Properties

Level $18$
Weight $0$
Character 18.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 18 = 2 \cdot 3^{2} \)
Weight: \( 0 \)
Character: 18.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 9.46886989067 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-0.285043562\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.162139289\) \(a_{8}=+0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-0.201556236\)
\(a_{11}=+0.309776512\) \(a_{12}=+0.000000000\) \(a_{13}=-1.013516525\) \(a_{14}=-0.114649791\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.742076554\) \(a_{18}=+0.000000000\) \(a_{19}=+1.341321791\) \(a_{20}=-0.142521781\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.219045072\) \(a_{23}=+0.421794355\) \(a_{24}=+0.000000000\) \(a_{25}=-0.918750168\)
\(a_{26}=-0.716664408\) \(a_{27}=+0.000000000\) \(a_{28}=-0.081069645\) \(a_{29}=-0.711249477\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.254037569\) \(a_{32}=+0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-1.231834144\) \(a_{35}=+0.046216761\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.653455686\) \(a_{38}=+0.948457734\) \(a_{39}=+0.000000000\) \(a_{40}=-0.100778118\)
\(a_{41}=-0.317580797\) \(a_{42}=+0.000000000\) \(a_{43}=-0.864967876\) \(a_{44}=+0.154888256\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.298253649\) \(a_{47}=-1.122012900\) \(a_{48}=+0.000000000\) \(a_{49}=-0.973710851\) \(a_{50}=-0.649654474\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.506758263\) \(a_{53}=+0.887021324\) \(a_{54}=+0.000000000\) \(a_{55}=-0.088299800\)
\(a_{56}=-0.057324895\) \(a_{57}=+0.000000000\) \(a_{58}=-0.502929329\) \(a_{59}=+1.727671858\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.694372350\) \(a_{62}=-0.886738469\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=+0.288896360\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.013269105\) \(a_{68}=-0.871038277\) \(a_{69}=+0.000000000\) \(a_{70}=+0.032680185\)
\(a_{71}=+0.358777270\) \(a_{72}=+0.000000000\) \(a_{73}=-1.579703013\) \(a_{74}=-1.169169728\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.670660895\) \(a_{77}=-0.050226943\) \(a_{78}=+0.000000000\) \(a_{79}=+0.383856418\) \(a_{80}=-0.071260890\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.224563535\) \(a_{83}=+1.096136445\) \(a_{84}=+0.000000000\) \(a_{85}=+0.496567706\)
\(a_{86}=-0.611624651\) \(a_{87}=+0.000000000\) \(a_{88}=+0.109522536\) \(a_{89}=+1.834931719\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.164330850\) \(a_{92}=+0.210897178\) \(a_{93}=+0.000000000\) \(a_{94}=-0.793382930\) \(a_{95}=-0.382335141\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.333894278\) \(a_{98}=-0.688517546\) \(a_{99}=+0.000000000\) \(a_{100}=-0.459375084\)

Showing 100 of 250 available coefficients

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