Properties

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

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.53600209294 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.256003345\) \(a_{3}=+0.000000000\) \(a_{4}=+0.577544402\) \(a_{5}=+0.740055765\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.853500122\) \(a_{8}=-0.530605644\) \(a_{9}=+0.000000000\) \(a_{10}=+0.929512516\)
\(a_{11}=+0.905072463\) \(a_{12}=+0.000000000\) \(a_{13}=+0.046679518\) \(a_{14}=-1.071999007\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.243986866\) \(a_{17}=+0.633121893\) \(a_{18}=+0.000000000\) \(a_{19}=+0.508962440\) \(a_{20}=+0.427415064\)
\(a_{21}=+0.000000000\) \(a_{22}=+1.136774042\) \(a_{23}=-1.026071043\) \(a_{24}=+0.000000000\) \(a_{25}=-0.452317467\)
\(a_{26}=+0.058629628\) \(a_{27}=+0.000000000\) \(a_{28}=-0.492934207\) \(a_{29}=+1.409110524\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.048355396\) \(a_{32}=-1.031846020\) \(a_{33}=+0.000000000\) \(a_{34}=+0.795203215\) \(a_{35}=-0.631637685\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.305699763\) \(a_{38}=+0.639258527\) \(a_{39}=+0.000000000\) \(a_{40}=-0.392677766\)
\(a_{41}=+0.365914423\) \(a_{42}=+0.000000000\) \(a_{43}=+0.117304677\) \(a_{44}=+0.522719534\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.288748662\) \(a_{47}=-1.303294712\) \(a_{48}=+0.000000000\) \(a_{49}=-0.271537542\) \(a_{50}=-0.568112249\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.026959494\) \(a_{53}=+1.273859142\) \(a_{54}=+0.000000000\) \(a_{55}=+0.669804093\)
\(a_{56}=+0.452871984\) \(a_{57}=+0.000000000\) \(a_{58}=+1.769847515\) \(a_{59}=+0.014440004\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.023483803\) \(a_{62}=-1.316737853\) \(a_{63}=+0.000000000\) \(a_{64}=-0.052015193\) \(a_{65}=+0.034545680\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.462149987\) \(a_{68}=+0.365657257\) \(a_{69}=+0.000000000\) \(a_{70}=-0.793339021\)
\(a_{71}=-0.096001859\) \(a_{72}=+0.000000000\) \(a_{73}=-0.553484025\) \(a_{74}=+1.639963270\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.293948408\) \(a_{77}=-0.772479457\) \(a_{78}=+0.000000000\) \(a_{79}=+1.333995050\) \(a_{80}=-0.920619654\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.459589739\) \(a_{83}=-0.698574015\) \(a_{84}=+0.000000000\) \(a_{85}=+0.468545508\)
\(a_{86}=+0.147335091\) \(a_{87}=+0.000000000\) \(a_{88}=-0.480236559\) \(a_{89}=+1.847120212\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.039840975\) \(a_{92}=-0.592601572\) \(a_{93}=+0.000000000\) \(a_{94}=-1.636942512\) \(a_{95}=+0.376659872\)
\(a_{96}=-0.000002286\) \(a_{97}=+0.460206299\) \(a_{98}=-0.341049893\) \(a_{99}=-0.000001028\) \(a_{100}=-0.261233423\)

Showing 100 of 1500 available coefficients

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