Properties

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

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 16.042693059 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.360608935\)
\(a_{6}=+0.408248290\) \(a_{7}=-1.804737378\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.962095805\)
\(a_{11}=+0.174747052\) \(a_{12}=-0.288675135\) \(a_{13}=+0.444488360\) \(a_{14}=+1.276142038\) \(a_{15}=-0.785547935\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.442300487\) \(a_{18}=-0.235702260\) \(a_{19}=-1.218732311\) \(a_{20}=+0.680304468\)
\(a_{21}=+1.041965611\) \(a_{22}=-0.123564826\) \(a_{23}=+1.280383085\) \(a_{24}=+0.204124145\) \(a_{25}=+0.851256674\)
\(a_{26}=-0.314300734\) \(a_{27}=-0.192450090\) \(a_{28}=-0.902368689\) \(a_{29}=-0.532005666\) \(a_{30}=+0.555466272\)
\(a_{31}=-0.180493671\) \(a_{32}=-0.176776695\) \(a_{33}=-0.100890258\) \(a_{34}=-1.019860455\) \(a_{35}=-2.455541802\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.966062367\) \(a_{38}=+0.861773882\) \(a_{39}=-0.256625475\) \(a_{40}=-0.481047902\)
\(a_{41}=+0.147362621\) \(a_{42}=-0.736780949\) \(a_{43}=-0.228383983\) \(a_{44}=+0.087373526\) \(a_{45}=+0.453536312\)
\(a_{46}=-0.905367562\) \(a_{47}=-1.534132509\) \(a_{48}=-0.144337567\) \(a_{49}=+2.257077003\) \(a_{50}=-0.601929367\)
\(a_{51}=-0.832712574\) \(a_{52}=+0.222244180\) \(a_{53}=-0.552380035\) \(a_{54}=+0.136082763\) \(a_{55}=+0.237762401\)
\(a_{56}=+0.638071019\) \(a_{57}=+0.703635428\) \(a_{58}=+0.376184814\) \(a_{59}=-1.423468027\) \(a_{60}=-0.392773967\)
\(a_{61}=-0.319673308\) \(a_{62}=+0.127628298\) \(a_{63}=-0.601579126\) \(a_{64}=+0.125000000\) \(a_{65}=+0.604774835\)
\(a_{66}=+0.071340185\) \(a_{67}=-0.459122550\) \(a_{68}=+0.721150244\) \(a_{69}=-0.739229519\) \(a_{70}=+1.736330260\)
\(a_{71}=+0.121303276\) \(a_{72}=-0.117851130\) \(a_{73}=-0.821226800\) \(a_{74}=+0.683109250\) \(a_{75}=-0.491473270\)
\(a_{76}=-0.609366156\) \(a_{77}=-0.315372537\) \(a_{78}=+0.181461613\) \(a_{79}=-0.950327000\) \(a_{80}=+0.340152234\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.104201108\) \(a_{83}=-0.612526000\) \(a_{84}=+0.520982805\) \(a_{85}=+1.962406930\)
\(a_{86}=+0.161491863\) \(a_{87}=+0.307153615\) \(a_{88}=-0.061782413\) \(a_{89}=-0.729700029\) \(a_{90}=-0.320698602\)
\(a_{91}=-0.802184758\) \(a_{92}=+0.640191542\) \(a_{93}=+0.104208069\) \(a_{94}=+1.084795500\) \(a_{95}=-1.658218072\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.089996338\) \(a_{98}=-1.595994454\) \(a_{99}=+0.058249017\) \(a_{100}=+0.425628337\)

Showing all 100 available coefficients

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