Properties

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

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 16.2709585691 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.130624613\) \(a_{3}=-0.577350269\) \(a_{4}=-0.982937210\) \(a_{5}=-1.091210210\)
\(a_{6}=+0.075416156\) \(a_{7}=-1.257859083\) \(a_{8}=+0.259020406\) \(a_{9}=+0.333333333\) \(a_{10}=+0.142538912\)
\(a_{11}=-1.074417703\) \(a_{12}=+0.567499063\) \(a_{13}=-1.367031275\) \(a_{14}=+0.164307356\) \(a_{15}=+0.630010508\)
\(a_{16}=+0.949102770\) \(a_{17}=+1.042281725\) \(a_{18}=-0.043541538\) \(a_{19}=+0.489372347\) \(a_{20}=+1.072591120\)
\(a_{21}=+0.726225280\) \(a_{22}=+0.140345397\) \(a_{23}=+0.019090199\) \(a_{24}=-0.149545501\) \(a_{25}=+0.190739722\)
\(a_{26}=+0.178567932\) \(a_{27}=-0.192450090\) \(a_{28}=+1.236396498\) \(a_{29}=-0.533382606\) \(a_{30}=-0.082294879\)
\(a_{31}=-0.578947728\) \(a_{32}=-0.382996589\) \(a_{33}=+0.620315350\) \(a_{34}=-0.136147647\) \(a_{35}=+1.372588674\)
\(a_{36}=-0.327645737\) \(a_{37}=-1.079153382\) \(a_{38}=-0.063924074\) \(a_{39}=+0.789255874\) \(a_{40}=-0.282645712\)
\(a_{41}=-0.983634314\) \(a_{42}=-0.094862896\) \(a_{43}=+1.043528157\) \(a_{44}=+1.056085139\) \(a_{45}=-0.363736737\)
\(a_{46}=-0.002493650\) \(a_{47}=-1.003978967\) \(a_{48}=-0.547964740\) \(a_{49}=+0.582209472\) \(a_{50}=-0.024915302\)
\(a_{51}=-0.601761634\) \(a_{52}=+1.343705908\) \(a_{53}=-0.702770174\) \(a_{54}=+0.025138719\) \(a_{55}=+1.172415567\)
\(a_{56}=-0.325811171\) \(a_{57}=-0.282539256\) \(a_{58}=+0.069672897\) \(a_{59}=-1.078609265\) \(a_{60}=-0.619260772\)
\(a_{61}=+1.274237037\) \(a_{62}=+0.075624823\) \(a_{63}=-0.419286361\) \(a_{64}=-0.899073989\) \(a_{65}=+1.491718484\)
\(a_{66}=-0.081028453\) \(a_{67}=+1.491022165\) \(a_{68}=-1.024497491\) \(a_{69}=-0.011021732\) \(a_{70}=-0.179293865\)
\(a_{71}=-1.527576088\) \(a_{72}=+0.086340135\) \(a_{73}=+0.518466052\) \(a_{74}=+0.140963993\) \(a_{75}=-0.110123630\)
\(a_{76}=-0.481022289\) \(a_{77}=+1.351466066\) \(a_{78}=-0.103096243\) \(a_{79}=+0.771454198\) \(a_{80}=-1.035670633\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.128486852\) \(a_{83}=+0.864028533\) \(a_{84}=-0.713833851\) \(a_{85}=-1.137348460\)
\(a_{86}=-0.136310462\) \(a_{87}=+0.307948591\) \(a_{88}=-0.278296110\) \(a_{89}=-0.416874374\) \(a_{90}=+0.047512971\)
\(a_{91}=+1.719532705\) \(a_{92}=-0.018764467\) \(a_{93}=+0.334255627\) \(a_{94}=+0.131144364\) \(a_{95}=-0.534008101\)
\(a_{96}=+0.221123184\) \(a_{97}=-0.637468226\) \(a_{98}=-0.076050887\) \(a_{99}=-0.358139234\) \(a_{100}=-0.187485171\)

Showing 100 of 1228 available coefficients

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