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: \( 14.8197544572 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.264364223\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.186933735\) \(a_{7}=-1.315500342\) \(a_{8}=+0.353553391\) \(a_{9}=-0.930111558\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.671694046\) \(a_{12}=-0.132182112\) \(a_{13}=+1.453023759\) \(a_{14}=-0.930199213\) \(a_{15}=-0.118227275\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.241896709\) \(a_{18}=-0.657688190\) \(a_{19}=-1.362882451\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.347771226\) \(a_{22}=+0.474959414\) \(a_{23}=+1.850622538\) \(a_{24}=-0.093466867\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.027442953\) \(a_{27}=+0.510252442\) \(a_{28}=-0.657750171\) \(a_{29}=-1.331542723\) \(a_{30}=-0.083599308\)
\(a_{31}=+0.812315774\) \(a_{32}=+0.176776695\) \(a_{33}=-0.177571874\) \(a_{34}=+0.171046804\) \(a_{35}=-0.588309638\)
\(a_{36}=-0.465055779\) \(a_{37}=+0.733883506\) \(a_{38}=-0.963703423\) \(a_{39}=-0.384127497\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.422560661\) \(a_{42}=+0.245911392\) \(a_{43}=+0.594910049\) \(a_{44}=+0.335847023\) \(a_{45}=-0.415958534\)
\(a_{46}=+1.308587746\) \(a_{47}=+0.882991435\) \(a_{48}=-0.066091056\) \(a_{49}=+0.730541150\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.063948836\) \(a_{52}=+0.726511879\) \(a_{53}=+0.626951178\) \(a_{54}=+0.360802962\) \(a_{55}=+0.300390709\)
\(a_{56}=-0.465099606\) \(a_{57}=+0.360297360\) \(a_{58}=-0.941542889\) \(a_{59}=+1.288902634\) \(a_{60}=-0.059113637\)
\(a_{61}=+0.011932288\) \(a_{62}=+0.574393992\) \(a_{63}=+1.223562072\) \(a_{64}=+0.125000000\) \(a_{65}=+0.649811979\)
\(a_{66}=-0.125562277\) \(a_{67}=-0.544010900\) \(a_{68}=+0.120948355\) \(a_{69}=-0.489238389\) \(a_{70}=-0.415997734\)
\(a_{71}=+1.510243653\) \(a_{72}=-0.328844095\) \(a_{73}=-0.805608168\) \(a_{74}=+0.518934004\) \(a_{75}=-0.052872845\)
\(a_{76}=-0.681441225\) \(a_{77}=-0.883613747\) \(a_{78}=-0.271619158\) \(a_{79}=+1.002893712\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.795219067\) \(a_{82}=+1.005902290\) \(a_{83}=-0.724513758\) \(a_{84}=+0.173885613\) \(a_{85}=+0.108179497\)
\(a_{86}=+0.420664929\) \(a_{87}=+0.352012257\) \(a_{88}=+0.237479707\) \(a_{89}=+0.020656092\) \(a_{90}=-0.294127100\)
\(a_{91}=-1.911453252\) \(a_{92}=+0.925311269\) \(a_{93}=-0.214747228\) \(a_{94}=+0.624369232\) \(a_{95}=-0.609499561\)
\(a_{96}=-0.046733434\) \(a_{97}=-1.708935470\) \(a_{98}=+0.516570601\) \(a_{99}=-0.624750392\) \(a_{100}=+0.099975586\)

Showing 100 of 174 available coefficients

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