Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 13.5079113404 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.096065050\) \(a_{3}=-0.577350269\) \(a_{4}=+0.201358594\) \(a_{5}=+0.496545018\)
\(a_{6}=+0.632813452\) \(a_{7}=+0.969293001\) \(a_{8}=+0.875362933\) \(a_{9}=+0.333333333\) \(a_{10}=-0.544245640\)
\(a_{11}=-1.368972119\) \(a_{12}=-0.116254438\) \(a_{13}=-0.490588552\) \(a_{14}=-1.062408182\) \(a_{15}=-0.286680400\)
\(a_{16}=-1.160813310\) \(a_{17}=+1.777482034\) \(a_{18}=-0.365355017\) \(a_{19}=-1.247253371\) \(a_{20}=+0.099983607\)
\(a_{21}=-0.559621575\) \(a_{22}=+1.500482494\) \(a_{23}=+0.055880889\) \(a_{24}=-0.505391025\) \(a_{25}=-0.753443045\)
\(a_{26}=+0.537716966\) \(a_{27}=-0.192450090\) \(a_{28}=+0.195175476\) \(a_{29}=-0.200685359\) \(a_{30}=+0.314220367\)
\(a_{31}=-0.141547324\) \(a_{32}=+0.396963966\) \(a_{33}=+0.790376422\) \(a_{34}=-1.948235934\) \(a_{35}=+0.481297611\)
\(a_{36}=+0.067119531\) \(a_{37}=-0.922175472\) \(a_{38}=+1.367070828\) \(a_{39}=+0.283241432\) \(a_{40}=+0.434657103\)
\(a_{41}=-0.528912047\) \(a_{42}=+0.613381650\) \(a_{43}=-1.658804876\) \(a_{44}=-0.275654301\) \(a_{45}=+0.165515006\)
\(a_{46}=-0.061249089\) \(a_{47}=+0.748481529\) \(a_{48}=+0.670195877\) \(a_{49}=-0.060471078\) \(a_{50}=+0.825822589\)
\(a_{51}=-1.026229731\) \(a_{52}=-0.098784221\) \(a_{53}=-0.932734053\) \(a_{54}=+0.210937817\) \(a_{55}=-0.679756286\)
\(a_{56}=+0.848483164\) \(a_{57}=+0.720102069\) \(a_{58}=+0.219964208\) \(a_{59}=-0.735093180\) \(a_{60}=-0.057725562\)
\(a_{61}=+0.052839259\) \(a_{62}=+0.155145075\) \(a_{63}=+0.323097667\) \(a_{64}=+0.725714981\) \(a_{65}=-0.243599301\)
\(a_{66}=-0.866303972\) \(a_{67}=-0.855656612\) \(a_{68}=+0.357911283\) \(a_{69}=-0.032262846\) \(a_{70}=-0.527533490\)
\(a_{71}=+0.324427884\) \(a_{72}=+0.291787644\) \(a_{73}=+0.740288250\) \(a_{74}=+1.010764305\) \(a_{75}=+0.435000545\)
\(a_{76}=-0.251145185\) \(a_{77}=-1.326935094\) \(a_{78}=-0.310451035\) \(a_{79}=-0.197413924\) \(a_{80}=-0.576396066\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.579722010\) \(a_{83}=-0.972608992\) \(a_{84}=-0.112684613\) \(a_{85}=+0.882599849\)
\(a_{86}=+1.818158049\) \(a_{87}=+0.115865746\) \(a_{88}=-1.198347449\) \(a_{89}=+0.556556918\) \(a_{90}=-0.181415213\)
\(a_{91}=-0.475524050\) \(a_{92}=+0.011252097\) \(a_{93}=+0.081722386\) \(a_{94}=-0.820384445\) \(a_{95}=-0.619317448\)
\(a_{96}=-0.229187253\) \(a_{97}=+1.673555240\) \(a_{98}=+0.066280235\) \(a_{99}=-0.456324040\) \(a_{100}=-0.151712232\)

Showing 100 of 1228 available coefficients

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