Properties

Level $13$
Weight $0$
Character 13.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 7.44755875439 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.764193892\) \(a_{3}=+1.578268181\) \(a_{4}=-0.416007696\) \(a_{5}=-1.367549152\)
\(a_{6}=+1.206102903\) \(a_{7}=-1.728517767\) \(a_{8}=-1.082104432\) \(a_{9}=+1.490930451\) \(a_{10}=-1.045072708\)
\(a_{11}=+0.121063246\) \(a_{12}=-0.656571709\) \(a_{13}=+0.277350098\) \(a_{14}=-1.320922719\) \(a_{15}=-2.158359312\)
\(a_{16}=-0.410929901\) \(a_{17}=+0.053485653\) \(a_{18}=+1.139359944\) \(a_{19}=+0.392717878\) \(a_{20}=+0.568910972\)
\(a_{21}=-2.728064591\) \(a_{22}=+0.092515793\) \(a_{23}=+0.347630789\) \(a_{24}=-1.707850993\) \(a_{25}=+0.870190682\)
\(a_{26}=+0.211949250\) \(a_{27}=+0.774819910\) \(a_{28}=+0.719076693\) \(a_{29}=-1.217058987\) \(a_{30}=-1.649405002\)
\(a_{31}=-0.242327658\) \(a_{32}=+0.768074311\) \(a_{33}=+0.191070268\) \(a_{34}=+0.040873409\) \(a_{35}=+2.363833005\)
\(a_{36}=-0.620238542\) \(a_{37}=-1.950667850\) \(a_{38}=+0.300112604\) \(a_{39}=+0.437732834\) \(a_{40}=+1.479830998\)
\(a_{41}=+0.798663784\) \(a_{42}=-2.084770297\) \(a_{43}=+0.216195891\) \(a_{44}=-0.050363242\) \(a_{45}=-2.038920673\)
\(a_{46}=+0.265657326\) \(a_{47}=-0.651266865\) \(a_{48}=-0.648557588\) \(a_{49}=+1.987773670\) \(a_{50}=+0.664994404\)
\(a_{51}=+0.084414704\) \(a_{52}=-0.115379775\) \(a_{53}=-0.516212866\) \(a_{54}=+0.592112642\) \(a_{55}=-0.165559939\)
\(a_{56}=+1.870436736\) \(a_{57}=+0.619814132\) \(a_{58}=-0.930069044\) \(a_{59}=-1.341653467\) \(a_{60}=+0.897894084\)
\(a_{61}=+0.359183269\) \(a_{62}=-0.185185316\) \(a_{63}=-2.577099773\) \(a_{64}=+0.997887598\) \(a_{65}=-0.379289891\)
\(a_{66}=+0.146014732\) \(a_{67}=-0.124675202\) \(a_{68}=-0.022250443\) \(a_{69}=+0.548654614\) \(a_{70}=+1.806426744\)
\(a_{71}=-1.189407810\) \(a_{72}=-1.613342448\) \(a_{73}=-0.026356861\) \(a_{74}=-1.490688456\) \(a_{75}=+1.373394265\)
\(a_{76}=-0.163373660\) \(a_{77}=-0.209259971\) \(a_{78}=+0.334512758\) \(a_{79}=+1.849754702\) \(a_{80}=+0.561966838\)
\(a_{81}=-0.268056842\) \(a_{82}=+0.610333985\) \(a_{83}=+0.222820367\) \(a_{84}=+1.134895865\) \(a_{85}=-0.073144259\)
\(a_{86}=+0.165215580\) \(a_{87}=-1.920845473\) \(a_{88}=-0.131003075\) \(a_{89}=+0.738911236\) \(a_{90}=-1.558130724\)
\(a_{91}=-0.479404571\) \(a_{92}=-0.144617084\) \(a_{93}=-0.382458031\) \(a_{94}=-0.497694160\) \(a_{95}=-0.537061002\)
\(a_{96}=+1.212227246\) \(a_{97}=-0.925920328\) \(a_{98}=+1.519044496\) \(a_{99}=+0.180496879\) \(a_{100}=-0.362006021\)

Showing 100 of 546 available coefficients

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