Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 16.1350656627 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.118041446\)
\(a_{6}=-0.408248290\) \(a_{7}=+1.576501296\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.790574688\)
\(a_{11}=-0.548590932\) \(a_{12}=-0.288675135\) \(a_{13}=-1.480769761\) \(a_{14}=+1.114754757\) \(a_{15}=-0.645501530\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.839544952\) \(a_{18}=+0.235702260\) \(a_{19}=+1.469956201\) \(a_{20}=+0.559020723\)
\(a_{21}=-0.910193447\) \(a_{22}=-0.387912368\) \(a_{23}=-0.189378086\) \(a_{24}=-0.204124145\) \(a_{25}=+0.250016674\)
\(a_{26}=-1.047062340\) \(a_{27}=-0.192450090\) \(a_{28}=+0.788250648\) \(a_{29}=+1.465750561\) \(a_{30}=-0.456438509\)
\(a_{31}=+0.033775590\) \(a_{32}=+0.176776695\) \(a_{33}=+0.316729122\) \(a_{34}=+0.593647929\) \(a_{35}=+1.762593788\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.003106245\) \(a_{38}=+1.039415998\) \(a_{39}=+0.854922820\) \(a_{40}=+0.395287344\)
\(a_{41}=-0.900206747\) \(a_{42}=-0.643603959\) \(a_{43}=+1.411857779\) \(a_{44}=-0.274295466\) \(a_{45}=+0.372680482\)
\(a_{46}=-0.133910529\) \(a_{47}=+0.697585435\) \(a_{48}=-0.144337567\) \(a_{49}=+1.485356335\) \(a_{50}=+0.176788486\)
\(a_{51}=-0.484711504\) \(a_{52}=-0.740384881\) \(a_{53}=-0.035773340\) \(a_{54}=-0.136082763\) \(a_{55}=-0.613347399\)
\(a_{56}=+0.557377378\) \(a_{57}=-0.848679608\) \(a_{58}=+1.036442161\) \(a_{59}=-0.234521100\) \(a_{60}=-0.322750765\)
\(a_{61}=+1.800217500\) \(a_{62}=+0.023882948\) \(a_{63}=+0.525500432\) \(a_{64}=+0.125000000\) \(a_{65}=-1.655561965\)
\(a_{66}=+0.223961310\) \(a_{67}=-1.564664001\) \(a_{68}=+0.419772476\) \(a_{69}=+0.109337489\) \(a_{70}=+1.246342020\)
\(a_{71}=-0.528389998\) \(a_{72}=+0.117851130\) \(a_{73}=-0.339500010\) \(a_{74}=+0.002196447\) \(a_{75}=-0.144347194\)
\(a_{76}=+0.734978100\) \(a_{77}=-0.864854315\) \(a_{78}=+0.604521724\) \(a_{79}=+0.830400467\) \(a_{80}=+0.279510361\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.636542295\) \(a_{83}=-1.099000000\) \(a_{84}=-0.455096724\) \(a_{85}=+0.938646052\)
\(a_{86}=+0.998334210\) \(a_{87}=-0.846251481\) \(a_{88}=-0.193956184\) \(a_{89}=+0.480010986\) \(a_{90}=+0.263524896\)
\(a_{91}=-2.334435448\) \(a_{92}=-0.094689043\) \(a_{93}=-0.019500346\) \(a_{94}=+0.493267392\) \(a_{95}=+1.643471956\)
\(a_{96}=-0.102062073\)

Showing all 96 available coefficients

Rows: Cols: