Properties

Level $5$
Weight $0$
Character 5.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 8.4800158394 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.433451555\) \(a_{3}=-0.762904312\) \(a_{4}=-0.812119749\) \(a_{5}=-0.447213596\)
\(a_{6}=+0.330682061\) \(a_{7}=+1.310361122\) \(a_{8}=+0.785466124\) \(a_{9}=-0.417977010\) \(a_{10}=+0.193845429\)
\(a_{11}=+1.210684872\) \(a_{12}=+0.619569659\) \(a_{13}=-0.642669966\) \(a_{14}=-0.567978067\) \(a_{15}=+0.341181181\)
\(a_{16}=+0.471658236\) \(a_{17}=-0.667700087\) \(a_{18}=+0.181172785\) \(a_{19}=+0.944095923\) \(a_{20}=+0.363190993\)
\(a_{21}=-0.999680151\) \(a_{22}=-0.524773240\) \(a_{23}=+0.450700591\) \(a_{24}=-0.599235494\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.278566298\) \(a_{27}=+1.081780775\) \(a_{28}=-1.064170149\) \(a_{29}=+0.570709969\) \(a_{30}=-0.147885513\)
\(a_{31}=+0.884522834\) \(a_{32}=-0.989907120\) \(a_{33}=-0.923636709\) \(a_{34}=+0.289415641\) \(a_{35}=-0.586011309\)
\(a_{36}=+0.339447385\) \(a_{37}=+1.016353839\) \(a_{38}=-0.409219846\) \(a_{39}=+0.490295689\) \(a_{40}=-0.351271130\)
\(a_{41}=+1.556726722\) \(a_{42}=+0.433312917\) \(a_{43}=-1.909796544\) \(a_{44}=-0.983221095\) \(a_{45}=+0.186925002\)
\(a_{46}=-0.195356870\) \(a_{47}=+0.357630082\) \(a_{48}=-0.359830105\) \(a_{49}=+0.717046273\) \(a_{50}=-0.086690306\)
\(a_{51}=+0.509391267\) \(a_{52}=+0.521924955\) \(a_{53}=+0.042817233\) \(a_{54}=-0.468899538\) \(a_{55}=-0.541434804\)
\(a_{56}=+1.029244239\) \(a_{57}=-0.720254851\) \(a_{58}=-0.247375124\) \(a_{59}=+1.070401665\) \(a_{60}=-0.277079975\)
\(a_{61}=-0.982479694\) \(a_{62}=-0.383397798\) \(a_{63}=-0.547700824\) \(a_{64}=-0.042581455\) \(a_{65}=+0.287410746\)
\(a_{66}=+0.400351768\) \(a_{67}=+0.756356920\) \(a_{68}=+0.542252427\) \(a_{69}=-0.343841425\) \(a_{70}=+0.254007513\)
\(a_{71}=+0.997862524\) \(a_{72}=-0.328306782\) \(a_{73}=-0.744857883\) \(a_{74}=-0.440540153\) \(a_{75}=-0.152580861\)
\(a_{76}=-0.766718946\) \(a_{77}=+1.586434386\) \(a_{78}=-0.212519427\) \(a_{79}=-0.885367316\) \(a_{80}=-0.210931977\)
\(a_{81}=-0.407318212\) \(a_{82}=-0.674765617\) \(a_{83}=+0.044716676\) \(a_{84}=+0.811859990\) \(a_{85}=+0.298604558\)
\(a_{86}=+0.827804300\) \(a_{87}=-0.435397107\) \(a_{88}=+0.950951931\) \(a_{89}=+1.245549901\) \(a_{90}=-0.081022942\)
\(a_{91}=-0.842129758\) \(a_{92}=-0.366022835\) \(a_{93}=-0.674806216\) \(a_{94}=-0.155015354\) \(a_{95}=-0.422212597\)
\(a_{96}=+0.755204402\) \(a_{97}=-0.558294147\) \(a_{98}=-0.310804821\) \(a_{99}=-0.506038443\) \(a_{100}=-0.162423949\)

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