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: \( 9.0800693497 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.533986110\) \(a_{3}=+0.000000000\) \(a_{4}=+1.353113385\) \(a_{5}=+1.292302536\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.624660334\) \(a_{8}=-0.541671027\) \(a_{9}=+0.000000000\) \(a_{10}=-1.982374140\)
\(a_{11}=-0.391087427\) \(a_{12}=+0.000000000\) \(a_{13}=+0.382324332\) \(a_{14}=+2.492206385\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.522197553\) \(a_{17}=+0.320927606\) \(a_{18}=+0.000000000\) \(a_{19}=-0.320785478\) \(a_{20}=+1.748631858\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.599922680\) \(a_{23}=+0.382129313\) \(a_{24}=+0.000000000\) \(a_{25}=+0.670045844\)
\(a_{26}=-0.586480215\) \(a_{27}=+0.000000000\) \(a_{28}=-2.198349643\) \(a_{29}=+0.538649026\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.626768885\) \(a_{32}=+1.342714820\) \(a_{33}=+0.000000000\) \(a_{34}=-0.492298491\) \(a_{35}=-2.099552670\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.064257484\) \(a_{38}=+0.492080469\) \(a_{39}=+0.000000000\) \(a_{40}=-0.700002865\)
\(a_{41}=+1.227251280\) \(a_{42}=+0.000000000\) \(a_{43}=-0.792676128\) \(a_{44}=-0.529185631\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.586181059\) \(a_{47}=-0.149178637\) \(a_{48}=+0.000000000\) \(a_{49}=+1.639521200\) \(a_{50}=-1.027841018\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.517328171\) \(a_{53}=+0.789768237\) \(a_{54}=+0.000000000\) \(a_{55}=-0.505403273\)
\(a_{56}=+0.880031432\) \(a_{57}=+0.000000000\) \(a_{58}=-0.826280124\) \(a_{59}=+0.545109069\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.798190861\) \(a_{62}=-2.495440873\) \(a_{63}=+0.000000000\) \(a_{64}=-1.537508330\) \(a_{65}=+0.494078704\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.698660941\) \(a_{68}=+0.434251439\) \(a_{69}=+0.000000000\) \(a_{70}=+3.220684631\)
\(a_{71}=+1.766156343\) \(a_{72}=+0.000000000\) \(a_{73}=-0.524248458\) \(a_{74}=-1.632556191\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.434059119\) \(a_{77}=+0.635384227\) \(a_{78}=+0.000000000\) \(a_{79}=+0.443076995\) \(a_{80}=-0.674837223\)
\(a_{81}=+0.000000000\) \(a_{82}=-1.882586430\) \(a_{83}=-1.263243241\) \(a_{84}=+0.000000000\) \(a_{85}=+0.414735590\)
\(a_{86}=+1.215954311\) \(a_{87}=+0.000000000\) \(a_{88}=+0.211840728\) \(a_{89}=+1.029331589\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.621147177\) \(a_{92}=+0.517064288\) \(a_{93}=+0.000000000\) \(a_{94}=+0.228837958\) \(a_{95}=-0.414551886\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.689971937\) \(a_{98}=-2.515002747\) \(a_{99}=+0.000000000\) \(a_{100}=+0.906648000\)

Showing 100 of 1500 available coefficients

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