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: \( 22.6711177685 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.064709540\) \(a_{3}=-0.577350269\) \(a_{4}=-0.995812675\) \(a_{5}=+1.717197914\)
\(a_{6}=-0.037360070\) \(a_{7}=-1.393683542\) \(a_{8}=-0.129148120\) \(a_{9}=+0.333333333\) \(a_{10}=+0.111119087\)
\(a_{11}=+0.596091434\) \(a_{12}=+0.574932716\) \(a_{13}=+0.675982583\) \(a_{14}=-0.090184621\) \(a_{15}=-0.991424678\)
\(a_{16}=+0.987455560\) \(a_{17}=+0.348289653\) \(a_{18}=+0.021569847\) \(a_{19}=+0.273962786\) \(a_{20}=-1.710007449\)
\(a_{21}=+0.804643568\) \(a_{22}=+0.038572802\) \(a_{23}=-1.190189164\) \(a_{24}=+0.074563702\) \(a_{25}=+1.948768675\)
\(a_{26}=+0.043742522\) \(a_{27}=-0.192450090\) \(a_{28}=+1.387847737\) \(a_{29}=-0.945039072\) \(a_{30}=-0.064154635\)
\(a_{31}=-1.110584250\) \(a_{32}=+0.193045915\) \(a_{33}=-0.344153550\) \(a_{34}=+0.022537663\) \(a_{35}=-2.393230470\)
\(a_{36}=-0.331937558\) \(a_{37}=-0.836460805\) \(a_{38}=+0.017728006\) \(a_{39}=-0.390278726\) \(a_{40}=-0.221772882\)
\(a_{41}=-0.210890302\) \(a_{42}=+0.052068115\) \(a_{43}=-1.293724326\) \(a_{44}=-0.593595406\) \(a_{45}=+0.572399305\)
\(a_{46}=-0.077016593\) \(a_{47}=+0.035213527\) \(a_{48}=-0.570107733\) \(a_{49}=+0.942353815\) \(a_{50}=+0.126103924\)
\(a_{51}=-0.201085125\) \(a_{52}=-0.673152025\) \(a_{53}=-0.905821125\) \(a_{54}=-0.012453357\) \(a_{55}=+1.023606967\)
\(a_{56}=+0.179991609\) \(a_{57}=-0.158172488\) \(a_{58}=-0.061153043\) \(a_{59}=+0.113066806\) \(a_{60}=+0.987273261\)
\(a_{61}=-1.028775929\) \(a_{62}=-0.071865396\) \(a_{63}=-0.464561181\) \(a_{64}=-0.974963648\) \(a_{65}=+1.160795882\)
\(a_{66}=-0.022270018\) \(a_{67}=+0.610475953\) \(a_{68}=-0.346831251\) \(a_{69}=+0.687156034\) \(a_{70}=-0.154864842\)
\(a_{71}=-0.773128103\) \(a_{72}=-0.043049373\) \(a_{73}=+1.045629627\) \(a_{74}=-0.054126994\) \(a_{75}=-1.125122119\)
\(a_{76}=-0.272815615\) \(a_{77}=-0.830762821\) \(a_{78}=-0.025254757\) \(a_{79}=+1.211445303\) \(a_{80}=+1.695656628\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.013646614\) \(a_{83}=-1.475169641\) \(a_{84}=-0.801274264\) \(a_{85}=+0.598082266\)
\(a_{86}=-0.083716306\) \(a_{87}=+0.545618563\) \(a_{88}=-0.076984088\) \(a_{89}=-0.739069241\) \(a_{90}=+0.037039696\)
\(a_{91}=-0.942105801\) \(a_{92}=+1.185205456\) \(a_{93}=+0.641196116\) \(a_{94}=+0.002278651\) \(a_{95}=+0.470448324\)
\(a_{96}=-0.111455111\) \(a_{97}=-0.196817354\) \(a_{98}=+0.060979282\) \(a_{99}=+0.198697145\) \(a_{100}=-1.940608548\)

Showing 100 of 1228 available coefficients

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