Properties

Level $81$
Weight $0$
Character 81.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 81 = 3^{4} \)
Weight: \( 0 \)
Character: 81.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.228251533 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.922796081\) \(a_{3}=+0.000000000\) \(a_{4}=+2.697143551\) \(a_{5}=+0.257393832\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.293779764\) \(a_{8}=+3.263262613\) \(a_{9}=+0.000000000\) \(a_{10}=+0.494917387\)
\(a_{11}=-0.272045184\) \(a_{12}=+0.000000000\) \(a_{13}=+0.856430386\) \(a_{14}=+0.564874980\) \(a_{15}=+0.000000000\)
\(a_{16}=+3.577444894\) \(a_{17}=+0.499276789\) \(a_{18}=+0.000000000\) \(a_{19}=-0.900461931\) \(a_{20}=+0.694230403\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.523086539\) \(a_{23}=-1.367186635\) \(a_{24}=+0.000000000\) \(a_{25}=-0.933749439\)
\(a_{26}=+1.646740408\) \(a_{27}=+0.000000000\) \(a_{28}=+0.792362911\) \(a_{29}=+0.563376452\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.316770316\) \(a_{32}=+3.615434190\) \(a_{33}=+0.000000000\) \(a_{34}=+0.960005590\) \(a_{35}=+0.075616968\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.450685974\) \(a_{38}=-1.731406109\) \(a_{39}=+0.000000000\) \(a_{40}=+0.839948848\)
\(a_{41}=-1.323708392\) \(a_{42}=+0.000000000\) \(a_{43}=-0.777203861\) \(a_{44}=-0.733745806\) \(a_{45}=+0.000000000\)
\(a_{46}=-2.628820680\) \(a_{47}=+0.644939282\) \(a_{48}=+0.000000000\) \(a_{49}=-0.913690623\) \(a_{50}=-1.795407211\)
\(a_{51}=+0.000000000\) \(a_{52}=+2.309907637\) \(a_{53}=+1.354081176\) \(a_{54}=+0.000000000\) \(a_{55}=-0.070019665\)
\(a_{56}=+0.958676638\) \(a_{57}=+0.000000000\) \(a_{58}=+1.083268171\) \(a_{59}=+0.672462244\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.020168708\) \(a_{62}=-2.531882909\) \(a_{63}=+0.000000000\) \(a_{64}=+3.374302172\) \(a_{65}=+0.220441356\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.085691419\) \(a_{68}=+1.346625566\) \(a_{69}=+0.000000000\) \(a_{70}=+0.145366150\)
\(a_{71}=+1.636571868\) \(a_{72}=+0.000000000\) \(a_{73}=+0.666361398\) \(a_{74}=+0.866577065\) \(a_{75}=+0.000000000\)
\(a_{76}=-2.428657180\) \(a_{77}=-0.079920229\) \(a_{78}=+0.000000000\) \(a_{79}=-0.461576357\) \(a_{80}=+0.920814519\)
\(a_{81}=+0.000000000\) \(a_{82}=-2.545201039\) \(a_{83}=+0.701288800\) \(a_{84}=+0.000000000\) \(a_{85}=+0.128555309\)
\(a_{86}=-1.494394740\) \(a_{87}=+0.000000000\) \(a_{88}=-0.887837613\) \(a_{89}=+0.216903531\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.251627802\) \(a_{92}=-3.687496143\) \(a_{93}=+0.000000000\) \(a_{94}=+1.240154490\) \(a_{95}=-0.231764127\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.250813088\) \(a_{98}=-1.756838560\) \(a_{99}=+0.000000000\) \(a_{100}=-2.518405459\)

Showing 100 of 166 available coefficients

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