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: \( 27.5537953828 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.892505842\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.631096933\) \(a_{7}=-0.843897313\) \(a_{8}=-0.353553391\) \(a_{9}=-0.203433322\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.128946502\) \(a_{12}=-0.446252921\) \(a_{13}=+1.739479777\) \(a_{14}=+0.596725513\) \(a_{15}=+0.399140747\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.052721992\) \(a_{18}=+0.143849082\) \(a_{19}=+0.706002799\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.753183282\) \(a_{22}=-0.798285727\) \(a_{23}=-1.660102280\) \(a_{24}=+0.315548467\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.229997946\) \(a_{27}=+1.074071270\) \(a_{28}=-0.421948657\) \(a_{29}=+0.391538669\) \(a_{30}=-0.282235129\)
\(a_{31}=+1.162407046\) \(a_{32}=-0.176776695\) \(a_{33}=-1.007591348\) \(a_{34}=-0.744386859\) \(a_{35}=+0.377402352\)
\(a_{36}=-0.101716661\) \(a_{37}=+1.369248196\) \(a_{38}=-0.499219367\) \(a_{39}=-1.552495863\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.683393682\) \(a_{42}=-0.532581006\) \(a_{43}=+1.579213698\) \(a_{44}=+0.564473251\) \(a_{45}=+0.090978147\)
\(a_{46}=+1.173869580\) \(a_{47}=+1.653377921\) \(a_{48}=-0.223126460\) \(a_{49}=-0.287837325\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.939560528\) \(a_{52}=+0.869739889\) \(a_{53}=-0.989129371\) \(a_{54}=-0.759483079\) \(a_{55}=-0.504880224\)
\(a_{56}=+0.298362756\) \(a_{57}=-0.630111623\) \(a_{58}=-0.276859648\) \(a_{59}=-0.613309754\) \(a_{60}=+0.199570373\)
\(a_{61}=+0.427027302\) \(a_{62}=-0.821945904\) \(a_{63}=+0.171676834\) \(a_{64}=+0.125000000\) \(a_{65}=-0.777919005\)
\(a_{66}=+0.712474675\) \(a_{67}=-1.081391253\) \(a_{68}=+0.526360996\) \(a_{69}=+1.481650983\) \(a_{70}=-0.266863762\)
\(a_{71}=-1.578465800\) \(a_{72}=+0.071924541\) \(a_{73}=+0.248297782\) \(a_{74}=-0.968204684\) \(a_{75}=-0.178501168\)
\(a_{76}=+0.353001400\) \(a_{77}=-0.952714920\) \(a_{78}=+1.097780352\) \(a_{79}=+0.532715929\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.755181561\) \(a_{82}=+0.483232307\) \(a_{83}=+0.256717147\) \(a_{84}=+0.376591641\) \(a_{85}=-0.470791587\)
\(a_{86}=-1.116672715\) \(a_{87}=-0.349450550\) \(a_{88}=-0.399142864\) \(a_{89}=+0.958058833\) \(a_{90}=-0.064331265\)
\(a_{91}=-1.467942310\) \(a_{92}=-0.830051140\) \(a_{93}=-1.037455079\) \(a_{94}=-1.169114740\) \(a_{95}=-0.315734050\)
\(a_{96}=+0.157774233\) \(a_{97}=+0.383692148\) \(a_{98}=+0.203531724\) \(a_{99}=-0.229665337\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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