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: \( 24.2096219473 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.450265524\) \(a_{3}=-0.577350269\) \(a_{4}=-0.797260958\) \(a_{5}=-0.671791503\)
\(a_{6}=+0.259960921\) \(a_{7}=-0.602629116\) \(a_{8}=+0.809244647\) \(a_{9}=+0.333333333\) \(a_{10}=+0.302484553\)
\(a_{11}=+0.546370629\) \(a_{12}=+0.460298829\) \(a_{13}=+0.461260741\) \(a_{14}=+0.271343115\) \(a_{15}=+0.387859005\)
\(a_{16}=+0.432885993\) \(a_{17}=-1.034327726\) \(a_{18}=-0.150088508\) \(a_{19}=+1.414524945\) \(a_{20}=+0.535593137\)
\(a_{21}=+0.347928082\) \(a_{22}=-0.246011858\) \(a_{23}=+0.699102245\) \(a_{24}=-0.467217615\) \(a_{25}=-0.548696176\)
\(a_{26}=-0.207689809\) \(a_{27}=-0.192450090\) \(a_{28}=+0.480452666\) \(a_{29}=+1.249085777\) \(a_{30}=-0.174639538\)
\(a_{31}=+1.613780272\) \(a_{32}=-1.004158285\) \(a_{33}=-0.315447230\) \(a_{34}=+0.465722116\) \(a_{35}=+0.404841120\)
\(a_{36}=-0.265753653\) \(a_{37}=-1.592550004\) \(a_{38}=-0.636911816\) \(a_{39}=-0.266309013\) \(a_{40}=-0.543643678\)
\(a_{41}=-1.588355060\) \(a_{42}=-0.156660020\) \(a_{43}=-0.073511336\) \(a_{44}=-0.435599971\) \(a_{45}=-0.223930501\)
\(a_{46}=-0.314781638\) \(a_{47}=-1.145534072\) \(a_{48}=-0.249926845\) \(a_{49}=-0.636838148\) \(a_{50}=+0.247058971\)
\(a_{51}=+0.597169391\) \(a_{52}=-0.367745180\) \(a_{53}=+0.296994435\) \(a_{54}=+0.086653640\) \(a_{55}=-0.367047146\)
\(a_{56}=-0.487674386\) \(a_{57}=-0.816676358\) \(a_{58}=-0.562420262\) \(a_{59}=+1.439709201\) \(a_{60}=-0.309224842\)
\(a_{61}=+1.353661004\) \(a_{62}=-0.726629619\) \(a_{63}=-0.200876372\) \(a_{64}=+0.019251863\) \(a_{65}=-0.309871046\)
\(a_{66}=+0.142035012\) \(a_{67}=-0.947175188\) \(a_{68}=+0.824629114\) \(a_{69}=-0.403626869\) \(a_{70}=-0.182285999\)
\(a_{71}=+0.601100203\) \(a_{72}=+0.269748216\) \(a_{73}=-0.185812731\) \(a_{74}=+0.717070362\) \(a_{75}=+0.316789885\)
\(a_{76}=-1.127745513\) \(a_{77}=-0.329258849\) \(a_{78}=+0.119909767\) \(a_{79}=-0.224131373\) \(a_{80}=-0.290809132\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.715181523\) \(a_{83}=+0.018503818\) \(a_{84}=-0.277389476\) \(a_{85}=+0.694852578\)
\(a_{86}=+0.033099620\) \(a_{87}=-0.721160010\) \(a_{88}=+0.442147507\) \(a_{89}=+0.236028853\) \(a_{90}=+0.100828184\)
\(a_{91}=-0.277969152\) \(a_{92}=-0.557366925\) \(a_{93}=-0.931716474\) \(a_{94}=+0.515794499\) \(a_{95}=-0.950265839\)
\(a_{96}=+0.579751056\) \(a_{97}=+1.397092609\) \(a_{98}=+0.286746263\) \(a_{99}=+0.182123543\) \(a_{100}=+0.437454039\)

Showing 100 of 1228 available coefficients

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