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: \( 5.50405667968 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.581788720\) \(a_{3}=+0.000000000\) \(a_{4}=-0.661521885\) \(a_{5}=+1.574896813\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.459187495\) \(a_{8}=+0.966654691\) \(a_{9}=+0.000000000\) \(a_{10}=-0.916257202\)
\(a_{11}=+0.272057828\) \(a_{12}=+0.000000000\) \(a_{13}=+0.897137845\) \(a_{14}=-0.267150105\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.099133089\) \(a_{17}=+0.771916064\) \(a_{18}=+0.000000000\) \(a_{19}=-0.936333821\) \(a_{20}=-1.041828708\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.158280176\) \(a_{23}=+0.906341238\) \(a_{24}=+0.000000000\) \(a_{25}=+1.480299972\)
\(a_{26}=-0.521944679\) \(a_{27}=+0.000000000\) \(a_{28}=-0.303762577\) \(a_{29}=+0.573503646\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.678793024\) \(a_{32}=-1.024329206\) \(a_{33}=+0.000000000\) \(a_{34}=-0.449092050\) \(a_{35}=+0.723172932\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.294944340\) \(a_{38}=+0.544748456\) \(a_{39}=+0.000000000\) \(a_{40}=+1.522381393\)
\(a_{41}=-0.980272283\) \(a_{42}=+0.000000000\) \(a_{43}=+0.386995796\) \(a_{44}=-0.179972207\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.527299109\) \(a_{47}=+1.083276034\) \(a_{48}=+0.000000000\) \(a_{49}=-0.789146844\) \(a_{50}=-0.861221827\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.593476318\) \(a_{53}=+0.469400245\) \(a_{54}=+0.000000000\) \(a_{55}=+0.428463007\)
\(a_{56}=+0.443875747\) \(a_{57}=+0.000000000\) \(a_{58}=-0.333657952\) \(a_{59}=-1.519512057\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.709369805\) \(a_{62}=+0.394914124\) \(a_{63}=+0.000000000\) \(a_{64}=+0.496810088\) \(a_{65}=+1.412899534\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.892552456\) \(a_{68}=-0.510639370\) \(a_{69}=+0.000000000\) \(a_{70}=-0.420733850\)
\(a_{71}=-0.798755260\) \(a_{72}=+0.000000000\) \(a_{73}=-1.159812085\) \(a_{74}=+0.171595292\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.619405318\) \(a_{77}=+0.124925539\) \(a_{78}=+0.000000000\) \(a_{79}=-0.618539838\) \(a_{80}=+0.156124385\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.570311357\) \(a_{83}=-0.014047470\) \(a_{84}=+0.000000000\) \(a_{85}=+1.215688149\)
\(a_{86}=-0.225149789\) \(a_{87}=+0.000000000\) \(a_{88}=+0.262985976\) \(a_{89}=+1.086063010\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.411954480\) \(a_{92}=-0.599564564\) \(a_{93}=+0.000000000\) \(a_{94}=-0.630237778\) \(a_{95}=-1.474629150\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.078951696\) \(a_{98}=+0.459116733\) \(a_{99}=+0.000000000\) \(a_{100}=-0.979250828\)

Showing 100 of 1500 available coefficients

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