi\) |
−0.712131 | + | 0.702047i | \(0.752270\pi\) | |||||||
\(108\) | 2.07295 | + | 6.37988i | 0.199470 | + | 0.613904i | ||||
\(109\) | 8.47214 | 0.811483 | 0.405742 | − | 0.913988i | \(-0.367013\pi\) | ||||
0.405742 | + | 0.913988i | \(0.367013\pi\) | |||||||
\(110\) | −14.4721 | − | 3.24920i | −1.37986 | − | 0.309799i | ||||
\(111\) | −0.944272 | −0.0896263 | ||||||||
\(112\) | −0.190983 | − | 0.587785i | −0.0180462 | − | 0.0555405i | ||||
\(113\) | 3.23607 | + | 2.35114i | 0.304424 | + | 0.221177i | 0.729500 | − | 0.683981i | \(-0.239753\pi\) |
−0.425076 | + | 0.905157i | \(0.639753\pi\) | |||||||
\(114\) | −0.527864 | + | 0.383516i | −0.0494390 | + | 0.0359195i | ||||
\(115\) | −1.76393 | + | 5.42882i | −0.164488 | + | 0.506240i | ||||
\(116\) | −7.14590 | + | 21.9928i | −0.663480 | + | 2.04198i | ||||
\(117\) | −3.73607 | + | 2.71441i | −0.345400 | + | 0.250948i | ||||
\(118\) | −0.527864 | − | 0.383516i | −0.0485938 | − | 0.0353055i | ||||
\(119\) | −0.190983 | − | 0.587785i | −0.0175074 | − | 0.0538822i | ||||
\(120\) | 1.70820 | 0.155937 | ||||||||
\(121\) | 9.94427 | + | 4.70228i | 0.904025 | + | 0.427480i | ||||
\(122\) | 1.70820 | 0.154654 | ||||||||
\(123\) | 0.819660 | + | 2.52265i | 0.0739063 | + | 0.227460i | ||||
\(124\) | 15.7082 | + | 11.4127i | 1.41064 | + | 1.02489i | ||||
\(125\) | −9.70820 | + | 7.05342i | −0.868328 | + | 0.630877i | ||||
\(126\) | −1.21885 | + | 3.75123i | −0.108584 | + | 0.334186i | ||||
\(127\) | 3.23607 | − | 9.95959i | 0.287155 | − | 0.883771i | −0.698590 | − | 0.715522i | \(-0.746189\pi\) |
0.985745 | − | 0.168249i | \(-0.0538112\pi\) | |||||||
\(128\) | 12.6631 | − | 9.20029i | 1.11927 | − | 0.813199i | ||||
\(129\) | 0.854102 | + | 0.620541i | 0.0751995 | + | 0.0546356i | ||||
\(130\) | 2.23607 | + | 6.88191i | 0.196116 | + | 0.603583i | ||||
\(131\) | 19.6180 | 1.71404 | 0.857018 | − | 0.515287i | \(-0.172315\pi\) | ||||
0.857018 | + | 0.515287i | \(0.172315\pi\) | |||||||
\(132\) | −3.70820 | − | 0.832544i | −0.322758 | − | 0.0724636i | ||||
\(133\) | −0.472136 | −0.0409394 | ||||||||
\(134\) | −8.29180 | − | 25.5195i | −0.716302 | − | 2.20455i | ||||
\(135\) | 3.61803 | + | 2.62866i | 0.311391 | + | 0.226239i | ||||
\(136\) | 1.80902 | − | 1.31433i | 0.155122 | − | 0.112703i | ||||
\(137\) | −6.61803 | + | 20.3682i | −0.565417 | + | 1.74017i | 0.101293 | + | 0.994857i | \(0.467702\pi\) |
−0.666710 | + | 0.745317i | \(0.732298\pi\) | |||||||
\(138\) | −0.753289 | + | 2.31838i | −0.0641242 | + | 0.197354i | ||||
\(139\) | −3.23607 | + | 2.35114i | −0.274480 | + | 0.199421i | −0.716506 | − | 0.697581i | \(-0.754260\pi\) |
0.442026 | + | 0.897002i | \(0.354260\pi\) | |||||||
\(140\) | 3.00000 | + | 2.17963i | 0.253546 | + | 0.184212i | ||||
\(141\) | −1.05573 | − | 3.24920i | −0.0889083 | − | 0.273632i | ||||
\(142\) | 23.4164 | 1.96506 | ||||||||
\(143\) | −0.500000 | − | 5.34307i | −0.0418121 | − | 0.446810i | ||||
\(144\) | 2.85410 | 0.237842 | ||||||||
\(145\) | 4.76393 | + | 14.6619i | 0.395623 | + | 1.21760i | ||||
\(146\) | −8.61803 | − | 6.26137i | −0.713234 | − | 0.518195i | ||||
\(147\) | −2.04508 | + | 1.48584i | −0.168676 | + | 0.122550i | ||||
\(148\) | 2.29180 | − | 7.05342i | 0.188384 | − | 0.579788i | ||||
\(149\) | −4.37132 | + | 13.4535i | −0.358113 | + | 1.10216i | 0.596070 | + | 0.802933i | \(0.296728\pi\) |
−0.954183 | + | 0.299225i | \(0.903272\pi\) | |||||||
\(150\) | −0.690983 | + | 0.502029i | −0.0564185 | + | 0.0409905i | ||||
\(151\) | 2.61803 | + | 1.90211i | 0.213053 | + | 0.154792i | 0.689194 | − | 0.724577i | \(-0.257965\pi\) |
−0.476141 | + | 0.879369i | \(0.657965\pi\) | |||||||
\(152\) | −0.527864 | − | 1.62460i | −0.0428154 | − | 0.131772i | ||||
\(153\) | 2.85410 | 0.230740 | ||||||||
\(154\) | −3.02786 | − | 3.44095i | −0.243992 | − | 0.277280i | ||||
\(155\) | 12.9443 | 1.03971 | ||||||||
\(156\) | 0.572949 | + | 1.76336i | 0.0458726 | + | 0.141181i | ||||
\(157\) | −0.0729490 | − | 0.0530006i | −0.00582197 | − | 0.00422991i | 0.584870 | − | 0.811127i | \(-0.301145\pi\) |
−0.590692 | + | 0.806897i | \(0.701145\pi\) | |||||||
\(158\) | 17.2984 | − | 12.5680i | 1.37618 | − | 0.999857i | ||||
\(159\) | 0.510643 | − | 1.57160i | 0.0404966 | − | 0.124636i | ||||
\(160\) | 4.14590 | − | 12.7598i | 0.327762 | − | 1.00875i | ||||
\(161\) | −1.42705 | + | 1.03681i | −0.112467 | + | 0.0817123i | ||||
\(162\) | −13.9443 | − | 10.1311i | −1.09557 | − | 0.795975i | ||||
\(163\) | 2.19098 | + | 6.74315i | 0.171611 | + | 0.528164i | 0.999462 | − | 0.0327829i | \(-0.0104370\pi\) |
−0.827851 | + | 0.560947i | \(0.810437\pi\) | |||||||
\(164\) | −20.8328 | −1.62677 | ||||||||
\(165\) | −2.32624 | + | 1.00406i | −0.181097 | + | 0.0781657i | ||||
\(166\) | 17.2361 | 1.33778 | ||||||||
\(167\) | 4.11803 | + | 12.6740i | 0.318663 | + | 0.980744i | 0.974220 | + | 0.225599i | \(0.0724338\pi\) |
−0.655557 | + | 0.755145i | \(0.727566\pi\) | |||||||
\(168\) | 0.427051 | + | 0.310271i | 0.0329477 | + | 0.0239379i | ||||
\(169\) | 8.39919 | − | 6.10237i | 0.646091 | − | 0.469413i | ||||
\(170\) | 1.38197 | − | 4.25325i | 0.105992 | − | 0.326210i | ||||
\(171\) | 0.673762 | − | 2.07363i | 0.0515239 | − | 0.158574i | ||||
\(172\) | −6.70820 | + | 4.87380i | −0.511496 | + | 0.371623i | ||||
\(173\) | −7.61803 | − | 5.53483i | −0.579188 | − | 0.420805i | 0.259243 | − | 0.965812i | \(-0.416527\pi\) |
−0.838431 | + | 0.545007i | \(0.816527\pi\) | |||||||
\(174\) | 2.03444 | + | 6.26137i | 0.154231 | + | 0.474673i | ||||
\(175\) | −0.618034 | −0.0467190 | ||||||||
\(176\) | −1.69098 | + | 2.85317i | −0.127463 | + | 0.215066i | ||||
\(177\) | −0.111456 | −0.00837756 | ||||||||
\(178\) | −6.77051 | − | 20.8375i | −0.507471 | − | 1.56184i | ||||
\(179\) | −9.09017 | − | 6.60440i | −0.679431 | − | 0.493636i | 0.193738 | − | 0.981053i | \(-0.437939\pi\) |
−0.873169 | + | 0.487418i | \(0.837939\pi\) | |||||||
\(180\) | −13.8541 | + | 10.0656i | −1.03262 | + | 0.750245i | ||||
\(181\) | −1.61803 | + | 4.97980i | −0.120268 | + | 0.370145i | −0.993009 | − | 0.118037i | \(-0.962340\pi\) |
0.872742 | + | 0.488182i | \(0.162340\pi\) | |||||||
\(182\) | −0.690983 | + | 2.12663i | −0.0512191 | + | 0.157636i | ||||
\(183\) | 0.236068 | − | 0.171513i | 0.0174506 | − | 0.0126786i | ||||
\(184\) | −5.16312 | − | 3.75123i | −0.380630 | − | 0.276544i | ||||
\(185\) | −1.52786 | − | 4.70228i | −0.112331 | − | 0.345719i | ||||
\(186\) | 5.52786 | 0.405323 | ||||||||
\(187\) | −1.69098 | + | 2.85317i | −0.123657 | + | 0.208644i | ||||
\(188\) | 26.8328 | 1.95698 | ||||||||
\(189\) | 0.427051 | + | 1.31433i | 0.0310634 | + | 0.0956033i | ||||
\(190\) | −2.76393 | − | 2.00811i | −0.200517 | − | 0.145684i | ||||
\(191\) | 14.5623 | − | 10.5801i | 1.05369 | − | 0.765552i | 0.0807805 | − | 0.996732i | \(-0.474259\pi\) |
0.972911 | + | 0.231180i | \(0.0742587\pi\) | |||||||
\(192\) | 1.53444 | − | 4.72253i | 0.110739 | − | 0.340819i | ||||
\(193\) | −2.90983 | + | 8.95554i | −0.209454 | + | 0.644634i | 0.790047 | + | 0.613046i | \(0.210056\pi\) |
−0.999501 | + | 0.0315871i | \(0.989944\pi\) | |||||||
\(194\) | −10.8541 | + | 7.88597i | −0.779279 | + | 0.566179i | ||||
\(195\) | 1.00000 | + | 0.726543i | 0.0716115 | + | 0.0520288i | ||||
\(196\) | −6.13525 | − | 18.8824i | −0.438232 | − | 1.34874i | ||||
\(197\) | 23.7082 | 1.68914 | 0.844570 | − | 0.535445i | \(-0.179856\pi\) | ||||
0.844570 | + | 0.535445i | \(0.179856\pi\) | |||||||
\(198\) | 19.4336 | − | 8.38800i | 1.38109 | − | 0.596109i | ||||
\(199\) | −21.8541 | −1.54920 | −0.774598 | − | 0.632454i | \(-0.782048\pi\) | ||||
−0.774598 | + | 0.632454i | \(0.782048\pi\) | |||||||
\(200\) | −0.690983 | − | 2.12663i | −0.0488599 | − | 0.150375i | ||||
\(201\) | −3.70820 | − | 2.69417i | −0.261557 | − | 0.190032i | ||||
\(202\) | 25.0623 | − | 18.2088i | 1.76338 | − | 1.28117i | ||||
\(203\) | −1.47214 | + | 4.53077i | −0.103324 | + | 0.317998i | ||||
\(204\) | 0.354102 | − | 1.08981i | 0.0247921 | − | 0.0763022i | ||||
\(205\) | −11.2361 | + | 8.16348i | −0.784761 | + | 0.570162i | ||||
\(206\) | −25.6525 | − | 18.6376i | −1.78729 | − | 1.29854i | ||||
\(207\) | −2.51722 | − | 7.74721i | −0.174959 | − | 0.538468i | ||||
\(208\) | 1.61803 | 0.112190 | ||||||||
\(209\) | 1.67376 | + | 1.90211i | 0.115777 | + | 0.131572i | ||||
\(210\) | 1.05573 | 0.0728522 | ||||||||
\(211\) | −7.41641 | − | 22.8254i | −0.510567 | − | 1.57136i | −0.791206 | − | 0.611549i | \(-0.790547\pi\) |
0.280640 | − | 0.959813i | \(-0.409453\pi\) | |||||||
\(212\) | 10.5000 | + | 7.62870i | 0.721143 | + | 0.523941i | ||||
\(213\) | 3.23607 | − | 2.35114i | 0.221732 | − | 0.161098i | ||||
\(214\) | 2.33688 | − | 7.19218i | 0.159746 | − | 0.491647i | ||||
\(215\) | −1.70820 | + | 5.25731i | −0.116499 | + | 0.358546i | ||||
\(216\) | −4.04508 | + | 2.93893i | −0.275233 | + | 0.199969i | ||||
\(217\) | 3.23607 | + | 2.35114i | 0.219679 | + | 0.159606i | ||||
\(218\) | 5.85410 | + | 18.0171i | 0.396490 | + | 1.22027i | ||||
\(219\) | −1.81966 | −0.122961 | ||||||||
\(220\) | −1.85410 | − | 19.8132i | −0.125004 | − | 1.33580i | ||||
\(221\) | 1.61803 | 0.108841 | ||||||||
\(222\) | −0.652476 | − | 2.00811i | −0.0437913 | − | 0.134776i | ||||
\(223\) | 10.7082 | + | 7.77997i | 0.717074 | + | 0.520985i | 0.885448 | − | 0.464738i | \(-0.153852\pi\) |
−0.168374 | + | 0.985723i | \(0.553852\pi\) | |||||||
\(224\) | 3.35410 | − | 2.43690i | 0.224105 | − | 0.162822i | ||||
\(225\) | 0.881966 | − | 2.71441i | 0.0587977 | − | 0.180961i | ||||
\(226\) | −2.76393 | + | 8.50651i | −0.183854 | + | 0.565845i | ||||
\(227\) | −10.9721 | + | 7.97172i | −0.728246 | + | 0.529102i | −0.889008 | − | 0.457891i | \(-0.848605\pi\) |
0.160762 | + | 0.986993i | \(0.448605\pi\) | |||||||
\(228\) | −0.708204 | − | 0.514540i | −0.0469020 | − | 0.0340763i | ||||
\(229\) | −1.71885 | − | 5.29007i | −0.113585 | − | 0.349577i | 0.878065 | − | 0.478542i | \(-0.158835\pi\) |
−0.991649 | + | 0.128965i | \(0.958835\pi\) | |||||||
\(230\) | −12.7639 | −0.841629 | ||||||||
\(231\) | −0.763932 | − | 0.171513i | −0.0502630 | − | 0.0112848i | ||||
\(232\) | −17.2361 | −1.13160 | ||||||||
\(233\) | 7.67376 | + | 23.6174i | 0.502725 | + | 1.54723i | 0.804562 | + | 0.593869i | \(0.202400\pi\) |
−0.301837 | + | 0.953359i | \(0.597600\pi\) | |||||||
\(234\) | −8.35410 | − | 6.06961i | −0.546125 | − | 0.396783i | ||||
\(235\) | 14.4721 | − | 10.5146i | 0.944058 | − | 0.685898i | ||||
\(236\) | 0.270510 | − | 0.832544i | 0.0176087 | − | 0.0541940i | ||||
\(237\) | 1.12868 | − | 3.47371i | 0.0733155 | − | 0.225642i | ||||
\(238\) | 1.11803 | − | 0.812299i | 0.0724714 | − | 0.0526535i | ||||
\(239\) | 17.9443 | + | 13.0373i | 1.16072 | + | 0.843311i | 0.989869 | − | 0.141986i | \(-0.0453487\pi\) |
0.170850 | + | 0.985297i | \(0.445349\pi\) | |||||||
\(240\) | −0.236068 | − | 0.726543i | −0.0152381 | − | 0.0468981i | ||||
\(241\) | 9.70820 | 0.625360 | 0.312680 | − | 0.949858i | \(-0.398773\pi\) | ||||
0.312680 | + | 0.949858i | \(0.398773\pi\) | |||||||
\(242\) | −3.12868 | + | 24.3970i | −0.201119 | + | 1.56830i | ||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | 0.708204 | + | 2.17963i | 0.0453381 | + | 0.139536i | ||||
\(245\) | −10.7082 | − | 7.77997i | −0.684122 | − | 0.497044i | ||||
\(246\) | −4.79837 | + | 3.48622i | −0.305933 | + | 0.222273i | ||||
\(247\) | 0.381966 | − | 1.17557i | 0.0243039 | − | 0.0747998i | ||||
\(248\) | −4.47214 | + | 13.7638i | −0.283981 | + | 0.874003i | ||||
\(249\) | 2.38197 | − | 1.73060i | 0.150951 | − | 0.109672i | ||||
\(250\) | −21.7082 | − | 15.7719i | −1.37295 | − | 0.997505i | ||||
\(251\) | −1.47214 | − | 4.53077i | −0.0929204 | − | 0.285980i | 0.893786 | − | 0.448494i | \(-0.148040\pi\) |
−0.986706 | + | 0.162515i | \(0.948040\pi\) | |||||||
\(252\) | −5.29180 | −0.333352 | ||||||||
\(253\) | 9.23607 | + | 2.07363i | 0.580667 | + | 0.130368i | ||||
\(254\) | 23.4164 | 1.46928 | ||||||||
\(255\) | −0.236068 | − | 0.726543i | −0.0147832 | − | 0.0454979i | ||||
\(256\) | 7.28115 | + | 5.29007i | 0.455072 | + | 0.330629i | ||||
\(257\) | 15.2082 | − | 11.0494i | 0.948662 | − | 0.689243i | −0.00182827 | − | 0.999998i | \(-0.500582\pi\) |
0.950490 | + | 0.310755i | \(0.100582\pi\) | |||||||
\(258\) | −0.729490 | + | 2.24514i | −0.0454161 | + | 0.139776i | ||||
\(259\) | 0.472136 | − | 1.45309i | 0.0293371 | − | 0.0902903i | ||||
\(260\) | −7.85410 | + | 5.70634i | −0.487091 | + | 0.353892i | ||||
\(261\) | −17.7984 | − | 12.9313i | −1.10169 | − | 0.800426i | ||||
\(262\) | 13.5557 | + | 41.7202i | 0.837476 | + | 2.57749i | ||||
\(263\) | 17.1246 | 1.05595 | 0.527974 | − | 0.849260i | \(-0.322952\pi\) | ||||
0.527974 | + | 0.849260i | \(0.322952\pi\) | |||||||
\(264\) | −0.263932 | − | 2.82041i | −0.0162439 | − | 0.173584i | ||||
\(265\) | 8.65248 | 0.531517 | ||||||||
\(266\) | −0.326238 | − | 1.00406i | −0.0200029 | − | 0.0615627i | ||||
\(267\) | −3.02786 | − | 2.19987i | −0.185302 | − | 0.134630i | ||||
\(268\) | 29.1246 | − | 21.1603i | 1.77907 | − | 1.29257i | ||||
\(269\) | −7.52786 | + | 23.1684i | −0.458982 | + | 1.41260i | 0.407414 | + | 0.913244i | \(0.366431\pi\) |
−0.866396 | + | 0.499358i | \(0.833569\pi\) | |||||||
\(270\) | −3.09017 | + | 9.51057i | −0.188062 | + | 0.578795i | ||||
\(271\) | −24.5623 | + | 17.8456i | −1.49205 | + | 1.08404i | −0.518638 | + | 0.854994i | \(0.673561\pi\) |
−0.973415 | + | 0.229047i | \(0.926439\pi\) | |||||||
\(272\) | −0.809017 | − | 0.587785i | −0.0490539 | − | 0.0356397i | ||||
\(273\) | 0.118034 | + | 0.363271i | 0.00714374 | + | 0.0219862i | ||||
\(274\) | −47.8885 | −2.89305 | ||||||||
\(275\) | 2.19098 | + | 2.48990i | 0.132121 | + | 0.150147i | ||||
\(276\) | −3.27051 | −0.196862 | ||||||||
\(277\) | 7.85410 | + | 24.1724i | 0.471907 | + | 1.45238i | 0.850084 | + | 0.526648i | \(0.176551\pi\) |
−0.378176 | + | 0.925734i | \(0.623449\pi\) | |||||||
\(278\) | −7.23607 | − | 5.25731i | −0.433991 | − | 0.315313i | ||||
\(279\) | −14.9443 | + | 10.8576i | −0.894690 | + | 0.650030i | ||||
\(280\) | −0.854102 | + | 2.62866i | −0.0510424 | + | 0.157092i | ||||
\(281\) | −4.26393 | + | 13.1230i | −0.254365 | + | 0.782855i | 0.739589 | + | 0.673058i | \(0.235020\pi\) |
−0.993954 | + | 0.109796i | \(0.964980\pi\) | |||||||
\(282\) | 6.18034 | − | 4.49028i | 0.368034 | − | 0.267392i | ||||
\(283\) | −15.4443 | − | 11.2209i | −0.918067 | − | 0.667014i | 0.0249754 | − | 0.999688i | \(-0.492049\pi\) |
−0.943042 | + | 0.332674i | \(0.892049\pi\) | |||||||
\(284\) | 9.70820 | + | 29.8788i | 0.576076 | + | 1.77298i | ||||
\(285\) | −0.583592 | −0.0345690 | ||||||||
\(286\) | 11.0172 | − | 4.75528i | 0.651462 | − | 0.281186i | ||||
\(287\) | −4.29180 | −0.253337 | ||||||||
\(288\) | 5.91641 | + | 18.2088i | 0.348628 | + | 1.07297i | ||||
\(289\) | −0.809017 | − | 0.587785i | −0.0475892 | − | 0.0345756i | ||||
\(290\) | −27.8885 | + | 20.2622i | −1.63767 | + | 1.18984i | ||||
\(291\) | −0.708204 | + | 2.17963i | −0.0415156 | + | 0.127772i | ||||
\(292\) | 4.41641 | − | 13.5923i | 0.258451 | − | 0.795430i | ||||
\(293\) | 7.92705 | − | 5.75934i | 0.463103 | − | 0.336464i | −0.331644 | − | 0.943405i | \(-0.607603\pi\) |
0.794747 | + | 0.606940i | \(0.207603\pi\) | |||||||
\(294\) | −4.57295 | − | 3.32244i | −0.266700 | − | 0.193769i | ||||
\(295\) | −0.180340 | − | 0.555029i | −0.0104998 | − | 0.0323150i | ||||
\(296\) | 5.52786 | 0.321301 | ||||||||
\(297\) | 3.78115 | − | 6.37988i | 0.219405 | − | 0.370198i | ||||
\(298\) | −31.6312 | −1.83235 | ||||||||
\(299\) | −1.42705 | − | 4.39201i | −0.0825285 | − | 0.253997i | ||||
\(300\) | −0.927051 | − | 0.673542i | −0.0535233 | − | 0.0388870i | ||||
\(301\) | −1.38197 | + | 1.00406i | −0.0796552 | + | 0.0578729i | ||||
\(302\) | −2.23607 | + | 6.88191i | −0.128671 | + | 0.396009i | ||||
\(303\) | 1.63525 | − | 5.03280i | 0.0939429 | − | 0.289127i | ||||
\(304\) | −0.618034 | + | 0.449028i | −0.0354467 | + | 0.0257535i | ||||
\(305\) | 1.23607 | + | 0.898056i | 0.0707770 | + | 0.0514225i | ||||
\(306\) | 1.97214 | + | 6.06961i | 0.112740 | + | 0.346977i | ||||
\(307\) | −25.7082 | −1.46724 | −0.733622 | − | 0.679557i | \(-0.762172\pi\) | ||||
−0.733622 | + | 0.679557i | \(0.762172\pi\) | |||||||
\(308\) | 3.13525 | − | 5.29007i | 0.178648 | − | 0.301430i | ||||
\(309\) | −5.41641 | −0.308129 | ||||||||
\(310\) | 8.94427 | + | 27.5276i | 0.508001 | + | 1.56346i | ||||
\(311\) | −20.9164 | − | 15.1967i | −1.18606 | − | 0.861724i | −0.193218 | − | 0.981156i | \(-0.561893\pi\) |
−0.992842 | + | 0.119432i | \(0.961893\pi\) | |||||||
\(312\) | −1.11803 | + | 0.812299i | −0.0632962 | + | 0.0459874i | ||||
\(313\) | −3.76393 | + | 11.5842i | −0.212750 | + | 0.654777i | 0.786556 | + | 0.617519i | \(0.211862\pi\) |
−0.999306 | + | 0.0372578i | \(0.988138\pi\) | |||||||
\(314\) | 0.0623059 | − | 0.191758i | 0.00351613 | − | 0.0108215i | ||||
\(315\) | −2.85410 | + | 2.07363i | −0.160810 | + | 0.116836i | ||||
\(316\) | 23.2082 | + | 16.8617i | 1.30556 | + | 0.948547i | ||||
\(317\) | −10.2361 | − | 31.5034i | −0.574915 | − | 1.76941i | −0.636469 | − | 0.771302i | \(-0.719606\pi\) |
0.0615542 | − | 0.998104i | \(-0.480394\pi\) | |||||||
\(318\) | 3.69505 | 0.207208 | ||||||||
\(319\) | 23.4721 | − | 10.1311i | 1.31419 | − | 0.567233i | ||||
\(320\) | 26.0000 | 1.45344 | ||||||||
\(321\) | −0.399187 | − | 1.22857i | −0.0222804 | − | 0.0685722i | ||||
\(322\) | −3.19098 | − | 2.31838i | −0.177827 | − | 0.129199i | ||||
\(323\) | −0.618034 | + | 0.449028i | −0.0343883 | + | 0.0249846i | ||||
\(324\) | 7.14590 | − | 21.9928i | 0.396994 | − | 1.22182i | ||||
\(325\) | 0.500000 | − | 1.53884i | 0.0277350 | − | 0.0853596i | ||||
\(326\) | −12.8262 | + | 9.31881i | −0.710380 | + | 0.516121i | ||||
\(327\) | 2.61803 | + | 1.90211i | 0.144778 | + | 0.105187i | ||||
\(328\) | −4.79837 | − | 14.7679i | −0.264946 | − | 0.815420i | ||||
\(329\) | 5.52786 | 0.304761 | ||||||||
\(330\) | −3.74265 | − | 4.25325i | −0.206026 | − | 0.234134i | ||||
\(331\) | 0.763932 | 0.0419895 | 0.0209948 | − | 0.999780i | \(-0.493317\pi\) | ||||
0.0209948 | + | 0.999780i | \(0.493317\pi\) | |||||||
\(332\) | 7.14590 | + | 21.9928i | 0.392182 | + | 1.20701i | ||||
\(333\) | 5.70820 | + | 4.14725i | 0.312808 | + | 0.227268i | ||||
\(334\) | −24.1074 | + | 17.5150i | −1.31910 | + | 0.958381i | ||||
\(335\) | 7.41641 | − | 22.8254i | 0.405202 | − | 1.24708i | ||||
\(336\) | 0.0729490 | − | 0.224514i | 0.00397970 | − | 0.0122482i | ||||
\(337\) | 20.0344 | − | 14.5559i | 1.09135 | − | 0.792909i | 0.111720 | − | 0.993740i | \(-0.464364\pi\) |
0.979626 | + | 0.200831i | \(0.0643641\pi\) | |||||||
\(338\) | 18.7812 | + | 13.6453i | 1.02156 | + | 0.742207i | ||||
\(339\) | 0.472136 | + | 1.45309i | 0.0256429 | + | 0.0789207i | ||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | −2.00000 | − | 21.3723i | −0.108306 | − | 1.15737i | ||||
\(342\) | 4.87539 | 0.263631 | ||||||||
\(343\) | −2.60081 | − | 8.00448i | −0.140431 | − | 0.432201i | ||||
\(344\) | −5.00000 | − | 3.63271i | −0.269582 | − | 0.195863i | ||||
\(345\) | −1.76393 | + | 1.28157i | −0.0949669 | + | 0.0689975i | ||||
\(346\) | 6.50658 | − | 20.0252i | 0.349796 | − | 1.07656i | ||||
\(347\) | 3.11803 | − | 9.59632i | 0.167385 | − | 0.515158i | −0.831819 | − | 0.555047i | \(-0.812700\pi\) |
0.999204 | + | 0.0398890i | \(0.0127004\pi\) | |||||||
\(348\) | −7.14590 | + | 5.19180i | −0.383060 | + | 0.278310i | ||||
\(349\) | −6.97214 | − | 5.06555i | −0.373210 | − | 0.271153i | 0.385331 | − | 0.922778i | \(-0.374087\pi\) |
−0.758541 | + | 0.651626i | \(0.774087\pi\) | |||||||
\(350\) | −0.427051 | − | 1.31433i | −0.0228268 | − | 0.0702538i | ||||
\(351\) | −3.61803 | −0.193116 | ||||||||
\(352\) | −21.7082 | − | 4.87380i | −1.15705 | − | 0.259774i | ||||
\(353\) | 32.9787 | 1.75528 | 0.877640 | − | 0.479321i | \(-0.159117\pi\) | ||||
0.877640 | + | 0.479321i | \(0.159117\pi\) | |||||||
\(354\) | −0.0770143 | − | 0.237026i | −0.00409327 | − | 0.0125978i | ||||
\(355\) | 16.9443 | + | 12.3107i | 0.899309 | + | 0.653386i | ||||
\(356\) | 23.7812 | − | 17.2780i | 1.26040 | − | 0.915733i | ||||
\(357\) | 0.0729490 | − | 0.224514i | 0.00386087 | − | 0.0118825i | ||||
\(358\) | 7.76393 | − | 23.8949i | 0.410337 | − | 1.26289i | ||||
\(359\) | −8.94427 | + | 6.49839i | −0.472061 | + | 0.342972i | −0.798244 | − | 0.602334i | \(-0.794237\pi\) |
0.326183 | + | 0.945307i | \(0.394237\pi\) | |||||||
\(360\) | −10.3262 | − | 7.50245i | −0.544241 | − | 0.395414i | ||||
\(361\) | −5.69098 | − | 17.5150i | −0.299525 | − | 0.921844i | ||||
\(362\) | −11.7082 | −0.615370 | ||||||||
\(363\) | 2.01722 | + | 3.68571i | 0.105877 | + | 0.193450i | ||||
\(364\) | −3.00000 | −0.157243 | ||||||||
\(365\) | −2.94427 | − | 9.06154i | −0.154110 | − | 0.474303i | ||||
\(366\) | 0.527864 | + | 0.383516i | 0.0275919 | + | 0.0200467i | ||||
\(367\) | 18.9164 | − | 13.7436i | 0.987428 | − | 0.717409i | 0.0280720 | − | 0.999606i | \(-0.491063\pi\) |
0.959356 | + | 0.282197i | \(0.0910632\pi\) | |||||||
\(368\) | −0.881966 | + | 2.71441i | −0.0459757 | + | 0.141499i | ||||
\(369\) | 6.12461 | − | 18.8496i | 0.318835 | − | 0.981272i | ||||
\(370\) | 8.94427 | − | 6.49839i | 0.464991 | − | 0.337835i | ||||
\(371\) | 2.16312 | + | 1.57160i | 0.112304 | + | 0.0815933i | ||||
\(372\) | 2.29180 | + | 7.05342i | 0.118824 | + | 0.365703i | ||||
\(373\) | −26.2148 | −1.35735 | −0.678675 | − | 0.734439i | \(-0.737445\pi\) | ||||
−0.678675 | + | 0.734439i | \(0.737445\pi\) | |||||||
\(374\) | −7.23607 | − | 1.62460i | −0.374168 | − | 0.0840060i | ||||
\(375\) | −4.58359 | −0.236696 | ||||||||
\(376\) | 6.18034 | + | 19.0211i | 0.318727 | + | 0.980940i | ||||
\(377\) | −10.0902 | − | 7.33094i | −0.519670 | − | 0.377562i | ||||
\(378\) | −2.50000 | + | 1.81636i | −0.128586 | + | 0.0934233i | ||||
\(379\) | −4.37132 | + | 13.4535i | −0.224540 | + | 0.691062i | 0.773798 | + | 0.633432i | \(0.218354\pi\) |
−0.998338 | + | 0.0576302i | \(0.981646\pi\) | |||||||
\(380\) | 1.41641 | − | 4.35926i | 0.0726602 | − | 0.223625i | ||||
\(381\) | 3.23607 | − | 2.35114i | 0.165789 | − | 0.120453i | ||||
\(382\) | 32.5623 | + | 23.6579i | 1.66603 | + | 1.21044i | ||||
\(383\) | −1.94427 | − | 5.98385i | −0.0993477 | − | 0.305761i | 0.889015 | − | 0.457879i | \(-0.151391\pi\) |
−0.988362 | + | 0.152118i | \(0.951391\pi\) | |||||||
\(384\) | 5.97871 | 0.305100 | ||||||||
\(385\) | −0.381966 | − | 4.08174i | −0.0194668 | − | 0.208025i | ||||
\(386\) | −21.0557 | −1.07171 | ||||||||
\(387\) | −2.43769 | − | 7.50245i | −0.123915 | − | 0.381371i | ||||
\(388\) | −14.5623 | − | 10.5801i | −0.739289 | − | 0.537125i | ||||
\(389\) | −9.50000 | + | 6.90215i | −0.481669 | + | 0.349953i | −0.801972 | − | 0.597362i | \(-0.796215\pi\) |
0.320302 | + | 0.947315i | \(0.396215\pi\) | |||||||
\(390\) | −0.854102 | + | 2.62866i | −0.0432491 | + | 0.133107i | ||||
\(391\) | −0.881966 | + | 2.71441i | −0.0446029 | + | 0.137274i | ||||
\(392\) | 11.9721 | − | 8.69827i | 0.604684 | − | 0.439329i | ||||
\(393\) | 6.06231 | + | 4.40452i | 0.305803 | + | 0.222179i | ||||
\(394\) | 16.3820 | + | 50.4185i | 0.825312 | + | 2.54005i | ||||
\(395\) | 19.1246 | 0.962264 | ||||||||
\(396\) | 18.7599 | + | 21.3193i | 0.942719 | + | 1.07133i | ||||
\(397\) | −27.5967 | −1.38504 | −0.692521 | − | 0.721398i | \(-0.743500\pi\) | ||||
−0.692521 | + | 0.721398i | \(0.743500\pi\) | |||||||
\(398\) | −15.1008 | − | 46.4755i | −0.756935 | − | 2.32961i | ||||
\(399\) | −0.145898 | − | 0.106001i | −0.00730404 | − | 0.00530669i | ||||
\(400\) | −0.809017 | + | 0.587785i | −0.0404508 | + | 0.0293893i | ||||
\(401\) | 9.03444 | − | 27.8052i | 0.451158 | − | 1.38852i | −0.424428 | − | 0.905462i | \(-0.639525\pi\) |
0.875586 | − | 0.483061i | \(-0.160475\pi\) | |||||||
\(402\) | 3.16718 | − | 9.74759i | 0.157965 | − | 0.486166i | ||||
\(403\) | −8.47214 | + | 6.15537i | −0.422027 | + | 0.306621i | ||||
\(404\) | 33.6246 | + | 24.4297i | 1.67289 | + | 1.21542i | ||||
\(405\) | −4.76393 | − | 14.6619i | −0.236722 | − | 0.728554i | ||||
\(406\) | −10.6525 | −0.528673 | ||||||||
\(407\) | −7.52786 | + | 3.24920i | −0.373142 | + | 0.161057i | ||||
\(408\) | 0.854102 | 0.0422843 | ||||||||
\(409\) | −10.9721 | − | 33.7688i | −0.542537 | − | 1.66976i | −0.726775 | − | 0.686876i | \(-0.758982\pi\) |
0.184237 | − | 0.982882i | \(-0.441018\pi\) | |||||||
\(410\) | −25.1246 | − | 18.2541i | −1.24082 | − | 0.901506i | ||||
\(411\) | −6.61803 | + | 4.80828i | −0.326444 | + | 0.237175i | ||||
\(412\) | 13.1459 | − | 40.4589i | 0.647652 | − | 1.99327i | ||||
\(413\) | 0.0557281 | − | 0.171513i | 0.00274220 | − | 0.00843962i | ||||
\(414\) | 14.7361 | − | 10.7064i | 0.724238 | − | 0.526190i | ||||
\(415\) | 12.4721 | + | 9.06154i | 0.612233 | + | 0.444813i | ||||
\(416\) | 3.35410 | + | 10.3229i | 0.164448 | + | 0.506120i | ||||
\(417\) | −1.52786 | −0.0748198 | ||||||||
\(418\) | −2.88854 | + | 4.87380i | −0.141283 | + | 0.238385i | ||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0.437694 | + | 1.34708i | 0.0213573 | + | 0.0657310i | ||||
\(421\) | 5.30902 | + | 3.85723i | 0.258746 | + | 0.187990i | 0.709594 | − | 0.704611i | \(-0.248878\pi\) |
−0.450848 | + | 0.892601i | \(0.648878\pi\) | |||||||
\(422\) | 43.4164 | − | 31.5439i | 2.11348 | − | 1.53553i | ||||
\(423\) | −7.88854 | + | 24.2784i | −0.383554 | + | 1.18046i | ||||
\(424\) | −2.98936 | + | 9.20029i | −0.145176 | + | 0.446806i | ||||
\(425\) | −0.809017 | + | 0.587785i | −0.0392431 | + | 0.0285118i | ||||
\(426\) | 7.23607 | + | 5.25731i | 0.350589 | + | 0.254718i | ||||
\(427\) | 0.145898 | + | 0.449028i | 0.00706050 | + | 0.0217300i | ||||
\(428\) | 10.1459 | 0.490420 | ||||||||
\(429\) | 1.04508 | − | 1.76336i | 0.0504572 | − | 0.0851356i | ||||
\(430\) | −12.3607 | −0.596085 | ||||||||
\(431\) | −0.0623059 | − | 0.191758i | −0.00300117 | − | 0.00923665i | 0.949545 | − | 0.313632i | \(-0.101546\pi\) |
−0.952546 | + | 0.304395i | \(0.901546\pi\) | |||||||
\(432\) | 1.80902 | + | 1.31433i | 0.0870364 | + | 0.0632356i | ||||
\(433\) | −30.1074 | + | 21.8743i | −1.44687 | + | 1.05121i | −0.460319 | + | 0.887754i | \(0.652265\pi\) |
−0.986550 | + | 0.163458i | \(0.947735\pi\) | |||||||
\(434\) | −2.76393 | + | 8.50651i | −0.132673 | + | 0.408325i | ||||
\(435\) | −1.81966 | + | 5.60034i | −0.0872460 | + | 0.268516i | ||||
\(436\) | −20.5623 | + | 14.9394i | −0.984756 | + | 0.715467i | ||||
\(437\) | 1.76393 | + | 1.28157i | 0.0843803 | + | 0.0613059i | ||||
\(438\) | −1.25735 | − | 3.86974i | −0.0600787 | − | 0.184903i | ||||
\(439\) | −5.14590 | −0.245600 | −0.122800 | − | 0.992431i | \(-0.539187\pi\) | ||||
−0.122800 | + | 0.992431i | \(0.539187\pi\) | |||||||
\(440\) | 13.6180 | − | 5.87785i | 0.649214 | − | 0.280216i | ||||
\(441\) | 18.8885 | 0.899454 | ||||||||
\(442\) | 1.11803 | + | 3.44095i | 0.0531795 | + | 0.163670i | ||||
\(443\) | 21.3262 | + | 15.4944i | 1.01324 | + | 0.736162i | 0.964886 | − | 0.262668i | \(-0.0846025\pi\) |
0.0483539 | + | 0.998830i | \(0.484602\pi\) | |||||||
\(444\) | 2.29180 | − | 1.66509i | 0.108764 | − | 0.0790215i | ||||
\(445\) | 6.05573 | − | 18.6376i | 0.287069 | − | 0.883508i | ||||
\(446\) | −9.14590 | + | 28.1482i | −0.433071 | + | 1.33285i | ||||
\(447\) | −4.37132 | + | 3.17595i | −0.206756 | + | 0.150217i | ||||
\(448\) | 6.50000 | + | 4.72253i | 0.307096 | + | 0.223118i | ||||
\(449\) | 8.05573 | + | 24.7930i | 0.380173 | + | 1.17005i | 0.939922 | + | 0.341390i | \(0.110898\pi\) |
−0.559748 | + | 0.828663i | \(0.689102\pi\) | |||||||
\(450\) | 6.38197 | 0.300849 | ||||||||
\(451\) | 15.2148 | + | 17.2905i | 0.716436 | + | 0.814179i | ||||
\(452\) | −12.0000 | −0.564433 | ||||||||
\(453\) | 0.381966 | + | 1.17557i | 0.0179463 | + | 0.0552331i | ||||
\(454\) | −24.5344 | − | 17.8253i | −1.15146 | − | 0.836584i | ||||
\(455\) | −1.61803 | + | 1.17557i | −0.0758546 | + | 0.0551116i | ||||
\(456\) | 0.201626 | − | 0.620541i | 0.00944201 | − | 0.0290595i | ||||
\(457\) | −1.80902 | + | 5.56758i | −0.0846222 | + | 0.260440i | −0.984410 | − | 0.175886i | \(-0.943721\pi\) |
0.899788 | + | 0.436327i | \(0.143721\pi\) | |||||||
\(458\) | 10.0623 | − | 7.31069i | 0.470181 | − | 0.341606i | ||||
\(459\) | 1.80902 | + | 1.31433i | 0.0844377 | + | 0.0613476i | ||||
\(460\) | −5.29180 | − | 16.2865i | −0.246731 | − | 0.759361i | ||||
\(461\) | −6.79837 | −0.316632 | −0.158316 | − | 0.987389i | \(-0.550606\pi\) | ||||
−0.158316 | + | 0.987389i | \(0.550606\pi\) | |||||||
\(462\) | −0.163119 | − | 1.74311i | −0.00758898 | − | 0.0810969i | ||||
\(463\) | −31.1246 | −1.44648 | −0.723242 | − | 0.690595i | \(-0.757349\pi\) | ||||
−0.723242 | + | 0.690595i | \(0.757349\pi\) | |||||||
\(464\) | 2.38197 | + | 7.33094i | 0.110580 | + | 0.340330i | ||||
\(465\) | 4.00000 | + | 2.90617i | 0.185496 | + | 0.134770i | ||||
\(466\) | −44.9230 | + | 32.6385i | −2.08102 | + | 1.51195i | ||||
\(467\) | 10.6180 | − | 32.6789i | 0.491344 | − | 1.51220i | −0.331234 | − | 0.943549i | \(-0.607465\pi\) |
0.822578 | − | 0.568653i | \(-0.192535\pi\) | |||||||
\(468\) | 4.28115 | − | 13.1760i | 0.197896 | − | 0.609062i | ||||
\(469\) | 6.00000 | − | 4.35926i | 0.277054 | − | 0.201292i | ||||
\(470\) | 32.3607 | + | 23.5114i | 1.49269 | + | 1.08450i | ||||
\(471\) | −0.0106431 | − | 0.0327561i | −0.000490409 | − | 0.00150932i | ||||
\(472\) | 0.652476 | 0.0300326 | ||||||||
\(473\) | 8.94427 | + | 2.00811i | 0.411258 | + | 0.0923332i | ||||
\(474\) | 8.16718 | 0.375131 | ||||||||
\(475\) | 0.236068 | + | 0.726543i | 0.0108315 | + | 0.0333361i | ||||
\(476\) | 1.50000 | + | 1.08981i | 0.0687524 | + | 0.0499515i | ||||
\(477\) | −9.98936 | + | 7.25769i | −0.457381 | + | 0.332307i | ||||
\(478\) | −15.3262 | + | 47.1693i | −0.701006 | + | 2.15747i | ||||
\(479\) | −3.42705 | + | 10.5474i | −0.156586 | + | 0.481922i | −0.998318 | − | 0.0579733i | \(-0.981536\pi\) |
0.841732 | + | 0.539895i | \(0.181536\pi\) | |||||||
\(480\) | 4.14590 | − | 3.01217i | 0.189233 | − | 0.137486i | ||||
\(481\) | 3.23607 | + | 2.35114i | 0.147552 | + | 0.107203i | ||||
\(482\) | 6.70820 | + | 20.6457i | 0.305550 | + | 0.940387i | ||||
\(483\) | −0.673762 | −0.0306572 | ||||||||
\(484\) | −32.4271 | + | 6.12261i | −1.47396 | + | 0.278300i | ||||
\(485\) | −12.0000 | −0.544892 | ||||||||
\(486\) | −6.66970 | − | 20.5272i | −0.302544 | − | 0.931133i | ||||
\(487\) | 6.20820 | + | 4.51052i | 0.281321 | + | 0.204391i | 0.719493 | − | 0.694499i | \(-0.244374\pi\) |
−0.438173 | + | 0.898891i | \(0.644374\pi\) | |||||||
\(488\) | −1.38197 | + | 1.00406i | −0.0625587 | + | 0.0454515i | ||||
\(489\) | −0.836881 | + | 2.57565i | −0.0378451 | + | 0.116475i | ||||
\(490\) | 9.14590 | − | 28.1482i | 0.413170 | − | 1.27161i | ||||
\(491\) | 14.1803 | − | 10.3026i | 0.639950 | − | 0.464951i | −0.219883 | − | 0.975526i | \(-0.570568\pi\) |
0.859833 | + | 0.510575i | \(0.170568\pi\) | |||||||
\(492\) | −6.43769 | − | 4.67726i | −0.290234 | − | 0.210867i | ||||
\(493\) | 2.38197 | + | 7.33094i | 0.107278 | + | 0.330169i | ||||
\(494\) | 2.76393 | 0.124355 | ||||||||
\(495\) | 18.4721 | + | 4.14725i | 0.830261 | + | 0.186405i | ||||
\(496\) | 6.47214 | 0.290607 | ||||||||
\(497\) | 2.00000 | + | 6.15537i | 0.0897123 | + | 0.276106i | ||||
\(498\) | 5.32624 | + | 3.86974i | 0.238674 | + | 0.173407i | ||||
\(499\) | −2.92705 | + | 2.12663i | −0.131033 | + | 0.0952009i | −0.651371 | − | 0.758759i | \(-0.725806\pi\) |
0.520338 | + | 0.853960i | \(0.325806\pi\) | |||||||
\(500\) | 11.1246 | − | 34.2380i | 0.497508 | − | 1.53117i | ||||
\(501\) | −1.57295 | + | 4.84104i | −0.0702742 | + | 0.216282i | ||||
\(502\) | 8.61803 | − | 6.26137i | 0.384642 | − | 0.279459i | ||||
\(503\) | 27.8713 | + | 20.2497i | 1.24272 | + | 0.902890i | 0.997777 | − | 0.0666476i | \(-0.0212303\pi\) |
0.244944 | + | 0.969537i | \(0.421230\pi\) | |||||||
\(504\) | −1.21885 | − | 3.75123i | −0.0542918 | − | 0.167093i | ||||
\(505\) | 27.7082 | 1.23300 | ||||||||
\(506\) | 1.97214 | + | 21.0745i | 0.0876721 | + | 0.936876i | ||||
\(507\) | 3.96556 | 0.176117 | ||||||||
\(508\) | 9.70820 | + | 29.8788i | 0.430732 | + | 1.32566i | ||||
\(509\) | −1.97214 | − | 1.43284i | −0.0874134 | − | 0.0635095i | 0.543220 | − | 0.839590i | \(-0.317205\pi\) |
−0.630634 | + | 0.776081i | \(0.717205\pi\) | |||||||
\(510\) | 1.38197 | − | 1.00406i | 0.0611945 | − | 0.0444604i | ||||
\(511\) | 0.909830 | − | 2.80017i | 0.0402485 | − | 0.123872i | ||||
\(512\) | 3.45492 | − | 10.6331i | 0.152687 | − | 0.469923i | ||||
\(513\) | 1.38197 | − | 1.00406i | 0.0610153 | − | 0.0443302i | ||||
\(514\) | 34.0066 | + | 24.7072i | 1.49997 | + | 1.08979i | ||||
\(515\) | −8.76393 | − | 26.9726i | −0.386185 | − | 1.18856i | ||||
\(516\) | −3.16718 | −0.139428 | ||||||||
\(517\) | −19.5967 | − | 22.2703i | −0.861864 | − | 0.979448i | ||||
\(518\) | 3.41641 | 0.150108 | ||||||||
\(519\) | −1.11146 | − | 3.42071i | −0.0487875 | − | 0.150153i | ||||
\(520\) | −5.85410 | − | 4.25325i | −0.256719 | − | 0.186518i | ||||
\(521\) | −4.94427 | + | 3.59222i | −0.216612 | + | 0.157378i | −0.690800 | − | 0.723045i | \(-0.742742\pi\) |
0.474188 | + | 0.880424i | \(0.342742\pi\) | |||||||
\(522\) | 15.2016 | − | 46.7858i | 0.665357 | − | 2.04776i | ||||
\(523\) | −0.326238 | + | 1.00406i | −0.0142654 | + | 0.0439044i | −0.957936 | − | 0.286982i | \(-0.907348\pi\) |
0.943670 | + | 0.330887i | \(0.107348\pi\) | |||||||
\(524\) | −47.6140 | + | 34.5936i | −2.08003 | + | 1.51123i | ||||
\(525\) | −0.190983 | − | 0.138757i | −0.00833518 | − | 0.00605586i | ||||
\(526\) | 11.8328 | + | 36.4177i | 0.515935 | + | 1.58789i | ||||
\(527\) | 6.47214 | 0.281931 | ||||||||
\(528\) | −1.16312 | + | 0.502029i | −0.0506183 | + | 0.0218480i | ||||
\(529\) | −14.8541 | −0.645831 | ||||||||
\(530\) | 5.97871 | + | 18.4006i | 0.259699 | + | 0.799271i | ||||
\(531\) | 0.673762 | + | 0.489517i | 0.0292388 | + | 0.0212432i | ||||
\(532\) | 1.14590 | − | 0.832544i | 0.0496810 | − | 0.0360953i | ||||
\(533\) | 3.47214 | − | 10.6861i | 0.150395 | − | 0.462868i | ||||
\(534\) | 2.58610 | − | 7.95921i | 0.111912 | − | 0.344429i | ||||
\(535\) | 5.47214 | − | 3.97574i | 0.236581 | − | 0.171886i | ||||
\(536\) | 21.7082 | + | 15.7719i | 0.937652 | + | 0.681244i | ||||
\(537\) | −1.32624 | − | 4.08174i | −0.0572314 | − | 0.176140i | ||||
\(538\) | −54.4721 | −2.34846 | ||||||||
\(539\) | −11.1910 | + | 18.8824i | −0.482030 | + | 0.813321i | ||||
\(540\) | −13.4164 | −0.577350 | ||||||||
\(541\) | −4.85410 | − | 14.9394i | −0.208694 | − | 0.642295i | −0.999541 | − | 0.0302810i | \(-0.990360\pi\) |
0.790847 | − | 0.612014i | \(-0.209640\pi\) | |||||||
\(542\) | −54.9230 | − | 39.9039i | −2.35914 | − | 1.71402i | ||||
\(543\) | −1.61803 | + | 1.17557i | −0.0694365 | + | 0.0504486i | ||||
\(544\) | 2.07295 | − | 6.37988i | 0.0888770 | − | 0.273535i | ||||
\(545\) | −5.23607 | + | 16.1150i | −0.224289 | + | 0.690289i | ||||
\(546\) | −0.690983 | + | 0.502029i | −0.0295713 | + | 0.0214848i | ||||
\(547\) | −15.2533 | − | 11.0822i | −0.652184 | − | 0.473839i | 0.211831 | − | 0.977306i | \(-0.432057\pi\) |
−0.864014 | + | 0.503467i | \(0.832057\pi\) | |||||||
\(548\) | −19.8541 | − | 61.1046i | −0.848125 | − | 2.61026i | ||||
\(549\) | −2.18034 | −0.0930546 | ||||||||
\(550\) | −3.78115 | + | 6.37988i | −0.161229 | + | 0.272039i | ||||
\(551\) | 5.88854 | 0.250860 | ||||||||
\(552\) | −0.753289 | − | 2.31838i | −0.0320621 | − | 0.0986770i | ||||
\(553\) | 4.78115 | + | 3.47371i | 0.203315 | + | 0.147717i | ||||
\(554\) | −45.9787 | + | 33.4055i | −1.95345 | + | 1.41926i | ||||
\(555\) | 0.583592 | − | 1.79611i | 0.0247721 | − | 0.0762407i | ||||
\(556\) | 3.70820 | − | 11.4127i | 0.157263 | − | 0.484005i | ||||
\(557\) | −16.1074 | + | 11.7027i | −0.682492 | + | 0.495860i | −0.874183 | − | 0.485596i | \(-0.838603\pi\) |
0.191691 | + | 0.981455i | \(0.438603\pi\) | |||||||
\(558\) | −33.4164 | − | 24.2784i | −1.41463 | − | 1.02779i | ||||
\(559\) | −1.38197 | − | 4.25325i | −0.0584509 | − | 0.179893i | ||||
\(560\) | 1.23607 | 0.0522334 | ||||||||
\(561\) | −1.16312 | + | 0.502029i | −0.0491069 | + | 0.0211957i | ||||
\(562\) | −30.8541 | −1.30150 | ||||||||
\(563\) | 11.3607 | + | 34.9646i | 0.478796 | + | 1.47358i | 0.840770 | + | 0.541393i | \(0.182103\pi\) |
−0.361974 | + | 0.932188i | \(0.617897\pi\) | |||||||
\(564\) | 8.29180 | + | 6.02434i | 0.349148 | + | 0.253671i | ||||
\(565\) | −6.47214 | + | 4.70228i | −0.272285 | + | 0.197826i | ||||
\(566\) | 13.1910 | − | 40.5977i | 0.554458 | − | 1.70645i | ||||
\(567\) | 1.47214 | − | 4.53077i | 0.0618239 | − | 0.190274i | ||||
\(568\) | −18.9443 | + | 13.7638i | −0.794884 | + | 0.577517i | ||||
\(569\) | 6.69098 | + | 4.86128i | 0.280501 | + | 0.203796i | 0.719136 | − | 0.694870i | \(-0.244538\pi\) |
−0.438635 | + | 0.898665i | \(0.644538\pi\) | |||||||
\(570\) | −0.403252 | − | 1.24108i | −0.0168904 | − | 0.0519832i | ||||
\(571\) | 10.0902 | 0.422260 | 0.211130 | − | 0.977458i | \(-0.432286\pi\) | ||||
0.211130 | + | 0.977458i | \(0.432286\pi\) | |||||||
\(572\) | 10.6353 | + | 12.0862i | 0.444682 | + | 0.505350i | ||||
\(573\) | 6.87539 | 0.287223 | ||||||||
\(574\) | −2.96556 | − | 9.12705i | −0.123780 | − | 0.380956i | ||||
\(575\) | 2.30902 | + | 1.67760i | 0.0962927 | + | 0.0699607i | ||||
\(576\) | −30.0172 | + | 21.8088i | −1.25072 | + | 0.908699i | ||||
\(577\) | 2.39261 | − | 7.36369i | 0.0996056 | − | 0.306555i | −0.888821 | − | 0.458255i | \(-0.848475\pi\) |
0.988427 | + | 0.151700i | \(0.0484748\pi\) | |||||||
\(578\) | 0.690983 | − | 2.12663i | 0.0287411 | − | 0.0884560i | ||||
\(579\) | −2.90983 | + | 2.11412i | −0.120928 | + | 0.0878596i | ||||
\(580\) | −37.4164 | − | 27.1846i | −1.55363 | − | 1.12878i | ||||
\(581\) | 1.47214 | + | 4.53077i | 0.0610745 | + | 0.187968i | ||||
\(582\) | −5.12461 | −0.212422 | ||||||||
\(583\) | −1.33688 | − | 14.2861i | −0.0553680 | − | 0.591669i | ||||
\(584\) | 10.6525 | 0.440803 | ||||||||
\(585\) | −2.85410 | − | 8.78402i | −0.118003 | − | 0.363175i | ||||
\(586\) | 17.7254 | + | 12.8783i | 0.732231 | + | 0.531997i | ||||
\(587\) | 10.9443 | − | 7.95148i | 0.451718 | − | 0.328193i | −0.338555 | − | 0.940946i | \(-0.609938\pi\) |
0.790274 | + | 0.612754i | \(0.209938\pi\) | |||||||
\(588\) | 2.34346 | − | 7.21242i | 0.0966426 | − | 0.297435i | ||||
\(589\) | 1.52786 | − | 4.70228i | 0.0629545 | − | 0.193754i | ||||
\(590\) | 1.05573 | − | 0.767031i | 0.0434636 | − | 0.0315782i | ||||
\(591\) | 7.32624 | + | 5.32282i | 0.301361 | + | 0.218952i | ||||
\(592\) | −0.763932 | − | 2.35114i | −0.0313974 | − | 0.0966313i | ||||
\(593\) | −14.9656 | −0.614562 | −0.307281 | − | 0.951619i | \(-0.599419\pi\) | ||||
−0.307281 | + | 0.951619i | \(0.599419\pi\) | |||||||
\(594\) | 16.1803 | + | 3.63271i | 0.663887 | + | 0.149052i | ||||
\(595\) | 1.23607 | 0.0506738 | ||||||||
\(596\) | −13.1140 | − | 40.3606i | −0.537169 | − | 1.65324i | ||||
\(597\) | −6.75329 | − | 4.90655i | −0.276394 | − | 0.200812i | ||||
\(598\) | 8.35410 | − | 6.06961i | 0.341625 | − | 0.248205i | ||||
\(599\) | 2.34752 | − | 7.22494i | 0.0959172 | − | 0.295203i | −0.891574 | − | 0.452874i | \(-0.850399\pi\) |
0.987492 | + | 0.157671i | \(0.0503987\pi\) | |||||||
\(600\) | 0.263932 | − | 0.812299i | 0.0107750 | − | 0.0331620i | ||||
\(601\) | 12.4164 | − | 9.02105i | 0.506476 | − | 0.367976i | −0.305009 | − | 0.952349i | \(-0.598660\pi\) |
0.811485 | + | 0.584373i | \(0.198660\pi\) | |||||||
\(602\) | −3.09017 | − | 2.24514i | −0.125946 | − | 0.0915051i | ||||
\(603\) | 10.5836 | + | 32.5729i | 0.430997 | + | 1.32647i | ||||
\(604\) | −9.70820 | −0.395021 | ||||||||
\(605\) | −15.0902 | + | 16.0090i | −0.613503 | + | 0.650857i | ||||
\(606\) | 11.8328 | 0.480675 | ||||||||
\(607\) | 6.00658 | + | 18.4863i | 0.243799 | + | 0.750338i | 0.995832 | + | 0.0912111i | \(0.0290738\pi\) |
−0.752032 | + | 0.659126i | \(0.770926\pi\) | |||||||
\(608\) | −4.14590 | − | 3.01217i | −0.168138 | − | 0.122160i | ||||
\(609\) | −1.47214 | + | 1.06957i | −0.0596540 | + | 0.0433411i | ||||
\(610\) | −1.05573 | + | 3.24920i | −0.0427452 | + | 0.131556i | ||||
\(611\) | −4.47214 | + | 13.7638i | −0.180923 | + | 0.556825i | ||||
\(612\) | −6.92705 | + | 5.03280i | −0.280009 | + | 0.203439i | ||||
\(613\) | 26.1074 | + | 18.9681i | 1.05447 | + | 0.766116i | 0.973057 | − | 0.230565i | \(-0.0740575\pi\) |
0.0814107 | + | 0.996681i | \(0.474057\pi\) | |||||||
\(614\) | −17.7639 | − | 54.6718i | −0.716894 | − | 2.20637i | ||||
\(615\) | −5.30495 | −0.213916 | ||||||||
\(616\) | 4.47214 | + | 1.00406i | 0.180187 | + | 0.0404546i | ||||
\(617\) | −16.0000 | −0.644136 | −0.322068 | − | 0.946717i | \(-0.604378\pi\) | ||||
−0.322068 | + | 0.946717i | \(0.604378\pi\) | |||||||
\(618\) | −3.74265 | − | 11.5187i | −0.150551 | − | 0.463349i | ||||
\(619\) | 19.4164 | + | 14.1068i | 0.780411 | + | 0.567002i | 0.905102 | − | 0.425194i | \(-0.139794\pi\) |
−0.124691 | + | 0.992196i | \(0.539794\pi\) | |||||||
\(620\) | −31.4164 | + | 22.8254i | −1.26171 | + | 0.916688i | ||||
\(621\) | 1.97214 | − | 6.06961i | 0.0791391 | − | 0.243565i | ||||
\(622\) | 17.8647 | − | 54.9820i | 0.716311 | − | 2.20458i | ||||
\(623\) | 4.89919 | − | 3.55947i | 0.196282 | − | 0.142607i | ||||
\(624\) | 0.500000 | + | 0.363271i | 0.0200160 | + | 0.0145425i | ||||
\(625\) | −5.87132 | − | 18.0701i | −0.234853 | − | 0.722803i | ||||
\(626\) | −27.2361 | −1.08857 | ||||||||
\(627\) | 0.0901699 | + | 0.963568i | 0.00360104 | + | 0.0384812i | ||||
\(628\) | 0.270510 | 0.0107945 | ||||||||
\(629\) | −0.763932 | − | 2.35114i | −0.0304600 | − | 0.0937461i | ||||
\(630\) | −6.38197 | − | 4.63677i | −0.254264 | − | 0.184733i | ||||
\(631\) | 30.8885 | − | 22.4418i | 1.22965 | − | 0.893396i | 0.232789 | − | 0.972527i | \(-0.425215\pi\) |
0.996864 | + | 0.0791316i | \(0.0252147\pi\) | |||||||
\(632\) | −6.60739 | + | 20.3355i | −0.262828 | + | 0.808901i | ||||
\(633\) | 2.83282 | − | 8.71851i | 0.112594 | − | 0.346530i | ||||
\(634\) | 59.9230 | − | 43.5366i | 2.37985 | − | 1.72906i | ||||
\(635\) | 16.9443 | + | 12.3107i | 0.672413 | + | 0.488537i | ||||
\(636\) | 1.53193 | + | 4.71479i | 0.0607450 | + | 0.186954i | ||||
\(637\) | 10.7082 | 0.424274 | ||||||||
\(638\) | 37.7639 | + | 42.9161i | 1.49509 | + | 1.69906i | ||||
\(639\) | −29.8885 | −1.18237 | ||||||||
\(640\) | 9.67376 | + | 29.7728i | 0.382389 | + | 1.17687i | ||||
\(641\) | 31.8885 | + | 23.1684i | 1.25952 | + | 0.915096i | 0.998734 | − | 0.0503001i | \(-0.0160178\pi\) |
0.260788 | + | 0.965396i | \(0.416018\pi\) | |||||||
\(642\) | 2.33688 | − | 1.69784i | 0.0922293 | − | 0.0670085i | ||||
\(643\) | −3.70163 | + | 11.3924i | −0.145978 | + | 0.449274i | −0.997135 | − | 0.0756365i | \(-0.975901\pi\) |
0.851158 | + | 0.524910i | \(0.175901\pi\) | |||||||
\(644\) | 1.63525 | − | 5.03280i | 0.0644381 | − | 0.198320i | ||||
\(645\) | −1.70820 | + | 1.24108i | −0.0672605 | + | 0.0488676i | ||||
\(646\) | −1.38197 | − | 1.00406i | −0.0543727 | − | 0.0395041i | ||||
\(647\) | 7.67376 | + | 23.6174i | 0.301687 | + | 0.928496i | 0.980893 | + | 0.194549i | \(0.0623242\pi\) |
−0.679206 | + | 0.733948i | \(0.737676\pi\) | |||||||
\(648\) | 17.2361 | 0.677097 | ||||||||
\(649\) | −0.888544 | + | 0.383516i | −0.0348784 | + | 0.0150543i | ||||
\(650\) | 3.61803 | 0.141911 | ||||||||
\(651\) | 0.472136 | + | 1.45309i | 0.0185045 | + | 0.0569509i | ||||
\(652\) | −17.2082 | − | 12.5025i | −0.673925 | − | 0.489635i | ||||
\(653\) | −8.85410 | + | 6.43288i | −0.346488 | + | 0.251738i | −0.747394 | − | 0.664381i | \(-0.768695\pi\) |
0.400906 | + | 0.916119i | \(0.368695\pi\) | |||||||
\(654\) | −2.23607 | + | 6.88191i | −0.0874372 | + | 0.269104i | ||||
\(655\) | −12.1246 | + | 37.3157i | −0.473748 | + | 1.45805i | ||||
\(656\) | −5.61803 | + | 4.08174i | −0.219347 | + | 0.159365i | ||||
\(657\) | 11.0000 | + | 7.99197i | 0.429151 | + | 0.311796i | ||||
\(658\) | 3.81966 | + | 11.7557i | 0.148906 | + | 0.458285i | ||||
\(659\) | −41.1246 | −1.60199 | −0.800994 | − | 0.598673i | \(-0.795695\pi\) | ||||
−0.800994 | + | 0.598673i | \(0.795695\pi\) | |||||||
\(660\) | 3.87539 | − | 6.53888i | 0.150849 | − | 0.254526i | ||||
\(661\) | 46.7426 | 1.81808 | 0.909039 | − | 0.416711i | \(-0.136817\pi\) | ||||
0.909039 | + | 0.416711i | \(0.136817\pi\) | |||||||
\(662\) | 0.527864 | + | 1.62460i | 0.0205160 | + | 0.0631418i | ||||
\(663\) | 0.500000 | + | 0.363271i | 0.0194184 | + | 0.0141083i | ||||
\(664\) | −13.9443 | + | 10.1311i | −0.541143 | + | 0.393163i | ||||
\(665\) | 0.291796 | − | 0.898056i | 0.0113154 | − | 0.0348251i | ||||
\(666\) | −4.87539 | + | 15.0049i | −0.188917 | + | 0.581428i | ||||
\(667\) | 17.7984 | − | 12.9313i | 0.689156 | − | 0.500701i | ||||
\(668\) | −32.3435 | − | 23.4989i | −1.25141 | − | 0.909200i | ||||
\(669\) | 1.56231 | + | 4.80828i | 0.0604022 | + | 0.185899i | ||||
\(670\) | 53.6656 | 2.07328 | ||||||||
\(671\) | 1.29180 | − | 2.17963i | 0.0498692 | − | 0.0841436i | ||||
\(672\) | 1.58359 | 0.0610884 | ||||||||
\(673\) | −0.326238 | − | 1.00406i | −0.0125755 | − | 0.0387036i | 0.944572 | − | 0.328305i | \(-0.106477\pi\) |
−0.957147 | + | 0.289601i | \(0.906477\pi\) | |||||||
\(674\) | 44.7984 | + | 32.5479i | 1.72557 | + | 1.25370i | ||||
\(675\) | 1.80902 | − | 1.31433i | 0.0696291 | − | 0.0505885i | ||||
\(676\) | −9.62461 | + | 29.6215i | −0.370177 | + | 1.13929i | ||||
\(677\) | −10.9443 | + | 33.6830i | −0.420623 | + | 1.29454i | 0.486502 | + | 0.873680i | \(0.338273\pi\) |
−0.907124 | + | 0.420863i | \(0.861727\pi\) | |||||||
\(678\) | −2.76393 | + | 2.00811i | −0.106148 | + | 0.0771212i | ||||
\(679\) | −3.00000 | − | 2.17963i | −0.115129 | − | 0.0836464i | ||||
\(680\) | 1.38197 | + | 4.25325i | 0.0529960 | + | 0.163105i | ||||
\(681\) | −5.18034 | −0.198511 | ||||||||
\(682\) | 44.0689 | − | 19.0211i | 1.68748 | − | 0.728357i | ||||
\(683\) | −17.8541 | −0.683168 | −0.341584 | − | 0.939851i | \(-0.610963\pi\) | ||||
−0.341584 | + | 0.939851i | \(0.610963\pi\) | |||||||
\(684\) | 2.02129 | + | 6.22088i | 0.0772858 | + | 0.237861i | ||||
\(685\) | −34.6525 | − | 25.1765i | −1.32400 | − | 0.961945i | ||||
\(686\) | 15.2254 | − | 11.0619i | 0.581309 | − | 0.422346i | ||||
\(687\) | 0.656541 | − | 2.02063i | 0.0250486 | − | 0.0770917i | ||||
\(688\) | −0.854102 | + | 2.62866i | −0.0325623 | + | 0.100217i | ||||
\(689\) | −5.66312 | + | 4.11450i | −0.215748 | + | 0.156750i | ||||
\(690\) | −3.94427 | − | 2.86568i | −0.150156 | − | 0.109095i | ||||
\(691\) | −2.35410 | − | 7.24518i | −0.0895543 | − | 0.275620i | 0.896242 | − | 0.443565i | \(-0.146287\pi\) |
−0.985796 | + | 0.167946i | \(0.946287\pi\) | |||||||
\(692\) | 28.2492 | 1.07387 | ||||||||
\(693\) | 3.86475 | + | 4.39201i | 0.146810 | + | 0.166839i | ||||
\(694\) | 22.5623 | 0.856453 | ||||||||
\(695\) | −2.47214 | − | 7.60845i | −0.0937735 | − | 0.288605i | ||||
\(696\) | −5.32624 | − | 3.86974i | −0.201891 | − | 0.146682i | ||||
\(697\) | −5.61803 | + | 4.08174i | −0.212798 | + | 0.154607i | ||||
\(698\) | 5.95492 | − | 18.3273i | 0.225397 | − | 0.693700i | ||||
\(699\) | −2.93112 | + | 9.02105i | −0.110865 | + | 0.341207i | ||||
\(700\) | 1.50000 | − | 1.08981i | 0.0566947 | − | 0.0411911i | ||||
\(701\) | −39.3435 | − | 28.5847i | −1.48598 | − | 1.07963i | −0.975567 | − | 0.219701i | \(-0.929492\pi\) |
−0.510415 | − | 0.859928i | \(-0.670508\pi\) | |||||||
\(702\) | −2.50000 | − | 7.69421i | −0.0943564 | − | 0.290399i | ||||
\(703\) | −1.88854 | −0.0712278 | ||||||||
\(704\) | −4.01722 | − | 42.9286i | −0.151405 | − | 1.61793i | ||||
\(705\) | 6.83282 | 0.257339 | ||||||||
\(706\) | 22.7877 | + | 70.1334i | 0.857628 | + | 2.63951i | ||||
\(707\) | 6.92705 | + | 5.03280i | 0.260519 | + | 0.189278i | ||||
\(708\) | 0.270510 | − | 0.196537i | 0.0101664 | − | 0.00738631i | ||||
\(709\) | −1.20163 | + | 3.69822i | −0.0451280 | + | 0.138890i | −0.971082 | − | 0.238747i | \(-0.923263\pi\) |
0.925954 | + | 0.377637i | \(0.123263\pi\) | |||||||
\(710\) | −14.4721 | + | 44.5407i | −0.543130 | + | 1.67158i | ||||
\(711\) | −22.0795 | + | 16.0417i | −0.828047 | + | 0.601611i | ||||
\(712\) | 17.7254 | + | 12.8783i | 0.664288 | + | 0.482634i | ||||
\(713\) | −5.70820 | − | 17.5680i | −0.213774 | − | 0.657928i | ||||
\(714\) | 0.527864 | 0.0197548 | ||||||||
\(715\) | 10.4721 | + | 2.35114i | 0.391636 | + | 0.0879277i | ||||
\(716\) | 33.7082 | 1.25973 | ||||||||
\(717\) | 2.61803 | + | 8.05748i | 0.0977723 | + | 0.300912i | ||||
\(718\) | −20.0000 | − | 14.5309i | −0.746393 | − | 0.542287i | ||||
\(719\) | 24.8156 | − | 18.0296i | 0.925466 | − | 0.672390i | −0.0194129 | − | 0.999812i | \(-0.506180\pi\) |
0.944878 | + | 0.327421i | \(0.106180\pi\) | |||||||
\(720\) | −1.76393 | + | 5.42882i | −0.0657379 | + | 0.202320i | ||||
\(721\) | 2.70820 | − | 8.33499i | 0.100859 | − | 0.310411i | ||||
\(722\) | 33.3156 | − | 24.2052i | 1.23988 | − | 0.900824i | ||||
\(723\) | 3.00000 | + | 2.17963i | 0.111571 | + | 0.0810612i | ||||
\(724\) | −4.85410 | − | 14.9394i | −0.180401 | − | 0.555218i | ||||
\(725\) | 7.70820 | 0.286276 | ||||||||
\(726\) | −6.44427 | + | 6.83664i | −0.239169 | + | 0.253732i | ||||
\(727\) | −39.4853 | −1.46443 | −0.732214 | − | 0.681074i | \(-0.761513\pi\) | ||||
−0.732214 | + | 0.681074i | \(0.761513\pi\) | |||||||
\(728\) | −0.690983 | − | 2.12663i | −0.0256095 | − | 0.0788180i | ||||
\(729\) | 15.7254 | + | 11.4252i | 0.582423 | + | 0.423155i | ||||
\(730\) | 17.2361 | − | 12.5227i | 0.637935 | − | 0.463487i | ||||
\(731\) | −0.854102 | + | 2.62866i | −0.0315901 | + | 0.0972243i | ||||
\(732\) | −0.270510 | + | 0.832544i | −0.00999833 | + | 0.0307717i | ||||
\(733\) | 16.8541 | − | 12.2452i | 0.622520 | − | 0.452288i | −0.231281 | − | 0.972887i | \(-0.574292\pi\) |
0.853801 | + | 0.520600i | \(0.174292\pi\) | |||||||
\(734\) | 42.2984 | + | 30.7316i | 1.56126 | + | 1.13432i | ||||
\(735\) | −1.56231 | − | 4.80828i | −0.0576265 | − | 0.177356i | ||||
\(736\) | −19.1459 | −0.705727 | ||||||||
\(737\) | −38.8328 | − | 8.71851i | −1.43043 | − | 0.321150i | ||||
\(738\) | 44.3181 | 1.63137 | ||||||||
\(739\) | −1.41641 | − | 4.35926i | −0.0521034 | − | 0.160358i | 0.921619 | − | 0.388096i | \(-0.126867\pi\) |
−0.973722 | + | 0.227738i | \(0.926867\pi\) | |||||||
\(740\) | 12.0000 | + | 8.71851i | 0.441129 | + | 0.320499i | ||||
\(741\) | 0.381966 | − | 0.277515i | 0.0140319 | − | 0.0101948i | ||||
\(742\) | −1.84752 | + | 5.68609i | −0.0678247 | + | 0.208743i | ||||
\(743\) | −7.82624 | + | 24.0867i | −0.287117 | + | 0.883655i | 0.698639 | + | 0.715474i | \(0.253789\pi\) |
−0.985756 | + | 0.168181i | \(0.946211\pi\) | |||||||
\(744\) | −4.47214 | + | 3.24920i | −0.163956 | + | 0.119121i | ||||
\(745\) | −22.8885 | − | 16.6295i | −0.838571 | − | 0.609258i | ||||
\(746\) | −18.1140 | − | 55.7491i | −0.663200 | − | 2.04112i | ||||
\(747\) | −22.0000 | −0.804938 | ||||||||
\(748\) | −0.927051 | − | 9.90659i | −0.0338963 | − | 0.362221i | ||||
\(749\) | 2.09017 | 0.0763731 | ||||||||
\(750\) | −3.16718 | − | 9.74759i | −0.115649 | − | 0.355932i | ||||
\(751\) | 0.635255 | + | 0.461540i | 0.0231808 | + | 0.0168418i | 0.599315 | − | 0.800513i | \(-0.295440\pi\) |
−0.576135 | + | 0.817355i | \(0.695440\pi\) | |||||||
\(752\) | 7.23607 | − | 5.25731i | 0.263872 | − | 0.191714i | ||||
\(753\) | 0.562306 | − | 1.73060i | 0.0204916 | − | 0.0630666i | ||||
\(754\) | 8.61803 | − | 26.5236i | 0.313850 | − | 0.965932i | ||||
\(755\) | −5.23607 | + | 3.80423i | −0.190560 | + | 0.138450i | ||||
\(756\) | −3.35410 | − | 2.43690i | −0.121988 | − | 0.0886291i | ||||
\(757\) | −6.14590 | − | 18.9151i | −0.223376 | − | 0.687482i | −0.998452 | − | 0.0556139i | \(-0.982288\pi\) |
0.775076 | − | 0.631868i | \(-0.217712\pi\) | |||||||
\(758\) | −31.6312 | −1.14890 | ||||||||
\(759\) | 2.38854 | + | 2.71441i | 0.0866986 | + | 0.0985269i | ||||
\(760\) | 3.41641 | 0.123926 | ||||||||
\(761\) | 7.98936 | + | 24.5887i | 0.289614 | + | 0.891340i | 0.984978 | + | 0.172682i | \(0.0552433\pi\) |
−0.695364 | + | 0.718658i | \(0.744757\pi\) | |||||||
\(762\) | 7.23607 | + | 5.25731i | 0.262135 | + | 0.190452i | ||||
\(763\) | −4.23607 | + | 3.07768i | −0.153356 | + | 0.111420i | ||||
\(764\) | −16.6869 | + | 51.3571i | −0.603711 | + | 1.85803i | ||||
\(765\) | −1.76393 | + | 5.42882i | −0.0637751 | + | 0.196280i | ||||
\(766\) | 11.3820 | − | 8.26948i | 0.411247 | − | 0.298789i | ||||
\(767\) | 0.381966 | + | 0.277515i | 0.0137920 | + | 0.0100205i | ||||
\(768\) | 1.06231 | + | 3.26944i | 0.0383327 | + | 0.117976i | ||||
\(769\) | −23.0902 | −0.832653 | −0.416326 | − | 0.909215i | \(-0.636683\pi\) | ||||
−0.416326 | + | 0.909215i | \(0.636683\pi\) | |||||||
\(770\) | 8.41641 | − | 3.63271i | 0.303306 | − | 0.130914i | ||||
\(771\) | 7.18034 | 0.258594 | ||||||||
\(772\) | −8.72949 | − | 26.8666i | −0.314181 | − | 0.966950i | ||||
\(773\) | −42.1525 | − | 30.6256i | −1.51612 | − | 1.10153i | −0.963369 | − | 0.268178i | \(-0.913579\pi\) |
−0.552750 | − | 0.833347i | \(-0.686421\pi\) | |||||||
\(774\) | 14.2705 | − | 10.3681i | 0.512943 | − | 0.372675i | ||||
\(775\) | 2.00000 | − | 6.15537i | 0.0718421 | − | 0.221107i | ||||
\(776\) | 4.14590 | − | 12.7598i | 0.148829 | − | 0.458049i | ||||
\(777\) | 0.472136 | − | 0.343027i | 0.0169378 | − | 0.0123060i | ||||
\(778\) | −21.2426 | − | 15.4337i | −0.761586 | − | 0.553324i | ||||
\(779\) | 1.63932 | + | 5.04531i | 0.0587347 | + | 0.180767i | ||||
\(780\) | −3.70820 | −0.132775 | ||||||||
\(781\) | 17.7082 | − | 29.8788i | 0.633649 | − | 1.06915i | ||||
\(782\) | −6.38197 | −0.228219 | ||||||||
\(783\) | −5.32624 | − | 16.3925i | −0.190344 | − | 0.585819i | ||||
\(784\) | −5.35410 | − | 3.88998i | −0.191218 | − | 0.138928i | ||||
\(785\) | 0.145898 | − | 0.106001i | 0.00520732 | − | 0.00378334i | ||||
\(786\) | −5.17783 | + | 15.9357i | −0.184687 | + | 0.568408i | ||||
\(787\) | 4.06231 | − | 12.5025i | 0.144806 | − | 0.445666i | −0.852180 | − | 0.523248i | \(-0.824720\pi\) |
0.996986 | + | 0.0775824i | \(0.0247201\pi\) | |||||||
\(788\) | −57.5410 | + | 41.8060i | −2.04981 | + | 1.48928i | ||||
\(789\) | 5.29180 | + | 3.84471i | 0.188393 | + | 0.136875i | ||||
\(790\) | 13.2148 | + | 40.6709i | 0.470161 | + | 1.44701i | ||||
\(791\) | −2.47214 | −0.0878990 | ||||||||
\(792\) | −10.7918 | + | 18.2088i | −0.383470 | + | 0.647023i | ||||
\(793\) | −1.23607 | −0.0438941 | ||||||||
\(794\) | −19.0689 | − | 58.6880i | −0.676729 | − | 2.08276i | ||||
\(795\) | 2.67376 | + | 1.94260i | 0.0948286 | + | 0.0688970i | ||||
\(796\) | 53.0410 | − | 38.5366i | 1.87999 | − | 1.36589i | ||||
\(797\) | 4.73607 | − | 14.5761i | 0.167760 | − | 0.516313i | −0.831469 | − | 0.555571i | \(-0.812500\pi\) |
0.999229 | + | 0.0392586i | \(0.0124996\pi\) | |||||||
\(798\) | 0.124612 | − | 0.383516i | 0.00441121 | − | 0.0135763i | ||||
\(799\) | 7.23607 | − | 5.25731i | 0.255994 | − | 0.185990i | ||||
\(800\) | −5.42705 | − | 3.94298i | −0.191875 | − | 0.139406i | ||||
\(801\) | 8.64183 | + | 26.5968i | 0.305344 | + | 0.939753i | ||||
\(802\) | 65.3738 | 2.30843 | ||||||||
\(803\) | −14.5066 | + | 6.26137i | −0.511926 | + | 0.220959i | ||||
\(804\) | 13.7508 | 0.484952 | ||||||||
\(805\) | −1.09017 | − | 3.35520i | −0.0384234 | − | 0.118255i | ||||
\(806\) | −18.9443 | − | 13.7638i | −0.667284 | − | 0.484810i | ||||
\(807\) | −7.52786 | + | 5.46931i | −0.264993 | + | 0.192529i | ||||
\(808\) | −9.57295 | + | 29.4625i | −0.336775 | + | 1.03649i | ||||
\(809\) | −4.79837 | + | 14.7679i | −0.168702 | + | 0.519211i | −0.999290 | − | 0.0376763i | \(-0.988004\pi\) |
0.830588 | + | 0.556887i | \(0.188004\pi\) | |||||||
\(810\) | 27.8885 | − | 20.2622i | 0.979904 | − | 0.711942i | ||||
\(811\) | −12.7812 | − | 9.28605i | −0.448807 | − | 0.326077i | 0.340318 | − | 0.940311i | \(-0.389465\pi\) |
−0.789125 | + | 0.614233i | \(0.789465\pi\) | |||||||
\(812\) | −4.41641 | − | 13.5923i | −0.154986 | − | 0.476996i | ||||
\(813\) | −11.5967 | −0.406716 | ||||||||
\(814\) | −12.1115 | − | 13.7638i | −0.424506 | − | 0.482422i | ||||
\(815\) | −14.1803 | −0.496716 | ||||||||
\(816\) | −0.118034 | − | 0.363271i | −0.00413202 | − | 0.0127170i | ||||
\(817\) | 1.70820 | + | 1.24108i | 0.0597625 | + | 0.0434200i | ||||
\(818\) | 64.2320 | − | 46.6673i | 2.24582 | − | 1.63168i | ||||
\(819\) | 0.881966 | − | 2.71441i | 0.0308184 | − | 0.0948492i | ||||
\(820\) | 12.8754 | − | 39.6264i | 0.449628 | − | 1.38381i | ||||
\(821\) | 20.6525 | − | 15.0049i | 0.720776 | − | 0.523675i | −0.165856 | − | 0.986150i | \(-0.553039\pi\) |
0.886632 | + | 0.462475i | \(0.153039\pi\) | |||||||
\(822\) | −14.7984 | − | 10.7516i | −0.516153 | − | 0.375007i | ||||
\(823\) | −1.80902 | − | 5.56758i | −0.0630584 | − | 0.194074i | 0.914564 | − | 0.404441i | \(-0.132534\pi\) |
−0.977622 | + | 0.210367i | \(0.932534\pi\) | |||||||
\(824\) | 31.7082 | 1.10461 | ||||||||
\(825\) | 0.118034 | + | 1.26133i | 0.00410942 | + | 0.0439138i | ||||
\(826\) | 0.403252 | 0.0140309 | ||||||||
\(827\) | −1.52786 | − | 4.70228i | −0.0531290 | − | 0.163514i | 0.920971 | − | 0.389630i | \(-0.127397\pi\) |
−0.974100 | + | 0.226116i | \(0.927397\pi\) | |||||||
\(828\) | 19.7705 | + | 14.3641i | 0.687073 | + | 0.499188i | ||||
\(829\) | 17.7361 | − | 12.8860i | 0.615999 | − | 0.447550i | −0.235523 | − | 0.971869i | \(-0.575680\pi\) |
0.851522 | + | 0.524319i | \(0.175680\pi\) | |||||||
\(830\) | −10.6525 | + | 32.7849i | −0.369753 | + | 1.13798i | ||||
\(831\) | −3.00000 | + | 9.23305i | −0.104069 | + | 0.320291i | ||||
\(832\) | −17.0172 | + | 12.3637i | −0.589966 | + | 0.428635i | ||||
\(833\) | −5.35410 | − | 3.88998i | −0.185509 | − | 0.134780i | ||||
\(834\) | −1.05573 | − | 3.24920i | −0.0365569 | − | 0.112510i | ||||
\(835\) | −26.6525 | −0.922347 | ||||||||
\(836\) | −7.41641 | − | 1.66509i | −0.256502 | − | 0.0575882i | ||||
\(837\) | −14.4721 | −0.500230 | ||||||||
\(838\) | 8.29180 | + | 25.5195i | 0.286435 | + | 0.881557i | ||||
\(839\) | 41.2877 | + | 29.9973i | 1.42541 | + | 1.03562i | 0.990848 | + | 0.134980i | \(0.0430970\pi\) |
0.434562 | + | 0.900642i | \(0.356903\pi\) | |||||||
\(840\) | −0.854102 | + | 0.620541i | −0.0294693 | + | 0.0214107i | ||||
\(841\) | 9.39919 | − | 28.9277i | 0.324110 | − | 0.997508i | ||||
\(842\) | −4.53444 | + | 13.9556i | −0.156267 | + | 0.480941i | ||||
\(843\) | −4.26393 | + | 3.09793i | −0.146858 | + | 0.106698i | ||||
\(844\) | 58.2492 | + | 42.3205i | 2.00502 | + | 1.45673i | ||||
\(845\) | 6.41641 | + | 19.7477i | 0.220731 | + | 0.679341i | ||||
\(846\) | −57.0820 | −1.96252 | ||||||||
\(847\) | −6.68034 | + | 1.26133i | −0.229539 | + | 0.0433397i | ||||
\(848\) | 4.32624 | 0.148564 | ||||||||
\(849\) | −2.25329 | − | 6.93491i | −0.0773327 | − | 0.238006i | ||||
\(850\) | −1.80902 | − | 1.31433i | −0.0620488 | − | 0.0450811i | ||||
\(851\) | −5.70820 | + | 4.14725i | −0.195675 | + | 0.142166i | ||||
\(852\) | −3.70820 | + | 11.4127i | −0.127041 | + | 0.390992i | ||||
\(853\) | 3.56231 | − | 10.9637i | 0.121971 | − | 0.375388i | −0.871366 | − | 0.490633i | \(-0.836765\pi\) |
0.993337 | + | 0.115245i | \(0.0367654\pi\) | |||||||
\(854\) | −0.854102 | + | 0.620541i | −0.0292268 | + | 0.0212345i | ||||
\(855\) | 3.52786 | + | 2.56314i | 0.120650 | + | 0.0876576i | ||||
\(856\) | 2.33688 | + | 7.19218i | 0.0798729 | + | 0.245824i | ||||
\(857\) | 52.1803 | 1.78245 | 0.891223 | − | 0.453565i | \(-0.149848\pi\) | ||||
0.891223 | + | 0.453565i | \(0.149848\pi\) | |||||||
\(858\) | 4.47214 | + | 1.00406i | 0.152676 | + | 0.0342779i | ||||
\(859\) | 53.8885 | 1.83865 | 0.919327 | − | 0.393495i | \(-0.128734\pi\) | ||||
0.919327 | + | 0.393495i | \(0.128734\pi\) | |||||||
\(860\) | −5.12461 | − | 15.7719i | −0.174748 | − | 0.537818i | ||||
\(861\) | −1.32624 | − | 0.963568i | −0.0451981 | − | 0.0328383i | ||||
\(862\) | 0.364745 | − | 0.265003i | 0.0124233 | − | 0.00902603i | ||||
\(863\) | −5.72949 | + | 17.6336i | −0.195034 | + | 0.600253i | 0.804942 | + | 0.593353i | \(0.202196\pi\) |
−0.999976 | + | 0.00689989i | \(0.997804\pi\) | |||||||
\(864\) | −4.63525 | + | 14.2658i | −0.157695 | + | 0.485334i | ||||
\(865\) | 15.2361 | − | 11.0697i | 0.518042 | − | 0.376379i | ||||
\(866\) | −67.3222 | − | 48.9124i | −2.28770 | − | 1.66211i | ||||
\(867\) | −0.118034 | − | 0.363271i | −0.00400864 | − | 0.0123373i | ||||
\(868\) | −12.0000 | −0.407307 | ||||||||
\(869\) | −2.95492 | − | 31.5766i | −0.100239 | − | 1.07116i | ||||
\(870\) | −13.1672 | −0.446409 | ||||||||
\(871\) | 6.00000 | + | 18.4661i | 0.203302 | + | 0.625700i | ||||
\(872\) | −15.3262 | − | 11.1352i | −0.519012 | − | 0.377084i | ||||
\(873\) | 13.8541 | − | 10.0656i | 0.468890 | − | 0.340669i | ||||
\(874\) | −1.50658 | + | 4.63677i | −0.0509608 | + | 0.156841i | ||||
\(875\) | 2.29180 | − | 7.05342i | 0.0774768 | − | 0.238449i | ||||
\(876\) | 4.41641 | − | 3.20871i | 0.149217 | − | 0.108412i | ||||
\(877\) | −1.00000 | − | 0.726543i | −0.0337676 | − | 0.0245336i | 0.570773 | − | 0.821108i | \(-0.306643\pi\) |
−0.604541 | + | 0.796574i | \(0.706643\pi\) | |||||||
\(878\) | −3.55573 | − | 10.9434i | −0.120000 | − | 0.369322i | ||||
\(879\) | 3.74265 | 0.126236 | ||||||||
\(880\) | −4.38197 | − | 4.97980i | −0.147716 | − | 0.167869i | ||||
\(881\) | −31.5967 | −1.06452 | −0.532261 | − | 0.846580i | \(-0.678657\pi\) | ||||
−0.532261 | + | 0.846580i | \(0.678657\pi\) | |||||||
\(882\) | 13.0517 | + | 40.1689i | 0.439472 | + | 1.35256i | ||||
\(883\) | −12.3262 | − | 8.95554i | −0.414811 | − | 0.301378i | 0.360736 | − | 0.932668i | \(-0.382526\pi\) |
−0.775547 | + | 0.631290i | \(0.782526\pi\) | |||||||
\(884\) | −3.92705 | + | 2.85317i | −0.132081 | + | 0.0959625i | ||||
\(885\) | 0.0688837 | − | 0.212002i | 0.00231550 | − | 0.00712638i | ||||
\(886\) | −18.2148 | + | 56.0593i | −0.611938 | + | 1.88335i | ||||
\(887\) | −34.1803 | + | 24.8335i | −1.14766 | + | 0.833826i | −0.988168 | − | 0.153372i | \(-0.950987\pi\) |
−0.159495 | + | 0.987199i | \(0.550987\pi\) | |||||||
\(888\) | 1.70820 | + | 1.24108i | 0.0573236 | + | 0.0416480i | ||||
\(889\) | 2.00000 | + | 6.15537i | 0.0670778 | + | 0.206444i | ||||
\(890\) | 43.8197 | 1.46884 | ||||||||
\(891\) | −23.4721 | + | 10.1311i | −0.786346 | + | 0.339405i | ||||
\(892\) | −39.7082 | −1.32953 | ||||||||
\(893\) | −2.11146 | − | 6.49839i | −0.0706572 | − | 0.217460i | ||||
\(894\) | −9.77458 | − | 7.10164i | −0.326911 | − | 0.237515i | ||||
\(895\) | 18.1803 | − | 13.2088i | 0.607702 | − | 0.441521i | ||||
\(896\) | −2.98936 | + | 9.20029i | −0.0998674 | + | 0.307360i | ||||
\(897\) | 0.545085 | − | 1.67760i | 0.0181999 | − | 0.0560134i | ||||
\(898\) | −47.1591 | + | 34.2631i | −1.57372 | + | 1.14337i | ||||
\(899\) | −40.3607 | − | 29.3238i | −1.34610 | − | 0.978002i | ||||
\(900\) | 2.64590 | + | 8.14324i | 0.0881966 | + | 0.271441i | ||||
\(901\) | 4.32624 | 0.144128 | ||||||||
\(902\) | −26.2574 | + | 44.3036i | −0.874274 | + | 1.47515i | ||||
\(903\) | −0.652476 | −0.0217130 | ||||||||
\(904\) | −2.76393 | − | 8.50651i | −0.0919270 | − | 0.282922i | ||||
\(905\) | −8.47214 | − | 6.15537i | −0.281623 | − | 0.204611i | ||||
\(906\) | −2.23607 | + | 1.62460i | −0.0742884 | + | 0.0539737i | ||||
\(907\) | −11.8197 | + | 36.3772i | −0.392465 | + | 1.20788i | 0.538453 | + | 0.842656i | \(0.319009\pi\) |
−0.930918 | + | 0.365228i | \(0.880991\pi\) | |||||||
\(908\) | 12.5729 | − | 38.6956i | 0.417248 | − | 1.28416i | ||||
\(909\) | −31.9894 | + | 23.2416i | −1.06102 | + | 0.770876i | ||||
\(910\) | −3.61803 | − | 2.62866i | −0.119937 | − | 0.0871391i | ||||
\(911\) | 4.82624 | + | 14.8536i | 0.159900 | + | 0.492123i | 0.998624 | − | 0.0524339i | \(-0.0166979\pi\) |
−0.838724 | + | 0.544557i | \(0.816698\pi\) | |||||||
\(912\) | −0.291796 | −0.00966233 | ||||||||
\(913\) | 13.0344 | − | 21.9928i | 0.431377 | − | 0.727856i | ||||
\(914\) | −13.0902 | −0.432984 | ||||||||
\(915\) | 0.180340 | + | 0.555029i | 0.00596185 | + | 0.0183487i | ||||
\(916\) | 13.5000 | + | 9.80832i | 0.446053 | + | 0.324076i | ||||
\(917\) | −9.80902 | + | 7.12667i | −0.323922 | + | 0.235343i | ||||
\(918\) | −1.54508 | + | 4.75528i | −0.0509954 | + | 0.156948i | ||||
\(919\) | 14.4377 | − | 44.4347i | 0.476256 | − | 1.46576i | −0.368001 | − | 0.929825i | \(-0.619958\pi\) |
0.844257 | − | 0.535939i | \(-0.180042\pi\) | |||||||
\(920\) | 10.3262 | − | 7.50245i | 0.340446 | − | 0.247348i | ||||
\(921\) | −7.94427 | − | 5.77185i | −0.261773 | − | 0.190189i | ||||
\(922\) | −4.69756 | − | 14.4576i | −0.154706 | − | 0.476136i | ||||
\(923\) | −16.9443 | −0.557728 | ||||||||
\(924\) | 2.15654 | − | 0.930812i | 0.0709450 | − | 0.0306215i | ||||
\(925\) | −2.47214 | −0.0812833 | ||||||||
\(926\) | −21.5066 | − | 66.1904i | −0.706750 | − | 2.17515i | ||||
\(927\) | 32.7426 | + | 23.7889i | 1.07541 | + | 0.781331i | ||||
\(928\) | −41.8328 | + | 30.3933i | −1.37323 | + | 0.997710i | ||||
\(929\) | −12.8197 | + | 39.4549i | −0.420599 | + | 1.29447i | 0.486546 | + | 0.873655i | \(0.338257\pi\) |
−0.907146 | + | 0.420817i | \(0.861743\pi\) | |||||||
\(930\) | −3.41641 | + | 10.5146i | −0.112028 | + | 0.344788i | ||||
\(931\) | −4.09017 | + | 2.97168i | −0.134050 | + | 0.0973930i | ||||
\(932\) | −60.2705 | − | 43.7891i | −1.97423 | − | 1.43436i | ||||
\(933\) | −3.05166 | − | 9.39205i | −0.0999070 | − | 0.307482i | ||||
\(934\) | 76.8328 | 2.51405 | ||||||||
\(935\) | −4.38197 | − | 4.97980i | −0.143306 | − | 0.162857i | ||||
\(936\) | 10.3262 | 0.337524 | ||||||||
\(937\) | 17.4443 | + | 53.6879i | 0.569880 | + | 1.75391i | 0.652988 | + | 0.757368i | \(0.273515\pi\) |
−0.0831084 | + | 0.996541i | \(0.526485\pi\) | |||||||
\(938\) | 13.4164 | + | 9.74759i | 0.438061 | + | 0.318270i | ||||
\(939\) | −3.76393 | + | 2.73466i | −0.122831 | + | 0.0892421i | ||||
\(940\) | −16.5836 | + | 51.0390i | −0.540897 | + | 1.66471i | ||||
\(941\) | 11.3820 | − | 35.0301i | 0.371041 | − | 1.14195i | −0.575069 | − | 0.818105i | \(-0.695025\pi\) |
0.946111 | − | 0.323843i | \(-0.104975\pi\) | |||||||
\(942\) | 0.0623059 | − | 0.0452679i | 0.00203004 | − | 0.00147491i | ||||
\(943\) | 16.0344 | + | 11.6497i | 0.522153 | + | 0.379367i | ||||
\(944\) | −0.0901699 | − | 0.277515i | −0.00293478 | − | 0.00903233i | ||||
\(945\) | −2.76393 | −0.0899107 | ||||||||
\(946\) | 1.90983 | + | 20.4087i | 0.0620939 | + | 0.663544i | ||||
\(947\) | −15.7984 | −0.513378 | −0.256689 | − | 0.966494i | \(-0.582632\pi\) | ||||
−0.256689 | + | 0.966494i | \(0.582632\pi\) | |||||||
\(948\) | 3.38603 | + | 10.4211i | 0.109973 | + | 0.338463i | ||||
\(949\) | 6.23607 | + | 4.53077i | 0.202431 | + | 0.147075i | ||||
\(950\) | −1.38197 | + | 1.00406i | −0.0448369 | + | 0.0325759i | ||||
\(951\) | 3.90983 | − | 12.0332i | 0.126785 | − | 0.390204i | ||||
\(952\) | −0.427051 | + | 1.31433i | −0.0138408 | + | 0.0425976i | ||||
\(953\) | 28.3885 | − | 20.6255i | 0.919595 | − | 0.668125i | −0.0238281 | − | 0.999716i | \(-0.507585\pi\) |
0.943423 | + | 0.331591i | \(0.107585\pi\) | |||||||
\(954\) | −22.3369 | − | 16.2287i | −0.723183 | − | 0.525423i | ||||
\(955\) | 11.1246 | + | 34.2380i | 0.359984 | + | 1.10792i | ||||
\(956\) | −66.5410 | −2.15209 | ||||||||
\(957\) | 9.52786 | + | 2.13914i | 0.307992 | + | 0.0691485i | ||||
\(958\) | −24.7984 | −0.801199 | ||||||||
\(959\) | −4.09017 | − | 12.5882i | −0.132078 | − | 0.406496i | ||||
\(960\) | 8.03444 | + | 5.83736i | 0.259310 | + | 0.188400i | ||||
\(961\) | −8.80902 | + | 6.40013i | −0.284162 | + | 0.206456i | ||||
\(962\) | −2.76393 | + | 8.50651i | −0.0891127 | + | 0.274261i | ||||
\(963\) | −2.98278 | + | 9.18005i | −0.0961187 | + | 0.295823i | ||||
\(964\) | −23.5623 | + | 17.1190i | −0.758891 | + | 0.551366i | ||||
\(965\) | −15.2361 | − | 11.0697i | −0.490466 | − | 0.356345i | ||||
\(966\) | −0.465558 | − | 1.43284i | −0.0149791 | − | 0.0461009i | ||||
\(967\) | −11.0557 | −0.355528 | −0.177764 | − | 0.984073i | \(-0.556886\pi\) | ||||
−0.177764 | + | 0.984073i | \(0.556886\pi\) | |||||||
\(968\) | −11.8090 | − | 21.5765i | −0.379556 | − | 0.693496i | ||||
\(969\) | −0.291796 | −0.00937384 | ||||||||
\(970\) | −8.29180 | − | 25.5195i | −0.266234 | − | 0.819383i | ||||
\(971\) | 14.5623 | + | 10.5801i | 0.467327 | + | 0.339533i | 0.796399 | − | 0.604772i | \(-0.206736\pi\) |
−0.329072 | + | 0.944305i | \(0.606736\pi\) | |||||||
\(972\) | 23.4271 | − | 17.0207i | 0.751423 | − | 0.545941i | ||||
\(973\) | 0.763932 | − | 2.35114i | 0.0244905 | − | 0.0753741i | ||||
\(974\) | −5.30244 | + | 16.3192i | −0.169901 | + | 0.522902i | ||||
\(975\) | 0.500000 | − | 0.363271i | 0.0160128 | − | 0.0116340i | ||||
\(976\) | 0.618034 | + | 0.449028i | 0.0197828 | + | 0.0143730i | ||||
\(977\) | 8.50000 | + | 26.1603i | 0.271939 | + | 0.836942i | 0.990013 | + | 0.140976i | \(0.0450239\pi\) |
−0.718074 | + | 0.695967i | \(0.754976\pi\) | |||||||
\(978\) | −6.05573 | −0.193641 | ||||||||
\(979\) | −31.7082 | − | 7.11894i | −1.01340 | − | 0.227522i | ||||
\(980\) | 39.7082 | 1.26843 | ||||||||
\(981\) | −7.47214 | − | 22.9969i | −0.238567 | − | 0.734234i | ||||
\(982\) | 31.7082 | + | 23.0374i | 1.01185 | + | 0.735152i | ||||
\(983\) | 26.1976 | − | 19.0336i | 0.835572 | − | 0.607079i | −0.0855579 | − | 0.996333i | \(-0.527267\pi\) |
0.921130 | + | 0.389254i | \(0.127267\pi\) | |||||||
\(984\) | 1.83282 | − | 5.64083i | 0.0584280 | − | 0.179823i | ||||
\(985\) | −14.6525 | + | 45.0957i | −0.466867 | + | 1.43687i | ||||
\(986\) | −13.9443 | + | 10.1311i | −0.444076 | + | 0.322640i | ||||
\(987\) | 1.70820 | + | 1.24108i | 0.0543727 | + | 0.0395041i | ||||
\(988\) | 1.14590 | + | 3.52671i | 0.0364559 | + | 0.112200i | ||||
\(989\) | 7.88854 | 0.250841 | ||||||||
\(990\) | 3.94427 | + | 42.1490i | 0.125357 | + | 1.33958i | ||||
\(991\) | 14.4508 | 0.459046 | 0.229523 | − | 0.973303i | \(-0.426283\pi\) | ||||
0.229523 | + | 0.973303i | \(0.426283\pi\) | |||||||
\(992\) | 13.4164 | + | 41.2915i | 0.425971 | + | 1.31101i | ||||
\(993\) | 0.236068 | + | 0.171513i | 0.00749139 | + | 0.00544281i | ||||
\(994\) | −11.7082 | + | 8.50651i | −0.371362 | + | 0.269810i | ||||
\(995\) | 13.5066 | − | 41.5690i | 0.428187 | − | 1.31783i | ||||
\(996\) | −2.72949 | + | 8.40051i | −0.0864872 | + | 0.266180i | ||||
\(997\) | 23.1803 | − | 16.8415i | 0.734129 | − | 0.533376i | −0.156738 | − | 0.987640i | \(-0.550098\pi\) |
0.890867 | + | 0.454264i | \(0.150098\pi\) | |||||||
\(998\) | −6.54508 | − | 4.75528i | −0.207181 | − | 0.150526i | ||||
\(999\) | 1.70820 | + | 5.25731i | 0.0540452 | + | 0.166334i |
(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 | 187.2.g.c.137.1 | yes | 4 | |
11.3 | even | 5 | 2057.2.a.k.1.2 | 2 | |||
11.8 | odd | 10 | 2057.2.a.j.1.1 | 2 | |||
11.9 | even | 5 | inner | 187.2.g.c.86.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.g.c.86.1 | ✓ | 4 | 11.9 | even | 5 | inner | |
187.2.g.c.137.1 | yes | 4 | 1.1 | even | 1 | trivial | |
2057.2.a.j.1.1 | 2 | 11.8 | odd | 10 | |||
2057.2.a.k.1.2 | 2 | 11.3 | even | 5 |