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: \( 15.2196073531 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.315014022\) \(a_{3}=+0.000000000\) \(a_{4}=-0.900766166\) \(a_{5}=-0.039445635\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.238337867\) \(a_{8}=+0.598767994\) \(a_{9}=+0.000000000\) \(a_{10}=+0.012425928\)
\(a_{11}=-1.345355905\) \(a_{12}=+0.000000000\) \(a_{13}=-0.237364478\) \(a_{14}=-0.075079770\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.712145852\) \(a_{17}=-0.902660453\) \(a_{18}=+0.000000000\) \(a_{19}=-0.882801366\) \(a_{20}=+0.035531293\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.423805974\) \(a_{23}=+1.023607790\) \(a_{24}=+0.000000000\) \(a_{25}=-0.998444042\)
\(a_{26}=+0.074773139\) \(a_{27}=+0.000000000\) \(a_{28}=-0.214686687\) \(a_{29}=-1.233991771\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.242424695\) \(a_{32}=-0.823103923\) \(a_{33}=+0.000000000\) \(a_{34}=+0.284350699\) \(a_{35}=-0.009401387\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.010327906\) \(a_{38}=+0.278094815\) \(a_{39}=+0.000000000\) \(a_{40}=-0.023618800\)
\(a_{41}=+1.519179689\) \(a_{42}=+0.000000000\) \(a_{43}=+1.268878721\) \(a_{44}=+1.211851229\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.322451196\) \(a_{47}=+1.679687248\) \(a_{48}=+0.000000000\) \(a_{49}=-0.943196867\) \(a_{50}=+0.314526977\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.213801900\) \(a_{53}=+1.723389904\) \(a_{54}=+0.000000000\) \(a_{55}=+0.053034852\)
\(a_{56}=+0.142762484\) \(a_{57}=+0.000000000\) \(a_{58}=+0.388590523\) \(a_{59}=+0.956074006\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.744061071\) \(a_{62}=-0.075641663\) \(a_{63}=+0.000000000\) \(a_{64}=-0.454629686\) \(a_{65}=+0.011840667\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.317416391\) \(a_{68}=+0.820877483\) \(a_{69}=+0.000000000\) \(a_{70}=-0.013319118\)
\(a_{71}=-0.235870103\) \(a_{72}=+0.000000000\) \(a_{73}=+0.732131650\) \(a_{74}=+0.364204859\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.725254720\) \(a_{77}=-0.231015796\) \(a_{78}=+0.000000000\)

Showing all 78 available coefficients

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