Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 29.5701919803 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.862510343\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.609886912\) \(a_{7}=-0.970934901\) \(a_{8}=+0.353553391\) \(a_{9}=-0.256075909\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.596676328\) \(a_{12}=-0.431255171\) \(a_{13}=+0.261226695\) \(a_{14}=-0.686554653\) \(a_{15}=+0.385726351\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.324595575\) \(a_{18}=-0.181073012\) \(a_{19}=+1.807009603\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.837441394\) \(a_{22}=-0.421913878\) \(a_{23}=-0.195882387\) \(a_{24}=-0.304943456\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.184715168\) \(a_{27}=+1.083378462\) \(a_{28}=-0.485467450\) \(a_{29}=-0.879409688\) \(a_{30}=+0.272749719\)
\(a_{31}=+1.704937888\) \(a_{32}=+0.176776695\) \(a_{33}=+0.514639504\) \(a_{34}=-0.229523732\) \(a_{35}=+0.434215288\)
\(a_{36}=-0.128037954\) \(a_{37}=-0.581293245\) \(a_{38}=+1.277748744\) \(a_{39}=-0.225310727\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.349912092\) \(a_{42}=+0.592160489\) \(a_{43}=+1.115387707\) \(a_{44}=-0.298338164\) \(a_{45}=+0.114520628\)
\(a_{46}=-0.138509764\) \(a_{47}=-1.181009705\) \(a_{48}=-0.215627586\) \(a_{49}=-0.057285418\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.279967040\) \(a_{52}=+0.130613348\) \(a_{53}=-1.850346843\) \(a_{54}=+0.766064257\) \(a_{55}=+0.266841766\)
\(a_{56}=-0.343277326\) \(a_{57}=-1.558564472\) \(a_{58}=-0.621836554\) \(a_{59}=+1.057044102\) \(a_{60}=+0.192863176\)
\(a_{61}=+0.014266475\) \(a_{62}=+1.205573142\) \(a_{63}=+0.248633037\) \(a_{64}=+0.125000000\) \(a_{65}=-0.116824130\)
\(a_{66}=+0.363905083\) \(a_{67}=-0.534303173\) \(a_{68}=-0.162297787\) \(a_{69}=+0.168950585\) \(a_{70}=+0.307036575\)
\(a_{71}=+0.996075879\) \(a_{72}=-0.090536506\) \(a_{73}=+0.855226254\) \(a_{74}=-0.411036395\) \(a_{75}=-0.172502069\)
\(a_{76}=+0.903504801\) \(a_{77}=+0.579333871\) \(a_{78}=-0.159318743\) \(a_{79}=-0.138218364\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.678349220\) \(a_{82}=+0.954531994\) \(a_{83}=+0.961889489\) \(a_{84}=+0.418720697\) \(a_{85}=+0.145163554\)
\(a_{86}=+0.788698211\) \(a_{87}=+0.758499951\) \(a_{88}=-0.210956939\) \(a_{89}=+0.252654909\) \(a_{90}=+0.080978313\)
\(a_{91}=-0.253634116\) \(a_{92}=-0.097941194\) \(a_{93}=-1.470526562\) \(a_{94}=-0.835099971\) \(a_{95}=-0.808119262\)
\(a_{96}=-0.152471728\) \(a_{97}=-1.123788312\) \(a_{98}=-0.040506908\) \(a_{99}=+0.152794433\) \(a_{100}=+0.099975586\)

Showing 100 of 247 available coefficients

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