Properties

Level $31$
Weight $0$
Character 31.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.39253774613 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.746021858\) \(a_{3}=-1.055870039\) \(a_{4}=+2.048592328\) \(a_{5}=+0.188435644\)
\(a_{6}=-1.843572167\) \(a_{7}=+1.515927361\) \(a_{8}=+1.830865124\) \(a_{9}=+0.114861539\) \(a_{10}=+0.329012753\)
\(a_{11}=-1.814595085\) \(a_{12}=-2.163047261\) \(a_{13}=+0.185349803\) \(a_{14}=+2.646842308\) \(a_{15}=-0.198963551\)
\(a_{16}=+1.148138198\) \(a_{17}=+0.432413107\) \(a_{18}=+0.200550759\) \(a_{19}=+0.473999825\) \(a_{20}=+0.386027815\)
\(a_{21}=-1.600622282\) \(a_{22}=-3.168322682\) \(a_{23}=+1.073134078\) \(a_{24}=-1.933155630\) \(a_{25}=-0.964492008\)
\(a_{26}=+0.323624807\) \(a_{27}=+0.934591181\) \(a_{28}=+3.105517162\) \(a_{29}=-1.123151872\) \(a_{30}=-0.347394709\)
\(a_{31}=-0.179605302\) \(a_{32}=+0.173809265\) \(a_{33}=+1.915976584\) \(a_{34}=+0.755002736\) \(a_{35}=+0.285654749\)
\(a_{36}=+0.235304469\) \(a_{37}=+0.353550419\) \(a_{38}=+0.827614055\) \(a_{39}=-0.195705304\) \(a_{40}=+0.345000249\)
\(a_{41}=-0.362109462\) \(a_{42}=-2.794721491\) \(a_{43}=+1.008249377\) \(a_{44}=-3.717365570\) \(a_{45}=+0.021644008\)
\(a_{46}=+1.873715556\) \(a_{47}=+0.559999425\) \(a_{48}=-1.212284724\) \(a_{49}=+1.298035765\) \(a_{50}=-1.684024128\)
\(a_{51}=-0.456572044\) \(a_{52}=+0.379706184\) \(a_{53}=-1.473605842\) \(a_{54}=+1.631816630\) \(a_{55}=-0.341934394\)
\(a_{56}=+2.775458536\) \(a_{57}=-0.500482214\) \(a_{58}=-1.961047718\) \(a_{59}=+0.300987282\) \(a_{60}=-0.407595204\)
\(a_{61}=+0.038704273\) \(a_{62}=-0.313594783\) \(a_{63}=+0.174121750\) \(a_{64}=-0.844663423\) \(a_{65}=+0.034926509\)
\(a_{66}=+3.345336994\) \(a_{67}=-0.019553177\) \(a_{68}=+0.885838173\) \(a_{69}=-1.133090121\) \(a_{70}=+0.498759435\)
\(a_{71}=+0.813221762\) \(a_{72}=+0.210295987\) \(a_{73}=-0.088570784\) \(a_{74}=+0.617306759\) \(a_{75}=+1.018378214\)
\(a_{76}=+0.971032405\) \(a_{77}=-2.750794340\) \(a_{78}=-0.341705738\) \(a_{79}=+0.416850404\) \(a_{80}=+0.216350161\)
\(a_{81}=-1.101668366\) \(a_{82}=-0.632251035\) \(a_{83}=-0.619580152\) \(a_{84}=-3.279022527\) \(a_{85}=+0.081482042\)
\(a_{86}=+1.760425451\) \(a_{87}=+1.185902411\) \(a_{88}=-3.322278856\) \(a_{89}=+1.204543573\) \(a_{90}=+0.037790911\)
\(a_{91}=+0.280976838\) \(a_{92}=+2.198414238\) \(a_{93}=+0.189639857\) \(a_{94}=+0.977771236\) \(a_{95}=+0.089318462\)
\(a_{96}=-0.183519995\) \(a_{97}=+0.444406511\) \(a_{98}=+2.266398817\) \(a_{99}=-0.208427185\) \(a_{100}=-1.975850928\)

Showing 100 of 546 available coefficients

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