Properties

Level $9$
Weight $0$
Character 9.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 11.728024516 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.627908079\) \(a_{3}=+0.000000000\) \(a_{4}=-0.605731445\) \(a_{5}=+0.337954619\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.422016282\) \(a_{8}=+1.008251746\) \(a_{9}=+0.000000000\) \(a_{10}=-0.212204436\)
\(a_{11}=-0.651460357\) \(a_{12}=+0.000000000\) \(a_{13}=+1.426865361\) \(a_{14}=+0.264987433\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.027357972\) \(a_{17}=+1.261451510\) \(a_{18}=+0.000000000\) \(a_{19}=+0.613740611\) \(a_{20}=-0.204709740\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.409057221\) \(a_{23}=-1.623594130\) \(a_{24}=+0.000000000\) \(a_{25}=-0.885786675\)
\(a_{26}=-0.895940287\) \(a_{27}=+0.000000000\) \(a_{28}=+0.255628533\) \(a_{29}=-1.740581407\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.055845253\) \(a_{32}=-0.991073457\) \(a_{33}=+0.000000000\) \(a_{34}=-0.792075586\) \(a_{35}=-0.142622367\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.573890537\) \(a_{38}=-0.385372772\) \(a_{39}=+0.000000000\) \(a_{40}=+0.340743574\)
\(a_{41}=-0.833600940\) \(a_{42}=+0.000000000\) \(a_{43}=+0.216110437\) \(a_{44}=+0.394607786\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.019473907\) \(a_{47}=-0.249270827\) \(a_{48}=+0.000000000\) \(a_{49}=-0.821874117\) \(a_{50}=+0.556145868\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.864173499\) \(a_{53}=-0.783803502\) \(a_{54}=+0.000000000\) \(a_{55}=-0.219651271\)
\(a_{56}=-0.426255783\) \(a_{57}=+0.000000000\) \(a_{58}=+1.094910480\) \(a_{59}=+1.230612640\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.152447472\) \(a_{62}=-0.671866038\) \(a_{63}=+0.000000000\) \(a_{64}=+0.673786774\) \(a_{65}=+0.456038446\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.885454892\) \(a_{68}=-0.835808291\) \(a_{69}=+0.000000000\) \(a_{70}=+0.274718486\)

Showing all 70 available coefficients

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