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: \( 9.78345165027 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.833725767\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.296639925\) \(a_{7}=+0.860362392\) \(a_{8}=+0.353553391\) \(a_{9}=+2.362550188\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.295956426\) \(a_{12}=+0.916862883\) \(a_{13}=-0.841264560\) \(a_{14}=+0.608368082\) \(a_{15}=+0.820067093\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.123057161\) \(a_{18}=+1.670575259\) \(a_{19}=+1.059662302\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.577668687\) \(a_{22}=-0.916379577\) \(a_{23}=-0.467215213\) \(a_{24}=+0.648319962\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.594863875\) \(a_{27}=+2.498543389\) \(a_{28}=+0.430181196\) \(a_{29}=-0.122080035\) \(a_{30}=+0.579875003\)
\(a_{31}=+0.054061459\) \(a_{32}=+0.176776695\) \(a_{33}=-2.376428691\) \(a_{34}=-0.794121334\) \(a_{35}=+0.384765759\)
\(a_{36}=+1.181275094\) \(a_{37}=+1.156702918\) \(a_{38}=+0.749294400\) \(a_{39}=-1.542648501\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.469035045\) \(a_{42}=+1.115580227\) \(a_{43}=+0.206837694\) \(a_{44}=-0.647978213\) \(a_{45}=+1.056564564\)
\(a_{46}=-0.330371045\) \(a_{47}=-0.373301188\) \(a_{48}=+0.458431442\) \(a_{49}=-0.259776554\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.059378854\) \(a_{52}=-0.420632280\) \(a_{53}=-0.441144835\) \(a_{54}=+1.766736973\) \(a_{55}=-0.579569333\)
\(a_{56}=+0.304184041\) \(a_{57}=+1.943130068\) \(a_{58}=-0.086323621\) \(a_{59}=-1.350114562\) \(a_{60}=+0.410033547\)
\(a_{61}=-0.048238886\) \(a_{62}=+0.038227225\) \(a_{63}=+2.032649331\) \(a_{64}=+0.125000000\) \(a_{65}=-0.376224949\)
\(a_{66}=-1.680388842\) \(a_{67}=-0.481277086\) \(a_{68}=-0.561528581\) \(a_{69}=-0.856744574\) \(a_{70}=+0.272070477\)
\(a_{71}=-0.843937118\) \(a_{72}=+0.835287629\) \(a_{73}=+1.357615944\) \(a_{74}=+0.817912477\) \(a_{75}=+0.366745153\)
\(a_{76}=+0.529831151\) \(a_{77}=-1.114992171\) \(a_{78}=-1.090817216\) \(a_{79}=-1.408586197\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.219093203\) \(a_{82}=-0.331657861\) \(a_{83}=-0.348212070\) \(a_{84}=+0.788834344\) \(a_{85}=-0.502246431\)
\(a_{86}=+0.146256336\) \(a_{87}=-0.223861306\) \(a_{88}=-0.458189788\) \(a_{89}=+1.818351399\) \(a_{90}=+0.747103968\)
\(a_{91}=-0.723792389\) \(a_{92}=-0.233607606\) \(a_{93}=+0.099133891\) \(a_{94}=-0.263963801\) \(a_{95}=+0.473895388\)
\(a_{96}=+0.324159981\) \(a_{97}=-1.706391600\) \(a_{98}=-0.183689763\) \(a_{99}=-3.061762098\) \(a_{100}=+0.099975586\)

Showing 100 of 148 available coefficients

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