Properties

Level $4$
Weight $0$
Character 4.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 5.87935415776 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.429270906\) \(a_{4}=+0.000000000\) \(a_{5}=-0.178782542\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.631662532\) \(a_{8}=+0.000000000\) \(a_{9}=+1.042815322\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.146881172\) \(a_{12}=+0.000000000\) \(a_{13}=+0.453179015\) \(a_{14}=+0.000000000\) \(a_{15}=+0.255528685\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.390250070\) \(a_{18}=+0.000000000\) \(a_{19}=-1.614812794\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.902816880\) \(a_{22}=+0.000000000\) \(a_{23}=+1.028470054\) \(a_{24}=+0.000000000\) \(a_{25}=-0.968036803\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.061194694\) \(a_{28}=+0.000000000\) \(a_{29}=-0.288409952\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.330172429\) \(a_{32}=+0.000000000\) \(a_{33}=+1.639203892\) \(a_{34}=+0.000000000\) \(a_{35}=+0.112930233\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.413819486\) \(a_{38}=+0.000000000\) \(a_{39}=-0.647715582\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.956706015\) \(a_{42}=+0.000000000\) \(a_{43}=+0.222109036\) \(a_{44}=+0.000000000\) \(a_{45}=-0.186437174\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.082803743\) \(a_{48}=+0.000000000\) \(a_{49}=-0.601002445\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.557773070\) \(a_{52}=+0.000000000\) \(a_{53}=-1.236373483\) \(a_{54}=+0.000000000\) \(a_{55}=+0.205042326\)
\(a_{56}=+0.000000000\) \(a_{57}=+2.308004942\) \(a_{58}=+0.000000000\) \(a_{59}=-0.576610126\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.073592637\) \(a_{62}=+0.000000000\) \(a_{63}=-0.658707367\) \(a_{64}=+0.000000000\) \(a_{65}=-0.081020496\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.258667034\) \(a_{68}=+0.000000000\) \(a_{69}=-1.469962325\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.567581432\) \(a_{72}=+0.000000000\) \(a_{73}=+0.395481806\) \(a_{74}=+0.000000000\) \(a_{75}=+1.383586838\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.724441866\) \(a_{78}=+0.000000000\) \(a_{79}=-1.348046782\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.955351526\) \(a_{82}=+0.000000000\) \(a_{83}=-0.187750759\) \(a_{84}=+0.000000000\) \(a_{85}=-0.069769900\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.412215954\) \(a_{88}=+0.000000000\) \(a_{89}=+0.395613277\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.286256199\) \(a_{92}=+0.000000000\) \(a_{93}=+0.471905834\) \(a_{94}=+0.000000000\) \(a_{95}=+0.288700311\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.503665893\) \(a_{98}=+0.000000000\) \(a_{99}=-1.195984900\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

Rows: Cols: