Properties

Label 33.6
Level $33$
Weight $0$
Character 33.1
Symmetry odd
\(R\) 1.823413
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: \(1.82341375433745470238292503006 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.78164212 \pm 3.2 \cdot 10^{-7} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.17424863 \pm 3.1 \cdot 10^{-7} \) \(a_{5}= +1.26092742 \pm 2.9 \cdot 10^{-7} \) \(a_{6}= -1.02863156 \pm 3.3 \cdot 10^{-7} \)
\(a_{7}= +0.62999702 \pm 2.6 \cdot 10^{-7} \) \(a_{8}= -2.09209081 \pm 2.9 \cdot 10^{-7} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -2.24652140 \pm 3.7 \cdot 10^{-7} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +1.25530303 \pm 3.2 \cdot 10^{-7} \)
\(a_{13}= +1.24475505 \pm 2.7 \cdot 10^{-7} \) \(a_{14}= -1.12242922 \pm 3.0 \cdot 10^{-7} \) \(a_{15}= +0.72799679 \pm 3.0 \cdot 10^{-7} \)
\(a_{16}= +1.55310847 \pm 3.0 \cdot 10^{-7} \) \(a_{17}= +0.04139104 \pm 2.6 \cdot 10^{-7} \) \(a_{18}= -0.59388071 \pm 3.3 \cdot 10^{-7} \)
\(a_{19}= -1.28817523 \pm 2.9 \cdot 10^{-7} \) \(a_{20}= +2.74156972 \pm 3.0 \cdot 10^{-7} \) \(a_{21}= +0.36372895 \pm 2.7 \cdot 10^{-7} \)
\(a_{22}= +0.53718531 \pm 3.3 \cdot 10^{-7} \) \(a_{23}= -0.71219819 \pm 2.4 \cdot 10^{-7} \) \(a_{24}= -1.20786919 \pm 3.1 \cdot 10^{-7} \)
\(a_{25}= +0.58993796 \pm 2.9 \cdot 10^{-7} \) \(a_{26}= -2.21770801 \pm 3.7 \cdot 10^{-7} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +1.36977015 \pm 2.7 \cdot 10^{-7} \) \(a_{29}= +0.12755783 \pm 2.6 \cdot 10^{-7} \) \(a_{30}= -1.29702974 \pm 6.2 \cdot 10^{-7} \)
\(a_{31}= -1.21788336 \pm 2.4 \cdot 10^{-7} \) \(a_{32}= -0.67499265 \pm 2.9 \cdot 10^{-7} \) \(a_{33}= -0.17407766 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -0.07374402 \pm 2.8 \cdot 10^{-7} \) \(a_{35}= +0.79438052 \pm 2.9 \cdot 10^{-7} \) \(a_{36}= +0.72474954 \pm 3.2 \cdot 10^{-7} \)
\(a_{37}= +1.16018336 \pm 2.7 \cdot 10^{-7} \) \(a_{38}= +2.29506725 \pm 3.4 \cdot 10^{-7} \) \(a_{39}= +0.71865966 \pm 2.8 \cdot 10^{-7} \)
\(a_{40}= -2.63797467 \pm 3.0 \cdot 10^{-7} \) \(a_{41}= -0.23743452 \pm 2.4 \cdot 10^{-7} \) \(a_{42}= -0.64803481 \pm 6.0 \cdot 10^{-7} \)
\(a_{43}= -0.34520001 \pm 2.1 \cdot 10^{-7} \) \(a_{44}= -0.65556063 \pm 3.2 \cdot 10^{-7} \) \(a_{45}= +0.42030914 \pm 3.0 \cdot 10^{-7} \)
\(a_{46}= +1.26888228 \pm 2.6 \cdot 10^{-7} \) \(a_{47}= -0.61618559 \pm 2.6 \cdot 10^{-7} \) \(a_{48}= +0.89668759 \pm 3.1 \cdot 10^{-7} \)
\(a_{49}= -0.60310376 \pm 2.5 \cdot 10^{-7} \) \(a_{50}= -1.05105832 \pm 3.5 \cdot 10^{-7} \) \(a_{51}= +0.02389713 \pm 2.7 \cdot 10^{-7} \)
\(a_{52}= +2.70640695 \pm 3.5 \cdot 10^{-7} \) \(a_{53}= -0.55979104 \pm 2.8 \cdot 10^{-7} \) \(a_{54}= -0.34287719 \pm 3.3 \cdot 10^{-7} \)
\(a_{55}= -0.38018392 \pm 3.0 \cdot 10^{-7} \) \(a_{56}= -1.31801097 \pm 2.6 \cdot 10^{-7} \) \(a_{57}= -0.74372832 \pm 3.0 \cdot 10^{-7} \)
\(a_{58}= -0.22726240 \pm 2.9 \cdot 10^{-7} \) \(a_{59}= +0.38874331 \pm 2.7 \cdot 10^{-7} \) \(a_{60}= +1.58284602 \pm 6.1 \cdot 10^{-7} \)

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