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: \( 5.50405667968 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.581788720\) \(a_{3}=+0.000000000\) \(a_{4}=-0.661521885\) \(a_{5}=-1.574896813\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.459187495\) \(a_{8}=-0.966654691\) \(a_{9}=+0.000000000\) \(a_{10}=-0.916257202\)
\(a_{11}=-0.272057828\) \(a_{12}=+0.000000000\) \(a_{13}=+0.897137845\) \(a_{14}=+0.267150105\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.099133089\) \(a_{17}=-0.771916064\) \(a_{18}=+0.000000000\) \(a_{19}=-0.936333821\) \(a_{20}=+1.041828708\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.158280176\) \(a_{23}=-0.906341238\) \(a_{24}=+0.000000000\) \(a_{25}=+1.480299972\)
\(a_{26}=+0.521944679\) \(a_{27}=+0.000000000\) \(a_{28}=-0.303762577\) \(a_{29}=-0.573503646\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.678793022\) \(a_{32}=+1.024329205\) \(a_{33}=+0.000000000\) \(a_{34}=-0.449092057\) \(a_{35}=-0.723172934\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.294944340\) \(a_{38}=-0.544748456\) \(a_{39}=+0.000000000\) \(a_{40}=+1.522381393\)
\(a_{41}=+0.980272283\) \(a_{42}=+0.000000000\) \(a_{43}=+0.386995796\) \(a_{44}=+0.179972207\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.527299109\) \(a_{47}=-1.083276034\) \(a_{48}=+0.000000000\) \(a_{49}=-0.789146844\) \(a_{50}=+0.861221827\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.593476318\) \(a_{53}=-0.469400245\) \(a_{54}=+0.000000000\) \(a_{55}=+0.428463007\)
\(a_{56}=-0.443875746\) \(a_{57}=+0.000000000\) \(a_{58}=-0.333657952\) \(a_{59}=+1.519512057\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.709369805\) \(a_{62}=-0.394914124\) \(a_{63}=+0.000000000\) \(a_{64}=+0.496810088\) \(a_{65}=-1.412899534\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.892552456\) \(a_{68}=+0.510639369\) \(a_{69}=+0.000000000\) \(a_{70}=-0.420733848\)
\(a_{71}=+0.798755260\) \(a_{72}=+0.000000000\) \(a_{73}=-1.159812089\) \(a_{74}=-0.171595290\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.619405320\) \(a_{77}=-0.124925563\) \(a_{78}=+0.000000000\) \(a_{79}=-0.618539838\) \(a_{80}=-0.156124385\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.570311357\) \(a_{83}=+0.014047470\) \(a_{84}=+0.000000000\) \(a_{85}=+1.215688149\)
\(a_{86}=+0.225149789\) \(a_{87}=+0.000000000\) \(a_{88}=+0.262985976\) \(a_{89}=-1.086063010\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.411954480\) \(a_{92}=+0.599564564\) \(a_{93}=+0.000000000\) \(a_{94}=-0.630237778\) \(a_{95}=+1.474629151\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.078951698\) \(a_{98}=-0.459116733\) \(a_{99}=+0.000000000\) \(a_{100}=-0.979250827\)

Showing 100 of 1500 available coefficients

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