Properties

Level $47$
Weight $0$
Character 47.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 47 \)
Weight: \( 0 \)
Character: 47.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.70586888077 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.386429954\) \(a_{3}=-0.355914798\) \(a_{4}=-0.850671891\) \(a_{5}=-1.514380232\)
\(a_{6}=+0.137536139\) \(a_{7}=+1.175309585\) \(a_{8}=+0.715155054\) \(a_{9}=-0.873324656\) \(a_{10}=+0.585201883\)
\(a_{11}=-0.045890814\) \(a_{12}=+0.302766714\) \(a_{13}=-1.222419296\) \(a_{14}=-0.454174830\) \(a_{15}=+0.538990334\)
\(a_{16}=+0.574314556\) \(a_{17}=+1.589352228\) \(a_{18}=+0.337478807\) \(a_{19}=-0.203818549\) \(a_{20}=+1.288240694\)
\(a_{21}=-0.418310074\) \(a_{22}=+0.017733585\) \(a_{23}=-0.964050407\) \(a_{24}=-0.254534266\) \(a_{25}=+1.293347485\)
\(a_{26}=+0.472379434\) \(a_{27}=+0.666743967\) \(a_{28}=-0.999802827\) \(a_{29}=+1.406409657\) \(a_{30}=-0.208282011\)
\(a_{31}=+0.147340187\) \(a_{32}=-0.937087402\) \(a_{33}=+0.016333220\) \(a_{34}=-0.614173308\) \(a_{35}=-1.779865602\)
\(a_{36}=+0.742912736\) \(a_{37}=+0.927193031\) \(a_{38}=+0.078761593\) \(a_{39}=+0.435077119\) \(a_{40}=-1.083016676\)
\(a_{41}=-0.552488769\) \(a_{42}=+0.161647543\) \(a_{43}=-0.826256381\) \(a_{44}=+0.039038025\) \(a_{45}=+1.322545595\)
\(a_{46}=+0.372537954\) \(a_{47}=-0.145864991\) \(a_{48}=-0.204407049\) \(a_{49}=+0.381352621\) \(a_{50}=-0.499788208\)
\(a_{51}=-0.565673978\) \(a_{52}=+1.039877736\) \(a_{53}=+0.263512493\) \(a_{54}=-0.257649840\) \(a_{55}=+0.069496142\)
\(a_{56}=+0.840528590\) \(a_{57}=+0.072542038\) \(a_{58}=-0.543478821\) \(a_{59}=+1.928414215\) \(a_{60}=-0.458503927\)
\(a_{61}=-0.766471255\) \(a_{62}=-0.056936664\) \(a_{63}=-1.026426841\) \(a_{64}=-0.212195912\) \(a_{65}=+1.851207620\)
\(a_{66}=-0.006311641\) \(a_{67}=+0.008549403\) \(a_{68}=-1.352017262\) \(a_{69}=+0.343119804\) \(a_{70}=+0.687793380\)
\(a_{71}=+0.986034585\) \(a_{72}=-0.624562545\) \(a_{73}=-0.145053195\) \(a_{74}=-0.358295162\) \(a_{75}=-0.460321506\)
\(a_{76}=+0.173382704\) \(a_{77}=-0.053935913\) \(a_{78}=-0.168126828\) \(a_{79}=+1.145007409\) \(a_{80}=-0.869730601\)
\(a_{81}=+0.636020605\) \(a_{82}=+0.213498228\) \(a_{83}=-1.083740180\) \(a_{84}=+0.355844612\) \(a_{85}=-2.406883590\)
\(a_{86}=+0.319290197\) \(a_{87}=-0.500561971\) \(a_{88}=-0.032819046\) \(a_{89}=+1.070834466\) \(a_{90}=-0.511071240\)
\(a_{91}=-1.436721122\) \(a_{92}=+0.820090582\) \(a_{93}=-0.052440558\) \(a_{94}=+0.056366605\) \(a_{95}=+0.308658774\)
\(a_{96}=+0.333523281\) \(a_{97}=+0.463539556\) \(a_{98}=-0.147366059\) \(a_{99}=+0.040077579\) \(a_{100}=-1.100214384\)

Showing 100 of 2000 available coefficients

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