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: \( 15.2196073531 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.315014022\) \(a_{3}=+0.000000000\) \(a_{4}=-0.900766166\) \(a_{5}=+0.039445635\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.238337867\) \(a_{8}=-0.598767994\) \(a_{9}=+0.000000000\) \(a_{10}=+0.012425928\)
\(a_{11}=+1.345355905\) \(a_{12}=+0.000000000\) \(a_{13}=-0.237364478\) \(a_{14}=+0.075079770\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.712145852\) \(a_{17}=+0.902660453\) \(a_{18}=+0.000000000\) \(a_{19}=-0.882801366\) \(a_{20}=-0.035531293\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.423805974\) \(a_{23}=-1.023607790\) \(a_{24}=+0.000000000\) \(a_{25}=-0.998444042\)
\(a_{26}=-0.074773139\) \(a_{27}=+0.000000000\) \(a_{28}=-0.214686687\) \(a_{29}=+1.233991771\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.242424695\) \(a_{32}=+0.823103923\) \(a_{33}=+0.000000000\) \(a_{34}=+0.284350700\) \(a_{35}=+0.009401388\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.010327903\) \(a_{38}=-0.278094809\) \(a_{39}=+0.000000000\) \(a_{40}=-0.023618784\)
\(a_{41}=-1.519179659\) \(a_{42}=+0.000000000\) \(a_{43}=+1.268878802\) \(a_{44}=-1.211851081\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.322450812\) \(a_{47}=-1.679686550\) \(a_{48}=+0.000000000\) \(a_{49}=-0.943195086\) \(a_{50}=-0.314523849\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.213809852\) \(a_{53}=-1.723376793\) \(a_{54}=+0.000000000\) \(a_{55}=+0.053068171\)
\(a_{56}=-0.142708907\) \(a_{57}=+0.000000000\) \(a_{58}=+0.388724233\) \(a_{59}=-0.955869161\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.744570100\) \(a_{62}=+0.076370022\) \(a_{63}=+0.000000000\) \(a_{64}=-0.452845084\) \(a_{65}=-0.009319776\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.311613531\) \(a_{68}=-0.812881693\) \(a_{69}=+0.000000000\) \(a_{70}=+0.003781206\)
\(a_{71}=+0.256595814\) \(a_{72}=+0.000000000\) \(a_{73}=+0.774220410\) \(a_{74}=-0.310006948\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.801624204\) \(a_{77}=+0.331332062\) \(a_{78}=+0.000000000\)

Showing all 78 available coefficients

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