Properties

Level 10
Weight 0
Character 10.1
Symmetry odd
Fricke sign +1

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: \(+1\)
Spectral parameter: \( 21.4106668814 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.998141554\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.705792661\) \(a_{7}=-1.342707789\) \(a_{8}=+0.353553391\) \(a_{9}=-0.003713439\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.266508738\) \(a_{12}=+0.499070777\) \(a_{13}=+1.197713450\) \(a_{14}=-0.949437783\) \(a_{15}=+0.446382473\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.069359012\) \(a_{18}=-0.002625798\) \(a_{19}=-0.947891856\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.340212439\) \(a_{22}=-0.895556917\) \(a_{23}=+0.858368339\) \(a_{24}=+0.352896331\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.846911302\) \(a_{27}=-1.001848091\) \(a_{28}=-0.671353895\) \(a_{29}=-0.811445338\) \(a_{30}=+0.315640074\)
\(a_{31}=-0.938913403\) \(a_{32}=+0.176776695\) \(a_{33}=-1.264155000\) \(a_{34}=+0.756151009\) \(a_{35}=-0.600477178\)
\(a_{36}=-0.001856719\) \(a_{37}=-0.665793955\) \(a_{38}=-0.670260759\) \(a_{39}=+1.195487564\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.284096424\) \(a_{42}=-0.947673304\) \(a_{43}=-0.642367711\) \(a_{44}=-0.633254369\) \(a_{45}=-0.001660700\)
\(a_{46}=+0.606958073\) \(a_{47}=-1.692308121\) \(a_{48}=+0.249535388\) \(a_{49}=+0.802864207\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.067371666\) \(a_{52}=+0.598856725\) \(a_{53}=-1.658525989\) \(a_{54}=-0.708413579\) \(a_{55}=-0.566399926\)
\(a_{56}=-0.474718891\) \(a_{57}=-0.946130250\) \(a_{58}=-0.573778501\) \(a_{59}=-0.822657882\) \(a_{60}=+0.223191237\)
\(a_{61}=+0.785139736\) \(a_{62}=-0.663912034\) \(a_{63}=+0.004986063\) \(a_{64}=+0.125000000\) \(a_{65}=+0.535633738\)
\(a_{66}=-0.893892573\) \(a_{67}=-1.837608402\) \(a_{68}=+0.534679506\) \(a_{69}=+0.856773108\) \(a_{70}=-0.424601485\)
\(a_{71}=+0.269358105\) \(a_{72}=-0.001312899\) \(a_{73}=+1.219459131\) \(a_{74}=-0.470787420\) \(a_{75}=+0.199628311\)
\(a_{76}=-0.473945928\) \(a_{77}=+1.700551148\) \(a_{78}=+0.845337363\) \(a_{79}=+0.316580429\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.996272772\) \(a_{82}=-0.200886508\) \(a_{83}=+1.623302301\) \(a_{84}=-0.670106219\) \(a_{85}=+0.478231889\)
\(a_{86}=-0.454222564\) \(a_{87}=-0.809937310\) \(a_{88}=-0.447778459\) \(a_{89}=+1.565204103\) \(a_{90}=-0.001174292\)
\(a_{91}=-1.608179178\) \(a_{92}=+0.429184170\) \(a_{93}=-0.937168483\) \(a_{94}=-1.196642548\) \(a_{95}=-0.423910125\)
\(a_{96}=+0.176448165\) \(a_{97}=-1.041297254\) \(a_{98}=+0.567710725\) \(a_{99}=+0.004703103\) \(a_{100}=+0.099975586\)

Showing 100 of 198 available coefficients

Rows: Cols: