Properties

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

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Maass form invariants

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

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.620994291\) \(a_{3}=+0.000000000\) \(a_{4}=-0.614366090\) \(a_{5}=+0.851940248\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.924899035\) \(a_{8}=-1.002512126\) \(a_{9}=+0.000000000\) \(a_{10}=+0.529050031\)
\(a_{11}=-1.851355930\) \(a_{12}=+0.000000000\) \(a_{13}=-0.662572969\) \(a_{14}=-0.574357021\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.008188217\) \(a_{17}=-0.353608519\) \(a_{18}=+0.000000000\) \(a_{19}=+1.127116328\) \(a_{20}=-0.523403199\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.149681463\) \(a_{23}=+0.632730371\) \(a_{24}=+0.000000000\) \(a_{25}=-0.274197814\)
\(a_{26}=-0.411454031\) \(a_{27}=+0.000000000\) \(a_{28}=+0.568226604\) \(a_{29}=-0.462569573\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.707134599\) \(a_{32}=+0.997427290\) \(a_{33}=+0.000000000\) \(a_{34}=-0.219588869\) \(a_{35}=-0.787958715\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.849208336\) \(a_{38}=+0.699932818\) \(a_{39}=+0.000000000\) \(a_{40}=-0.854080429\)
\(a_{41}=-1.250665275\) \(a_{42}=+0.000000000\) \(a_{43}=+1.439143360\) \(a_{44}=+1.137410304\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.392921949\) \(a_{47}=+0.013144534\) \(a_{48}=+0.000000000\) \(a_{49}=-0.144561775\) \(a_{50}=-0.170275277\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.407062364\) \(a_{53}=-0.911730379\) \(a_{54}=+0.000000000\) \(a_{55}=-1.577244630\)
\(a_{56}=+0.927222498\) \(a_{57}=+0.000000000\) \(a_{58}=-0.287253064\) \(a_{59}=-0.189322221\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.324157681\) \(a_{62}=+0.439126549\) \(a_{63}=+0.000000000\) \(a_{64}=+0.627584870\) \(a_{65}=-0.564472579\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.266504234\) \(a_{68}=+0.217245082\) \(a_{69}=+0.000000000\) \(a_{70}=-0.489317862\)
\(a_{71}=-0.384046390\) \(a_{72}=+0.000000000\) \(a_{73}=-0.236908938\) \(a_{74}=-0.527353521\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.692462048\) \(a_{77}=+1.712317309\) \(a_{78}=+0.000000000\) \(a_{79}=-0.174388604\) \(a_{80}=-0.006975851\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.776656031\) \(a_{83}=-1.763874938\) \(a_{84}=+0.000000000\) \(a_{85}=-0.301253329\)
\(a_{86}=+0.893699811\) \(a_{87}=+0.000000000\) \(a_{88}=+1.856006769\) \(a_{89}=-0.122186587\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.612813099\) \(a_{92}=-0.388728084\) \(a_{93}=+0.000000000\) \(a_{94}=+0.008162681\) \(a_{95}=+0.960235764\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.438744033\) \(a_{98}=-0.089772037\) \(a_{99}=+0.000000000\) \(a_{100}=+0.168457839\)

Showing 100 of 1500 available coefficients

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