Properties

Level $9$
Weight $0$
Character 9.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.43179917172 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.620994291\) \(a_{3}=+0.000000000\) \(a_{4}=-0.614366090\) \(a_{5}=-0.851940248\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.924899035\) \(a_{8}=+1.002512126\) \(a_{9}=+0.000000000\) \(a_{10}=+0.529050031\)
\(a_{11}=+1.851355930\) \(a_{12}=+0.000000000\) \(a_{13}=-0.662572969\) \(a_{14}=+0.574357021\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.008188217\) \(a_{17}=+0.353608519\) \(a_{18}=+0.000000000\) \(a_{19}=+1.127116328\) \(a_{20}=+0.523403199\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.149681463\) \(a_{23}=-0.632730371\) \(a_{24}=+0.000000000\) \(a_{25}=-0.274197814\)
\(a_{26}=+0.411454031\) \(a_{27}=+0.000000000\) \(a_{28}=+0.568226604\) \(a_{29}=+0.462569573\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.707134599\) \(a_{32}=-0.997427290\) \(a_{33}=+0.000000000\) \(a_{34}=-0.219588872\) \(a_{35}=+0.787958714\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.849208323\) \(a_{38}=-0.699932816\) \(a_{39}=+0.000000000\) \(a_{40}=-0.854080429\)
\(a_{41}=+1.250665275\) \(a_{42}=+0.000000000\) \(a_{43}=+1.439143360\) \(a_{44}=-1.137410304\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.392921949\) \(a_{47}=-0.013144534\) \(a_{48}=+0.000000000\) \(a_{49}=-0.144561775\) \(a_{50}=+0.170275277\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.407062364\) \(a_{53}=+0.911730379\) \(a_{54}=+0.000000000\) \(a_{55}=-1.577244630\)
\(a_{56}=-0.927222498\) \(a_{57}=+0.000000000\) \(a_{58}=-0.287253064\) \(a_{59}=+0.189322221\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.324157681\) \(a_{62}=-0.439126549\) \(a_{63}=+0.000000000\) \(a_{64}=+0.627584870\) \(a_{65}=+0.564472579\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.266504234\) \(a_{68}=-0.217245082\) \(a_{69}=+0.000000000\) \(a_{70}=-0.489317863\)
\(a_{71}=+0.384046391\) \(a_{72}=+0.000000000\) \(a_{73}=-0.236908934\) \(a_{74}=+0.527353522\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.692462052\) \(a_{77}=-1.712317308\) \(a_{78}=+0.000000000\) \(a_{79}=-0.174388605\) \(a_{80}=+0.006975850\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.776655999\) \(a_{83}=+1.763874938\) \(a_{84}=+0.000000000\) \(a_{85}=-0.301253329\)
\(a_{86}=-0.893699811\) \(a_{87}=+0.000000000\) \(a_{88}=+1.856006769\) \(a_{89}=+0.122186587\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.612813099\) \(a_{92}=+0.388728084\) \(a_{93}=+0.000000000\) \(a_{94}=+0.008162681\) \(a_{95}=-0.960235764\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.438744033\) \(a_{98}=+0.089772037\) \(a_{99}=+0.000000000\) \(a_{100}=+0.168457839\)

Showing 100 of 1500 available coefficients

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