Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 31.8145560802 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.774352401\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.547549834\) \(a_{7}=+1.068963416\) \(a_{8}=-0.353553391\) \(a_{9}=-0.400378359\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.202590863\) \(a_{12}=+0.387176200\) \(a_{13}=+1.032574038\) \(a_{14}=-0.755871280\) \(a_{15}=-0.346300921\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.046053985\) \(a_{18}=+0.283110253\) \(a_{19}=-0.180477361\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.827754388\) \(a_{22}=+0.143253373\) \(a_{23}=+0.821890944\) \(a_{24}=-0.273774917\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.730140104\) \(a_{27}=-1.084386345\) \(a_{28}=+0.534481708\) \(a_{29}=-0.890737959\) \(a_{30}=+0.244871730\)
\(a_{31}=+1.589012145\) \(a_{32}=-0.176776695\) \(a_{33}=-0.156876721\) \(a_{34}=+0.032565085\) \(a_{35}=-0.478054973\)
\(a_{36}=-0.200189180\) \(a_{37}=+1.456729338\) \(a_{38}=+0.127616766\) \(a_{39}=+0.799576185\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.865962609\) \(a_{42}=-0.585310741\) \(a_{43}=-0.120445476\) \(a_{44}=-0.101295431\) \(a_{45}=+0.179054646\)
\(a_{46}=-0.581164660\) \(a_{47}=-1.586019612\) \(a_{48}=+0.193588100\) \(a_{49}=+0.142682784\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.035662014\) \(a_{52}=+0.516287019\) \(a_{53}=-0.223018355\) \(a_{54}=+0.766776938\) \(a_{55}=+0.090601388\)
\(a_{56}=-0.377935640\) \(a_{57}=-0.139753078\) \(a_{58}=+0.629846851\) \(a_{59}=+0.528040480\) \(a_{60}=-0.173150461\)
\(a_{61}=-0.285924824\) \(a_{62}=-1.123601263\) \(a_{63}=-0.427989818\) \(a_{64}=+0.125000000\) \(a_{65}=-0.461781148\)
\(a_{66}=+0.110928593\) \(a_{67}=+1.476179463\) \(a_{68}=-0.023026992\) \(a_{69}=+0.636433226\) \(a_{70}=+0.338035913\)
\(a_{71}=+0.180143547\) \(a_{72}=+0.141555126\) \(a_{73}=+1.379118240\) \(a_{74}=-1.030063193\) \(a_{75}=+0.154870480\)
\(a_{76}=-0.090238680\) \(a_{77}=-0.216562221\) \(a_{78}=-0.565385743\) \(a_{79}=+1.708557702\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.439318810\) \(a_{82}=+0.612328033\) \(a_{83}=-0.354575641\) \(a_{84}=+0.413877194\) \(a_{85}=+0.020595968\)
\(a_{86}=+0.085167813\) \(a_{87}=-0.689745077\) \(a_{88}=+0.071626686\) \(a_{89}=+1.428464498\) \(a_{90}=-0.126610754\)
\(a_{91}=+1.103783870\) \(a_{92}=+0.410945472\) \(a_{93}=+1.230455370\) \(a_{94}=+1.121485222\) \(a_{95}=+0.080711929\)
\(a_{96}=-0.136887458\) \(a_{97}=-0.671814172\) \(a_{98}=-0.100891964\) \(a_{99}=+0.081112997\) \(a_{100}=+0.099975586\)

Showing 100 of 256 available coefficients

Rows: Cols: