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: \( 3.53600209294 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.256003345\) \(a_{3}=+0.000000000\) \(a_{4}=+0.577544402\) \(a_{5}=-0.740055765\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.853500122\) \(a_{8}=+0.530605644\) \(a_{9}=+0.000000000\) \(a_{10}=+0.929512516\)
\(a_{11}=-0.905072463\) \(a_{12}=+0.000000000\) \(a_{13}=+0.046679518\) \(a_{14}=+1.071999007\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.243986866\) \(a_{17}=-0.633121893\) \(a_{18}=+0.000000000\) \(a_{19}=+0.508962441\) \(a_{20}=-0.427415065\)
\(a_{21}=+0.000000000\) \(a_{22}=+1.136774040\) \(a_{23}=+1.026071047\) \(a_{24}=+0.000000000\) \(a_{25}=-0.452317459\)
\(a_{26}=-0.058629651\) \(a_{27}=+0.000000000\) \(a_{28}=-0.492934249\) \(a_{29}=-1.409110393\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.048355160\) \(a_{32}=+1.031846020\) \(a_{33}=+0.000000000\) \(a_{34}=+0.795203215\) \(a_{35}=+0.631637685\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.305699763\) \(a_{38}=-0.639258527\) \(a_{39}=+0.000000000\) \(a_{40}=-0.392677766\)
\(a_{41}=-0.365914423\) \(a_{42}=+0.000000000\) \(a_{43}=+0.117304677\) \(a_{44}=-0.522719535\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.288748662\) \(a_{47}=+1.303294713\) \(a_{48}=+0.000000000\) \(a_{49}=-0.271537542\) \(a_{50}=+0.568112249\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.026959494\) \(a_{53}=-1.273859148\) \(a_{54}=+0.000000000\) \(a_{55}=+0.669804090\)
\(a_{56}=-0.452871970\) \(a_{57}=+0.000000000\) \(a_{58}=+1.769847524\) \(a_{59}=-0.014440031\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.023483810\) \(a_{62}=+1.316737733\) \(a_{63}=+0.000000000\) \(a_{64}=-0.052015214\) \(a_{65}=-0.034545094\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.462149902\) \(a_{68}=-0.365654882\) \(a_{69}=+0.000000000\) \(a_{70}=-0.793339151\)
\(a_{71}=+0.096006694\) \(a_{72}=+0.000000000\) \(a_{73}=-0.553484025\) \(a_{74}=-1.639963272\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.293948409\) \(a_{77}=+0.772479461\) \(a_{78}=+0.000000000\) \(a_{79}=+1.333995049\) \(a_{80}=+0.920619651\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.459589736\) \(a_{83}=+0.698573979\) \(a_{84}=+0.000000000\) \(a_{85}=+0.468545514\)
\(a_{86}=-0.147335029\) \(a_{87}=+0.000000000\) \(a_{88}=-0.480236564\) \(a_{89}=-1.847120386\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.039840978\) \(a_{92}=+0.592601582\) \(a_{93}=+0.000000000\) \(a_{94}=-1.636942502\) \(a_{95}=-0.376661301\)
\(a_{96}=+0.000002294\) \(a_{97}=+0.460206283\) \(a_{98}=+0.341054218\) \(a_{99}=+0.000001033\) \(a_{100}=-0.261233392\)

Showing 100 of 1500 available coefficients

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