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: \( 27.8530777214 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.112004392\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.079199065\) \(a_{7}=+0.209422099\) \(a_{8}=-0.353553391\) \(a_{9}=-0.987455016\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.319088988\) \(a_{12}=-0.056002196\) \(a_{13}=+0.155097363\) \(a_{14}=-0.148083786\) \(a_{15}=-0.050089887\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.797503442\) \(a_{18}=+0.698236138\) \(a_{19}=+1.322180436\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.023456195\) \(a_{22}=+0.225629987\) \(a_{23}=+0.745465903\) \(a_{24}=+0.039599533\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.109670397\) \(a_{27}=+0.222603691\) \(a_{28}=+0.104711049\) \(a_{29}=-0.558778570\) \(a_{30}=+0.035418899\)
\(a_{31}=+0.037689483\) \(a_{32}=-0.176776695\) \(a_{33}=+0.035739368\) \(a_{34}=+0.563920092\) \(a_{35}=+0.093656410\)
\(a_{36}=-0.493727508\) \(a_{37}=-0.477609528\) \(a_{38}=-0.934922752\) \(a_{39}=-0.017371586\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.749384734\) \(a_{42}=+0.016586034\) \(a_{43}=+0.415116747\) \(a_{44}=-0.159544494\) \(a_{45}=-0.441603308\)
\(a_{46}=-0.527123995\) \(a_{47}=-1.355392705\) \(a_{48}=-0.028001098\) \(a_{49}=-0.956142385\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.089323888\) \(a_{52}=+0.077548681\) \(a_{53}=+1.547004575\) \(a_{54}=-0.157404579\) \(a_{55}=-0.142700934\)
\(a_{56}=-0.074041893\) \(a_{57}=-0.148090016\) \(a_{58}=+0.395116116\) \(a_{59}=+0.466423955\) \(a_{60}=-0.025044943\)
\(a_{61}=-0.490656888\) \(a_{62}=-0.026650489\) \(a_{63}=-0.206794902\) \(a_{64}=+0.125000000\) \(a_{65}=+0.069361649\)
\(a_{66}=-0.025271550\) \(a_{67}=-0.548220834\) \(a_{68}=-0.398751721\) \(a_{69}=-0.083495455\) \(a_{70}=-0.066225082\)
\(a_{71}=-0.827265212\) \(a_{72}=+0.349118069\) \(a_{73}=+0.892532637\) \(a_{74}=+0.337720936\) \(a_{75}=-0.022400878\)
\(a_{76}=+0.661090218\) \(a_{77}=-0.066824286\) \(a_{78}=+0.012283566\) \(a_{79}=-1.173840804\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.962522425\) \(a_{82}=-0.529895027\) \(a_{83}=+0.031757831\) \(a_{84}=-0.011728097\) \(a_{85}=-0.356654382\)
\(a_{86}=-0.293531867\) \(a_{87}=+0.062585654\) \(a_{88}=+0.112814994\) \(a_{89}=+1.570716890\) \(a_{90}=+0.312260694\)
\(a_{91}=+0.032480815\) \(a_{92}=+0.372732951\) \(a_{93}=-0.004221388\) \(a_{94}=+0.958407373\) \(a_{95}=+0.591297067\)
\(a_{96}=+0.019799766\) \(a_{97}=+0.427420108\) \(a_{98}=+0.676094764\) \(a_{99}=+0.315086022\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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