Properties

Level 10
Weight 0
Character 10.1
Symmetry even
Fricke sign -1

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: \(-1\)
Spectral parameter: \( 13.2036691317 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.120084055\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.084912249\) \(a_{7}=+0.364894062\) \(a_{8}=+0.353553391\) \(a_{9}=-0.985579820\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.502834787\) \(a_{12}=+0.060042027\) \(a_{13}=-0.081626489\) \(a_{14}=+0.258019066\) \(a_{15}=-0.053703222\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.994651782\) \(a_{18}=-0.696910174\) \(a_{19}=-1.353216184\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.043817959\) \(a_{22}=+0.355557887\) \(a_{23}=+0.870925053\) \(a_{24}=+0.042456125\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.057718644\) \(a_{27}=-0.238436475\) \(a_{28}=+0.182447031\) \(a_{29}=-1.101926243\) \(a_{30}=-0.037973912\)
\(a_{31}=+0.320578233\) \(a_{32}=+0.176776695\) \(a_{33}=+0.060382440\) \(a_{34}=-0.703325020\) \(a_{35}=-0.163185586\)
\(a_{36}=-0.492789910\) \(a_{37}=-1.055333999\) \(a_{38}=-0.956868340\) \(a_{39}=-0.009802040\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.943484714\) \(a_{42}=+0.030983976\) \(a_{43}=-0.282040871\) \(a_{44}=+0.251417393\) \(a_{45}=+0.440764695\)
\(a_{46}=+0.615837011\) \(a_{47}=-1.061162262\) \(a_{48}=+0.030021014\) \(a_{49}=-0.866852323\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.119441819\) \(a_{52}=-0.040813245\) \(a_{53}=-0.654916349\) \(a_{54}=-0.168600049\) \(a_{55}=-0.224874553\)
\(a_{56}=+0.129009533\) \(a_{57}=-0.162499686\) \(a_{58}=-0.779179519\) \(a_{59}=+1.167357148\) \(a_{60}=-0.026851611\)
\(a_{61}=-0.594876402\) \(a_{62}=+0.226683043\) \(a_{63}=-0.359632224\) \(a_{64}=+0.125000000\) \(a_{65}=+0.036504476\)
\(a_{66}=+0.042696833\) \(a_{67}=+1.343225978\) \(a_{68}=-0.497325891\) \(a_{69}=+0.104584212\) \(a_{70}=-0.115389634\)
\(a_{71}=-0.110043225\) \(a_{72}=-0.348455087\) \(a_{73}=+0.370182913\) \(a_{74}=-0.746233827\) \(a_{75}=+0.024016811\)
\(a_{76}=-0.676608092\) \(a_{77}=+0.183481428\) \(a_{78}=-0.006931089\) \(a_{79}=-0.365849939\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.956947399\) \(a_{82}=-1.374251220\) \(a_{83}=+1.089062392\) \(a_{84}=+0.021908979\) \(a_{85}=+0.444821800\)
\(a_{86}=-0.199433012\) \(a_{87}=-0.132323780\) \(a_{88}=+0.177778944\) \(a_{89}=+0.949944156\) \(a_{90}=+0.311667705\)
\(a_{91}=-0.029785002\) \(a_{92}=+0.435462526\) \(a_{93}=+0.038496305\) \(a_{94}=-0.750355032\) \(a_{95}=+0.605176675\)
\(a_{96}=+0.021228062\) \(a_{97}=-1.699299213\) \(a_{98}=-0.612957156\) \(a_{99}=-0.495583650\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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