Properties

Level $461$
Weight $0$
Character 461.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 461 \)
Weight: \( 0 \)
Character: 461.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.40706580221 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.552558829\) \(a_{3}=-0.880348277\) \(a_{4}=+1.410439325\) \(a_{5}=-1.772308925\)
\(a_{6}=-1.366792318\) \(a_{7}=+0.543708870\) \(a_{8}=+0.637231059\) \(a_{9}=-0.224987230\) \(a_{10}=-2.751613924\)
\(a_{11}=-0.561317578\) \(a_{12}=-1.241677471\) \(a_{13}=-1.520931637\) \(a_{14}=+0.844139861\) \(a_{15}=+1.560248945\)
\(a_{16}=-0.421100607\) \(a_{17}=+0.952816459\) \(a_{18}=-0.349305736\) \(a_{19}=-0.226175811\) \(a_{20}=-2.499734045\)
\(a_{21}=-0.478652892\) \(a_{22}=-0.871478949\) \(a_{23}=-0.153688027\) \(a_{24}=-0.560985154\) \(a_{25}=+2.141078885\)
\(a_{26}=-2.361336265\) \(a_{27}=+1.078415223\) \(a_{28}=+0.766868058\) \(a_{29}=-1.055362058\) \(a_{30}=+2.422378196\)
\(a_{31}=+1.413779449\) \(a_{32}=-1.291014264\) \(a_{33}=+0.494155018\) \(a_{34}=+1.479303840\) \(a_{35}=-0.963619912\)
\(a_{36}=-0.317330716\) \(a_{37}=-1.226166367\) \(a_{38}=-0.351151165\) \(a_{39}=+1.338949539\) \(a_{40}=-1.129370233\)
\(a_{41}=-0.785716620\) \(a_{42}=-0.743136952\) \(a_{43}=+0.648783372\) \(a_{44}=-0.791704452\) \(a_{45}=+0.398746774\)
\(a_{46}=-0.238609890\) \(a_{47}=-0.678475699\) \(a_{48}=+0.370714949\) \(a_{49}=-0.704380873\) \(a_{50}=+3.324151080\)
\(a_{51}=-0.838810066\) \(a_{52}=-2.145181808\) \(a_{53}=-0.175310949\) \(a_{54}=+1.674303012\) \(a_{55}=+0.994828292\)
\(a_{56}=+0.346468077\) \(a_{57}=+0.199113246\) \(a_{58}=-1.638511913\) \(a_{59}=+1.456826227\) \(a_{60}=+2.200636128\)
\(a_{61}=+0.949928976\) \(a_{62}=+2.194976219\) \(a_{63}=-0.122327371\) \(a_{64}=-1.583275340\) \(a_{65}=+2.695560786\)
\(a_{66}=+0.767204831\) \(a_{67}=+0.540587270\) \(a_{68}=+1.343889563\) \(a_{69}=+0.135298955\) \(a_{70}=-1.496076544\)
\(a_{71}=+0.471219630\) \(a_{72}=-0.143368766\) \(a_{73}=-0.741875937\) \(a_{74}=-1.903695415\) \(a_{75}=-1.884894720\)
\(a_{76}=-0.319006960\) \(a_{77}=-0.305193366\) \(a_{78}=+2.078797996\) \(a_{79}=-0.041791683\) \(a_{80}=+0.746320259\)
\(a_{81}=-0.724393609\) \(a_{82}=-1.219871242\) \(a_{83}=-1.190150616\) \(a_{84}=-0.675111002\) \(a_{85}=-1.688685103\)
\(a_{86}=+1.007274600\) \(a_{87}=+0.929086257\) \(a_{88}=-0.357689065\) \(a_{89}=+0.100590446\) \(a_{90}=+0.619077774\)
\(a_{91}=-0.826944082\) \(a_{92}=-0.216767646\) \(a_{93}=-1.244618276\) \(a_{94}=-1.053373302\) \(a_{95}=+0.400853232\)
\(a_{96}=+1.136542011\) \(a_{97}=-0.812891714\) \(a_{98}=-1.093592624\) \(a_{99}=+0.126289224\) \(a_{100}=+3.019861455\)

Showing 100 of 1372 available coefficients

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