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: \( 23.9699254626 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.867591225\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.613479639\) \(a_{7}=-0.746073291\) \(a_{8}=-0.353553391\) \(a_{9}=-0.247285466\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.627046933\) \(a_{12}=-0.433795613\) \(a_{13}=-0.309226097\) \(a_{14}=+0.527553484\) \(a_{15}=-0.387998591\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.940237465\) \(a_{18}=+0.174857230\) \(a_{19}=+0.422782211\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.647286641\) \(a_{22}=-0.443389139\) \(a_{23}=-1.631658077\) \(a_{24}=+0.306739819\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.218655870\) \(a_{27}=+1.082133926\) \(a_{28}=-0.373036646\) \(a_{29}=-1.213950832\) \(a_{30}=+0.274356435\)
\(a_{31}=-1.192982253\) \(a_{32}=-0.176776695\) \(a_{33}=-0.544020417\) \(a_{34}=-0.664848287\) \(a_{35}=-0.333654119\)
\(a_{36}=-0.123642733\) \(a_{37}=+1.012364577\) \(a_{38}=-0.298952169\) \(a_{39}=+0.268281848\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.532449103\) \(a_{42}=-0.457700773\) \(a_{43}=+0.393535991\) \(a_{44}=+0.313523467\) \(a_{45}=-0.110589422\)
\(a_{46}=+1.153756491\) \(a_{47}=+1.546563649\) \(a_{48}=-0.216897806\) \(a_{49}=-0.443374644\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.815741774\) \(a_{52}=-0.154613048\) \(a_{53}=+0.542698377\) \(a_{54}=-0.765184237\) \(a_{55}=+0.280423914\)
\(a_{56}=+0.263776742\) \(a_{57}=-0.366802137\) \(a_{58}=+0.858392866\) \(a_{59}=+0.849838736\) \(a_{60}=-0.193999296\)
\(a_{61}=-0.820362759\) \(a_{62}=+0.843565841\) \(a_{63}=+0.184493081\) \(a_{64}=+0.125000000\) \(a_{65}=-0.138290115\)
\(a_{66}=+0.384680526\) \(a_{67}=+1.574249604\) \(a_{68}=+0.470118733\) \(a_{69}=+1.415612230\) \(a_{70}=+0.235929090\)
\(a_{71}=+0.440629695\) \(a_{72}=+0.087428615\) \(a_{73}=-0.148278747\) \(a_{74}=-0.715849858\) \(a_{75}=-0.173518245\)
\(a_{76}=+0.211391106\) \(a_{77}=-0.467822969\) \(a_{78}=-0.189703914\) \(a_{79}=-0.208677964\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.691564432\) \(a_{82}=-0.376498371\) \(a_{83}=-0.178905326\) \(a_{84}=+0.323643320\) \(a_{85}=+0.420486977\)
\(a_{86}=-0.278271968\) \(a_{87}=+1.053213090\) \(a_{88}=-0.221694569\) \(a_{89}=+0.677831363\) \(a_{90}=+0.078198530\)
\(a_{91}=+0.230705332\) \(a_{92}=-0.815829039\) \(a_{93}=+1.035020935\) \(a_{94}=-1.093585644\) \(a_{95}=+0.189073953\)
\(a_{96}=+0.153369910\) \(a_{97}=+1.274361950\) \(a_{98}=+0.313513217\) \(a_{99}=-0.155059593\) \(a_{100}=+0.099975586\)

Showing 100 of 220 available coefficients

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