Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.38518054954 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.686782566\) \(a_{3}=-0.549317987\) \(a_{4}=+1.845235425\) \(a_{5}=-1.410242603\)
\(a_{6}=+0.926580003\) \(a_{7}=+1.070395083\) \(a_{8}=-1.425728378\) \(a_{9}=-0.698249749\) \(a_{10}=+2.378772636\)
\(a_{11}=+0.860240486\) \(a_{12}=-1.013621008\) \(a_{13}=+0.277350098\) \(a_{14}=-1.805523765\) \(a_{15}=+0.774671627\)
\(a_{16}=+0.559658347\) \(a_{17}=-0.293756789\) \(a_{18}=+1.177795504\) \(a_{19}=+1.118205309\) \(a_{20}=-2.602229608\)
\(a_{21}=-0.587987272\) \(a_{22}=-1.451038654\) \(a_{23}=+1.307341928\) \(a_{24}=+0.783178242\) \(a_{25}=+0.988784198\)
\(a_{26}=-0.467829310\) \(a_{27}=+0.932879133\) \(a_{28}=+1.975130926\) \(a_{29}=-1.370032262\) \(a_{30}=-1.306702595\)
\(a_{31}=-0.184877410\) \(a_{32}=+0.481706435\) \(a_{33}=-0.472545572\) \(a_{34}=+0.495503831\) \(a_{35}=-1.509516748\)
\(a_{36}=-1.288435173\) \(a_{37}=+1.428592956\) \(a_{38}=-1.886169220\) \(a_{39}=-0.152353398\) \(a_{40}=+2.010622899\)
\(a_{41}=+0.226620869\) \(a_{42}=+0.991806680\) \(a_{43}=+0.104145824\) \(a_{44}=+1.587346218\) \(a_{45}=+0.984701544\)
\(a_{46}=-2.205201571\) \(a_{47}=+0.698551370\) \(a_{48}=-0.307430397\) \(a_{49}=+0.145745635\) \(a_{50}=-1.667863947\)
\(a_{51}=+0.161365888\) \(a_{52}=+0.511776226\) \(a_{53}=+0.764060291\) \(a_{54}=-1.573564258\) \(a_{55}=-1.213147782\)
\(a_{56}=-1.526092646\) \(a_{57}=-0.614250289\) \(a_{58}=+2.310946534\) \(a_{59}=+1.172348917\) \(a_{60}=+1.429451529\)
\(a_{61}=+0.015423620\) \(a_{62}=+0.311847993\) \(a_{63}=-0.747403099\) \(a_{64}=-1.372192364\) \(a_{65}=-0.391130924\)
\(a_{66}=+0.797081632\) \(a_{67}=+0.095540616\) \(a_{68}=-0.542050434\) \(a_{69}=-0.718146436\) \(a_{70}=+2.546226534\)
\(a_{71}=-1.048472094\) \(a_{72}=+0.995514483\) \(a_{73}=+0.304582294\) \(a_{74}=-2.409725692\) \(a_{75}=-0.543156945\)
\(a_{76}=+2.063352048\) \(a_{77}=+0.920797187\) \(a_{78}=+0.256987055\) \(a_{79}=-0.121946034\) \(a_{80}=-0.789254045\)
\(a_{81}=+0.185802462\) \(a_{82}=-0.382260131\) \(a_{83}=-0.114213932\) \(a_{84}=-1.084974944\) \(a_{85}=+0.414268339\)
\(a_{86}=-0.175671360\) \(a_{87}=+0.752583364\) \(a_{88}=-1.226469273\) \(a_{89}=+0.591953607\) \(a_{90}=-1.660977397\)
\(a_{91}=+0.296874181\) \(a_{92}=+2.412353637\) \(a_{93}=+0.101556487\) \(a_{94}=-1.178304272\) \(a_{95}=-1.576940765\)
\(a_{96}=-0.264610009\) \(a_{97}=-0.024656206\) \(a_{98}=-0.245841195\) \(a_{99}=-0.600662704\) \(a_{100}=+1.824539630\)

Showing 100 of 546 available coefficients

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