Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 18.4370784198 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.053049325\) \(a_{4}=+0.500000000\) \(a_{5}=-1.490885079\)
\(a_{6}=-0.744618319\) \(a_{7}=+1.156612154\) \(a_{8}=-0.353553391\) \(a_{9}=+0.108912881\) \(a_{10}=+1.054214950\)
\(a_{11}=+0.173690843\) \(a_{12}=+0.526524663\) \(a_{13}=-0.473057566\) \(a_{14}=-0.817848298\) \(a_{15}=-1.569975526\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.321686760\) \(a_{18}=-0.077013037\) \(a_{19}=-0.673427974\) \(a_{20}=-0.745442540\)
\(a_{21}=+1.217969648\) \(a_{22}=-0.122817973\) \(a_{23}=-1.212806375\) \(a_{24}=-0.372309160\) \(a_{25}=+1.222738318\)
\(a_{26}=+0.334502213\) \(a_{27}=-0.938358689\) \(a_{28}=+0.578306077\) \(a_{29}=-1.301833016\) \(a_{30}=+1.110140341\)
\(a_{31}=-0.075644517\) \(a_{32}=-0.176776696\) \(a_{33}=+0.182905025\) \(a_{34}=+0.934573671\) \(a_{35}=-1.724375802\)
\(a_{36}=+0.054456441\) \(a_{37}=+0.472371222\) \(a_{38}=+0.476185487\) \(a_{39}=-0.498152951\) \(a_{40}=+0.527107475\)
\(a_{41}=+0.462240548\) \(a_{42}=-0.861234598\) \(a_{43}=-0.527143839\) \(a_{44}=+0.086845421\) \(a_{45}=-0.162376589\)
\(a_{46}=+0.857583613\) \(a_{47}=+0.187745911\) \(a_{48}=+0.263262332\) \(a_{49}=+0.337751675\) \(a_{50}=-0.864606557\)
\(a_{51}=-1.391801351\) \(a_{52}=-0.236528783\) \(a_{53}=+1.656928046\) \(a_{54}=+0.663519793\) \(a_{55}=-0.258953086\)
\(a_{56}=-0.408924149\) \(a_{57}=-0.709152874\) \(a_{58}=+0.920534954\) \(a_{59}=+0.343535399\) \(a_{60}=-0.784987764\)
\(a_{61}=-0.551754679\) \(a_{62}=+0.053488751\) \(a_{63}=+0.125969962\) \(a_{64}=+0.125000000\) \(a_{65}=+0.705274467\)
\(a_{66}=-0.129333383\) \(a_{67}=+1.016314955\) \(a_{68}=-0.660843381\) \(a_{69}=-1.277144935\) \(a_{70}=+1.219317824\)
\(a_{71}=-1.447845387\) \(a_{72}=-0.038506518\) \(a_{73}=+0.602649000\) \(a_{74}=-0.334016894\) \(a_{75}=+1.287603761\)
\(a_{76}=-0.336713987\) \(a_{77}=+0.200892940\) \(a_{78}=+0.352247330\) \(a_{79}=+0.026000673\) \(a_{80}=-0.372721270\)
\(a_{81}=-1.097050865\) \(a_{82}=-0.326853426\) \(a_{83}=-0.758418355\) \(a_{84}=+0.608984825\) \(a_{85}=+1.970483070\)
\(a_{86}=+0.372746984\) \(a_{87}=-1.370894379\) \(a_{88}=-0.061408986\) \(a_{89}=+0.841815288\) \(a_{90}=+0.114817587\)
\(a_{91}=-0.547144131\) \(a_{92}=-0.606403188\) \(a_{93}=-0.079657407\) \(a_{94}=-0.132756407\) \(a_{95}=+1.004003718\)
\(a_{96}=-0.186154580\) \(a_{97}=-0.930016835\) \(a_{98}=-0.238826500\) \(a_{99}=+0.018917170\) \(a_{100}=+0.611369160\)

Showing 100 of 1228 available coefficients

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