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: \( 12.8574162785 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.935085735\) \(a_{3}=+0.000000000\) \(a_{4}=+2.744556803\) \(a_{5}=-0.793499433\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.251461664\) \(a_{8}=+3.375866984\) \(a_{9}=+0.000000000\) \(a_{10}=-1.535489434\)
\(a_{11}=+1.022050668\) \(a_{12}=+0.000000000\) \(a_{13}=+0.548441518\) \(a_{14}=+0.486599879\) \(a_{15}=+0.000000000\)
\(a_{16}=+3.788035243\) \(a_{17}=+0.807790997\) \(a_{18}=+0.000000000\) \(a_{19}=+0.533178996\) \(a_{20}=-2.177804268\)
\(a_{21}=+0.000000000\) \(a_{22}=+1.977755669\) \(a_{23}=+0.223023007\) \(a_{24}=+0.000000000\) \(a_{25}=-0.370358649\)
\(a_{26}=+1.061281358\) \(a_{27}=+0.000000000\) \(a_{28}=+0.690150822\) \(a_{29}=-0.517738706\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.345263121\) \(a_{32}=+3.954305971\) \(a_{33}=+0.000000000\) \(a_{34}=+1.563144859\) \(a_{35}=-0.199534728\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.619352807\) \(a_{38}=+1.031746869\) \(a_{39}=+0.000000000\) \(a_{40}=-2.678747934\)
\(a_{41}=-0.184896294\) \(a_{42}=+0.000000000\) \(a_{43}=+1.559448390\) \(a_{44}=+2.805071412\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.431582165\) \(a_{47}=-1.171119237\) \(a_{48}=+0.000000000\) \(a_{49}=-0.936708927\) \(a_{50}=-0.716767149\)
\(a_{51}=+0.000000000\) \(a_{52}=+1.505466103\) \(a_{53}=+0.538558480\) \(a_{54}=+0.000000000\) \(a_{55}=-0.810131008\)
\(a_{56}=+0.847574884\) \(a_{57}=+0.000000000\) \(a_{58}=-0.998920357\) \(a_{59}=+1.339870722\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.259341026\) \(a_{62}=-2.618578354\) \(a_{63}=+0.000000000\) \(a_{64}=+3.887885599\) \(a_{65}=-0.475389838\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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