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: \( 23.5240326785 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.574187165\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.113118419\) \(a_{7}=-0.102639146\) \(a_{8}=+0.353553391\) \(a_{9}=+1.478065231\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.963101466\) \(a_{12}=+0.787093583\) \(a_{13}=+1.193470716\) \(a_{14}=-0.072576836\) \(a_{15}=+0.703997902\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.724895091\) \(a_{18}=+1.045149948\) \(a_{19}=+0.879568073\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.161573226\) \(a_{22}=-0.681015577\) \(a_{23}=+1.136306152\) \(a_{24}=+0.556559210\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.843911237\) \(a_{27}=+0.752564151\) \(a_{28}=-0.051319573\) \(a_{29}=+0.210817053\) \(a_{30}=+0.497801691\)
\(a_{31}=-0.696299778\) \(a_{32}=+0.176776695\) \(a_{33}=-1.516101966\) \(a_{34}=-0.512578235\) \(a_{35}=-0.045901621\)
\(a_{36}=+0.739032616\) \(a_{37}=+1.727690370\) \(a_{38}=+0.621948549\) \(a_{39}=+1.878746284\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.371808455\) \(a_{42}=-0.114249524\) \(a_{43}=-1.056254730\) \(a_{44}=-0.481550733\) \(a_{45}=+0.661010867\)
\(a_{46}=+0.803489786\) \(a_{47}=+1.642101497\) \(a_{48}=+0.393546791\) \(a_{49}=-0.989465206\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.141120549\) \(a_{52}=+0.596735358\) \(a_{53}=+1.696342983\) \(a_{54}=+0.532143215\) \(a_{55}=-0.430712069\)
\(a_{56}=-0.036288418\) \(a_{57}=+1.384604771\) \(a_{58}=+0.149070168\) \(a_{59}=-0.089729064\) \(a_{60}=+0.351998951\)
\(a_{61}=+0.241456078\) \(a_{62}=-0.492358295\) \(a_{63}=-0.151707353\) \(a_{64}=+0.125000000\) \(a_{65}=+0.533736330\)
\(a_{66}=-1.072045981\) \(a_{67}=+0.844041917\) \(a_{68}=-0.362447546\) \(a_{69}=+1.788758560\) \(a_{70}=-0.032457348\)
\(a_{71}=-0.512564298\) \(a_{72}=+0.522574974\) \(a_{73}=-0.582618136\) \(a_{74}=+1.221661577\) \(a_{75}=+0.314837433\)
\(a_{76}=+0.439784036\) \(a_{77}=+0.098851912\) \(a_{78}=+1.328474238\) \(a_{79}=+0.663508623\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.293388403\) \(a_{82}=+0.970015061\) \(a_{83}=-1.328583076\) \(a_{84}=-0.080786613\) \(a_{85}=-0.324182940\)
\(a_{86}=-0.746884882\) \(a_{87}=+0.331865500\) \(a_{88}=-0.340507789\) \(a_{89}=-0.947987451\) \(a_{90}=+0.467405266\)
\(a_{91}=-0.122496815\) \(a_{92}=+0.568153076\) \(a_{93}=-1.096106174\) \(a_{94}=+1.161141104\) \(a_{95}=+0.393354800\)
\(a_{96}=+0.278279605\) \(a_{97}=-1.452153096\) \(a_{98}=-0.699657557\) \(a_{99}=-1.423526791\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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