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: \( 14.4354503421 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.555194554\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.392581834\) \(a_{7}=+0.283360394\) \(a_{8}=-0.353553391\) \(a_{9}=-0.691759008\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.015196577\) \(a_{12}=-0.277597277\) \(a_{13}=-0.354935385\) \(a_{14}=-0.200366056\) \(a_{15}=-0.248290553\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.453974471\) \(a_{18}=+0.489147485\) \(a_{19}=+0.397805740\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.157320147\) \(a_{22}=-0.010745602\) \(a_{23}=-0.158607526\) \(a_{24}=+0.196290917\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.250977217\) \(a_{27}=+0.939255387\) \(a_{28}=+0.141680197\) \(a_{29}=+1.079601760\) \(a_{30}=+0.175567933\)
\(a_{31}=+0.645029753\) \(a_{32}=-0.176776695\) \(a_{33}=-0.008437057\) \(a_{34}=-0.321008427\) \(a_{35}=+0.126722621\)
\(a_{36}=-0.345879504\) \(a_{37}=+1.069811907\) \(a_{38}=-0.281291136\) \(a_{39}=+0.197058192\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.267528158\) \(a_{42}=+0.111242143\) \(a_{43}=-1.695119030\) \(a_{44}=+0.007598288\) \(a_{45}=-0.309364033\)
\(a_{46}=+0.112152458\) \(a_{47}=-1.592096401\) \(a_{48}=-0.138798638\) \(a_{49}=-0.919706887\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.252044154\) \(a_{52}=-0.177467692\) \(a_{53}=+1.461544421\) \(a_{54}=-0.664153853\) \(a_{55}=+0.006796116\)
\(a_{56}=-0.100183028\) \(a_{57}=-0.220859580\) \(a_{58}=-0.763393726\) \(a_{59}=-0.665649384\) \(a_{60}=-0.124145276\)
\(a_{61}=-1.076699372\) \(a_{62}=-0.456104912\) \(a_{63}=-0.196017105\) \(a_{64}=+0.125000000\) \(a_{65}=-0.158731930\)
\(a_{66}=+0.005965900\) \(a_{67}=+1.303756659\) \(a_{68}=+0.226987236\) \(a_{69}=+0.088058035\) \(a_{70}=-0.089606424\)
\(a_{71}=+0.369162602\) \(a_{72}=+0.244573743\) \(a_{73}=-0.352103973\) \(a_{74}=-0.756471254\) \(a_{75}=-0.111038911\)
\(a_{76}=+0.198902870\) \(a_{77}=+0.004306108\) \(a_{78}=-0.139341184\) \(a_{79}=-1.393188203\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.170289532\) \(a_{82}=+0.896277756\) \(a_{83}=-0.720323586\) \(a_{84}=-0.078660074\) \(a_{85}=+0.203023556\)
\(a_{86}=+1.198630161\) \(a_{87}=-0.599389018\) \(a_{88}=-0.005372801\) \(a_{89}=-0.583892242\) \(a_{90}=+0.218753406\)
\(a_{91}=-0.100574629\) \(a_{92}=-0.079303763\) \(a_{93}=-0.358117006\) \(a_{94}=+1.125782161\) \(a_{95}=+0.177904135\)
\(a_{96}=+0.098145458\) \(a_{97}=-0.097901644\) \(a_{98}=+0.650330977\) \(a_{99}=-0.010512365\) \(a_{100}=+0.099975586\)

Showing 100 of 166 available coefficients

Rows: Cols: