Properties

Label 33.41
Level $33$
Weight $0$
Character 33.1
Symmetry odd
\(R\) 5.035797
Fricke sign $-1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(5.0357970820392923672455543529 \pm 7 \cdot 10^{-10}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -1.95396768 \pm 4.8 \cdot 10^{-6} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.81798971 \pm 4.7 \cdot 10^{-6} \) \(a_{5}= -0.67966251 \pm 4.4 \cdot 10^{-6} \) \(a_{6}= -1.12812377 \pm 4.9 \cdot 10^{-6} \)
\(a_{7}= +1.16736394 \pm 4.0 \cdot 10^{-6} \) \(a_{8}= -3.55229314 \pm 4.5 \cdot 10^{-6} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +1.32803858 \pm 5.6 \cdot 10^{-6} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +1.62696712 \pm 4.7 \cdot 10^{-6} \)
\(a_{13}= -1.03715700 \pm 4.1 \cdot 10^{-6} \) \(a_{14}= -2.28099140 \pm 4.6 \cdot 10^{-6} \) \(a_{15}= -0.39240333 \pm 4.4 \cdot 10^{-6} \)
\(a_{16}= +4.12307629 \pm 4.5 \cdot 10^{-6} \) \(a_{17}= +0.68276297 \pm 3.9 \cdot 10^{-6} \) \(a_{18}= -0.65132256 \pm 4.9 \cdot 10^{-6} \)
\(a_{19}= -0.23690813 \pm 4.4 \cdot 10^{-6} \) \(a_{20}= -1.91528196 \pm 4.5 \cdot 10^{-6} \) \(a_{21}= +0.67397788 \pm 4.0 \cdot 10^{-6} \)
\(a_{22}= +0.58914342 \pm 4.9 \cdot 10^{-6} \) \(a_{23}= +0.86150772 \pm 3.6 \cdot 10^{-6} \) \(a_{24}= -2.05091740 \pm 4.5 \cdot 10^{-6} \)
\(a_{25}= -0.53805887 \pm 4.4 \cdot 10^{-6} \) \(a_{26}= +2.02657126 \pm 5.7 \cdot 10^{-6} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +3.28961956 \pm 4.1 \cdot 10^{-6} \) \(a_{29}= -0.46007634 \pm 4.0 \cdot 10^{-6} \) \(a_{30}= +0.76674343 \pm 9.3 \cdot 10^{-6} \)
\(a_{31}= +1.56499544 \pm 3.7 \cdot 10^{-6} \) \(a_{32}= -4.50406470 \pm 4.4 \cdot 10^{-6} \) \(a_{33}= -0.17407766 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -1.33409679 \pm 4.2 \cdot 10^{-6} \) \(a_{35}= -0.79341350 \pm 4.3 \cdot 10^{-6} \) \(a_{36}= +0.93932990 \pm 4.7 \cdot 10^{-6} \)
\(a_{37}= +1.38122276 \pm 4.0 \cdot 10^{-6} \) \(a_{38}= +0.46291083 \pm 5.1 \cdot 10^{-6} \) \(a_{39}= -0.59880287 \pm 4.1 \cdot 10^{-6} \)
\(a_{40}= +2.41436047 \pm 4.6 \cdot 10^{-6} \) \(a_{41}= +0.47227492 \pm 3.6 \cdot 10^{-6} \) \(a_{42}= -1.31693100 \pm 8.9 \cdot 10^{-6} \)
\(a_{43}= +0.36884794 \pm 3.2 \cdot 10^{-6} \) \(a_{44}= -0.84965587 \pm 4.7 \cdot 10^{-6} \) \(a_{45}= -0.22655417 \pm 4.4 \cdot 10^{-6} \)
\(a_{46}= -1.68335824 \pm 4.0 \cdot 10^{-6} \) \(a_{47}= +1.27426536 \pm 4.0 \cdot 10^{-6} \) \(a_{48}= +2.38045921 \pm 4.5 \cdot 10^{-6} \)
\(a_{49}= +0.36273856 \pm 3.8 \cdot 10^{-6} \) \(a_{50}= +1.05134965 \pm 5.3 \cdot 10^{-6} \) \(a_{51}= +0.39419339 \pm 3.9 \cdot 10^{-6} \)
\(a_{52}= -2.92269775 \pm 5.4 \cdot 10^{-6} \) \(a_{53}= -0.11654726 \pm 4.3 \cdot 10^{-6} \) \(a_{54}= -0.37604126 \pm 4.9 \cdot 10^{-6} \)
\(a_{55}= +0.20492596 \pm 4.4 \cdot 10^{-6} \) \(a_{56}= -4.14681890 \pm 4.0 \cdot 10^{-6} \) \(a_{57}= -0.13677897 \pm 4.4 \cdot 10^{-6} \)
\(a_{58}= +0.89897430 \pm 4.4 \cdot 10^{-6} \) \(a_{59}= +1.23532854 \pm 4.1 \cdot 10^{-6} \) \(a_{60}= -1.10578855 \pm 9.1 \cdot 10^{-6} \)

Displaying $a_n$ with $n$ up to: 60 180 1000