Properties

Level $18$
Weight $0$
Character 18.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 18 = 2 \cdot 3^{2} \)
Weight: \( 0 \)
Character: 18.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 11.9808819589 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=+1.168497611\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.808457330\) \(a_{8}=+0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=+0.826252584\)
\(a_{11}=+1.217112780\) \(a_{12}=+0.000000000\) \(a_{13}=+1.019124124\) \(a_{14}=+1.278772442\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.279760375\) \(a_{18}=+0.000000000\) \(a_{19}=-0.601347988\) \(a_{20}=+0.584248805\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.860628700\) \(a_{23}=+0.423597218\) \(a_{24}=+0.000000000\) \(a_{25}=+0.365386667\)
\(a_{26}=+0.720629579\) \(a_{27}=+0.000000000\) \(a_{28}=+0.904228665\) \(a_{29}=+0.294216517\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.559666872\) \(a_{32}=+0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-0.904927239\) \(a_{35}=+2.113178070\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.084014829\) \(a_{38}=-0.425217240\) \(a_{39}=+0.000000000\) \(a_{40}=+0.413126292\)
\(a_{41}=-1.069798354\) \(a_{42}=+0.000000000\) \(a_{43}=-0.834771186\) \(a_{44}=+0.608556390\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.299528465\) \(a_{47}=-0.024467929\) \(a_{48}=+0.000000000\) \(a_{49}=+2.270517915\) \(a_{50}=+0.258367390\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.509562062\) \(a_{53}=+0.627528028\) \(a_{54}=+0.000000000\) \(a_{55}=+1.422193376\)
\(a_{56}=+0.639386221\) \(a_{57}=+0.000000000\) \(a_{58}=+0.208042494\) \(a_{59}=-1.126547185\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.739780872\) \(a_{62}=-1.102851021\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=+1.190844104\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.031563370\) \(a_{68}=-0.639880187\) \(a_{69}=+0.000000000\) \(a_{70}=+1.494242543\)
\(a_{71}=-0.118230487\) \(a_{72}=+0.000000000\) \(a_{73}=+0.671013282\) \(a_{74}=-0.059407455\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.300673994\) \(a_{77}=+2.201096529\) \(a_{78}=+0.000000000\) \(a_{79}=+1.645296834\) \(a_{80}=+0.292124403\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.756461670\) \(a_{83}=-1.512357445\) \(a_{84}=+0.000000000\) \(a_{85}=-1.495396940\)
\(a_{86}=-0.590272366\) \(a_{87}=+0.000000000\) \(a_{88}=+0.430314350\) \(a_{89}=-0.409067905\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.843042493\) \(a_{92}=+0.211798609\) \(a_{93}=+0.000000000\) \(a_{94}=-0.017301438\) \(a_{95}=-0.702673688\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.134579881\) \(a_{98}=+1.605498615\) \(a_{99}=+0.000000000\) \(a_{100}=+0.182693333\)

Showing 100 of 280 available coefficients

Rows: Cols: