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: \( 9.08006934969 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.533986110\) \(a_{3}=+0.000000000\) \(a_{4}=+1.353113388\) \(a_{5}=-1.292302540\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.624660339\) \(a_{8}=+0.541671031\) \(a_{9}=+0.000000000\) \(a_{10}=-1.982374144\)
\(a_{11}=+0.391087431\) \(a_{12}=+0.000000000\) \(a_{13}=+0.382324335\) \(a_{14}=-2.492206395\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.522197550\) \(a_{17}=-0.320927604\) \(a_{18}=+0.000000000\) \(a_{19}=-0.320785481\) \(a_{20}=-1.748631867\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.599922695\) \(a_{23}=-0.382129316\) \(a_{24}=+0.000000000\) \(a_{25}=+0.670045844\)
\(a_{26}=+0.586480220\) \(a_{27}=+0.000000000\) \(a_{28}=-2.198349650\) \(a_{29}=-0.538649032\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.626768893\) \(a_{32}=-1.342714818\) \(a_{33}=+0.000000000\) \(a_{34}=-0.492298496\) \(a_{35}=+2.099552673\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.064257491\) \(a_{38}=-0.492080484\) \(a_{39}=+0.000000000\) \(a_{40}=-0.700002858\)
\(a_{41}=-1.227251250\) \(a_{42}=+0.000000000\) \(a_{43}=-0.792676235\) \(a_{44}=+0.529185631\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.586181074\) \(a_{47}=+0.149178625\) \(a_{48}=+0.000000000\) \(a_{49}=+1.639521245\) \(a_{50}=+1.027841031\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.517328117\) \(a_{53}=-0.789768244\) \(a_{54}=+0.000000000\) \(a_{55}=-0.505403279\)
\(a_{56}=-0.880031432\) \(a_{57}=+0.000000000\) \(a_{58}=-0.826280126\) \(a_{59}=-0.545109065\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.798190882\) \(a_{62}=+2.495440875\) \(a_{63}=+0.000000000\) \(a_{64}=-1.537508382\) \(a_{65}=-0.494078724\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.698660925\) \(a_{68}=-0.434251369\) \(a_{69}=+0.000000000\) \(a_{70}=+3.220684618\)
\(a_{71}=-1.766156296\) \(a_{72}=+0.000000000\) \(a_{73}=-0.524248434\) \(a_{74}=+1.632556202\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.434059138\) \(a_{77}=-0.635384240\) \(a_{78}=+0.000000000\) \(a_{79}=+0.443076988\) \(a_{80}=+0.674837211\)
\(a_{81}=+0.000000000\) \(a_{82}=-1.882586414\) \(a_{83}=+1.263243258\) \(a_{84}=+0.000000000\) \(a_{85}=+0.414735537\)
\(a_{86}=-1.215954290\) \(a_{87}=+0.000000000\) \(a_{88}=+0.211840688\) \(a_{89}=-1.029331607\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.621147178\) \(a_{92}=-0.517064295\) \(a_{93}=+0.000000000\) \(a_{94}=+0.228837956\) \(a_{95}=+0.414551913\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.689971959\) \(a_{98}=+2.515002749\) \(a_{99}=+0.000000000\) \(a_{100}=+0.906647983\)

Showing 100 of 1500 available coefficients

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