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: \( 7.78033646819 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.173212202\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213596\)
\(a_{6}=+0.829586304\) \(a_{7}=+1.327754185\) \(a_{8}=-0.353553391\) \(a_{9}=+0.376426871\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.307821200\) \(a_{12}=-0.586606101\) \(a_{13}=-0.953734545\) \(a_{14}=-0.938863988\) \(a_{15}=-0.524676447\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.467194687\) \(a_{18}=-0.266173993\) \(a_{19}=-1.336671565\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.557737411\) \(a_{22}=+0.217662458\) \(a_{23}=-0.507742080\) \(a_{24}=+0.414793152\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.674392164\) \(a_{27}=+0.731583604\) \(a_{28}=+0.663877093\) \(a_{29}=-1.749339215\) \(a_{30}=+0.371002273\)
\(a_{31}=-0.218533318\) \(a_{32}=-0.176776694\) \(a_{33}=+0.361139587\) \(a_{34}=-1.037463314\) \(a_{35}=+0.593789727\)
\(a_{36}=+0.188213436\) \(a_{37}=-1.750211833\) \(a_{38}=+0.945169542\) \(a_{39}=+1.118933036\) \(a_{40}=-0.158113955\)
\(a_{41}=-0.740017427\) \(a_{42}=+1.101486901\) \(a_{43}=-0.519393442\) \(a_{44}=-0.153910600\) \(a_{45}=+0.168343214\)
\(a_{46}=+0.359027868\) \(a_{47}=+0.596682929\) \(a_{48}=-0.293303050\) \(a_{49}=+0.762931176\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.721330710\) \(a_{52}=-0.476867273\) \(a_{53}=+0.074263218\) \(a_{54}=-0.517307727\) \(a_{55}=-0.137661826\)
\(a_{56}=-0.469431994\) \(a_{57}=+1.568199390\) \(a_{58}=+1.236969622\) \(a_{59}=-0.296050710\) \(a_{60}=-0.262338224\)
\(a_{61}=-1.024122931\) \(a_{62}=+0.154526391\) \(a_{63}=+0.499802353\) \(a_{64}=+0.125000000\) \(a_{65}=-0.426523056\)
\(a_{66}=-0.255364250\) \(a_{67}=+1.264397159\) \(a_{68}=+0.733597344\) \(a_{69}=+0.595689203\) \(a_{70}=-0.419872740\)
\(a_{71}=-0.446986942\) \(a_{72}=-0.133086998\) \(a_{73}=-1.711616763\) \(a_{74}=+1.237586649\) \(a_{75}=-0.234642452\)
\(a_{76}=-0.668335767\) \(a_{77}=-0.408710889\) \(a_{78}=-0.791205131\) \(a_{79}=+0.097741141\) \(a_{80}=+0.111803385\)
\(a_{81}=-1.234729651\) \(a_{82}=+0.523271333\) \(a_{83}=+1.212371802\) \(a_{84}=-0.778868705\) \(a_{85}=+0.656149411\)
\(a_{86}=+0.367266625\) \(a_{87}=+2.052346113\) \(a_{88}=+0.108831229\) \(a_{89}=+1.366177579\) \(a_{90}=-0.119036629\)
\(a_{91}=-1.266325034\) \(a_{92}=-0.253871039\) \(a_{93}=+0.256385955\) \(a_{94}=-0.421918544\) \(a_{95}=-0.597777698\)
\(a_{96}=+0.207396578\) \(a_{97}=-1.266651570\) \(a_{98}=-0.539473807\) \(a_{99}=-0.115872172\) \(a_{100}=+0.100000003\)

Showing 100 of 2000 available coefficients

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