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: \( 27.9703069143 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.078799352\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.055719556\) \(a_{7}=+1.731826195\) \(a_{8}=-0.353553391\) \(a_{9}=-0.993790662\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.751272706\) \(a_{12}=+0.039399676\) \(a_{13}=-1.823874552\) \(a_{14}=-1.224586047\) \(a_{15}=-0.035240141\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.670382666\) \(a_{18}=+0.702716116\) \(a_{19}=-1.943371203\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.136466781\) \(a_{22}=-0.531230025\) \(a_{23}=-0.134947250\) \(a_{24}=-0.027859778\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.289674063\) \(a_{27}=-0.157109411\) \(a_{28}=+0.865913098\) \(a_{29}=+1.061874122\) \(a_{30}=+0.024918543\)
\(a_{31}=+0.092196545\) \(a_{32}=-0.176776695\) \(a_{33}=+0.059199802\) \(a_{34}=-0.474032129\) \(a_{35}=-0.774496220\)
\(a_{36}=-0.496895331\) \(a_{37}=+0.234697687\) \(a_{38}=+1.374170956\) \(a_{39}=-0.143720132\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.084626408\) \(a_{42}=-0.096496586\) \(a_{43}=-0.923262228\) \(a_{44}=+0.375636353\) \(a_{45}=+0.444436695\)
\(a_{46}=+0.095422116\) \(a_{47}=+0.510151149\) \(a_{48}=+0.019699838\) \(a_{49}=+1.999221971\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.052825719\) \(a_{52}=-0.911937276\) \(a_{53}=+0.126112286\) \(a_{54}=+0.111093130\) \(a_{55}=-0.335979368\)
\(a_{56}=-0.612293023\) \(a_{57}=-0.153136391\) \(a_{58}=-0.750858392\) \(a_{59}=+1.625785263\) \(a_{60}=-0.017620071\)
\(a_{61}=+0.627185714\) \(a_{62}=-0.065192802\) \(a_{63}=-1.721072702\) \(a_{64}=+0.125000000\) \(a_{65}=+0.815661496\)
\(a_{66}=-0.041860582\) \(a_{67}=+1.469284987\) \(a_{68}=+0.335191333\) \(a_{69}=-0.010633756\) \(a_{70}=+0.547651529\)
\(a_{71}=-0.765647688\) \(a_{72}=+0.351358058\) \(a_{73}=-0.665887040\) \(a_{74}=-0.165956326\) \(a_{75}=+0.015759870\)
\(a_{76}=-0.971685601\) \(a_{77}=+1.301073752\) \(a_{78}=+0.101625480\) \(a_{79}=-1.216334574\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.981410542\) \(a_{82}=+0.766946688\) \(a_{83}=-1.126999981\) \(a_{84}=+0.068233391\) \(a_{85}=-0.299804242\)
\(a_{86}=+0.652844982\) \(a_{87}=+0.083674992\) \(a_{88}=-0.265615012\) \(a_{89}=+1.126994802\) \(a_{90}=-0.314264201\)
\(a_{91}=-3.158633726\) \(a_{92}=-0.067473625\) \(a_{93}=+0.007265028\) \(a_{94}=-0.360731337\) \(a_{95}=+0.869102023\)
\(a_{96}=-0.013929889\) \(a_{97}=-1.057814097\) \(a_{98}=-1.413663413\) \(a_{99}=-0.746607800\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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