Properties

Label 33.8
Level $33$
Weight $0$
Character 33.1
Symmetry even
\(R\) 2.090796
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(2.09079633498191046101564975894 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.95012409 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.80298397 \pm 1.0 \cdot 10^{-8} \) \(a_{5}= -0.26994891 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.12590467 \pm 1.9 \cdot 10^{-8} \)
\(a_{7}= -0.46225796 \pm 1 \cdot 10^{-8} \) \(a_{8}= -3.51604247 \pm 1.1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.52643388 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -1.61830355 \pm 2.1 \cdot 10^{-8} \)
\(a_{13}= -0.92068678 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.90146039 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.15585508 \pm 1.8 \cdot 10^{-8} \)
\(a_{16}= +4.05373516 \pm 1.2 \cdot 10^{-8} \) \(a_{17}= -0.29898392 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.65004136 \pm 1.9 \cdot 10^{-8} \)
\(a_{19}= -0.93732571 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.75666248 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.26688476 \pm 1.8 \cdot 10^{-8} \)
\(a_{22}= -0.58798454 \pm 1.9 \cdot 10^{-8} \) \(a_{23}= +0.38748749 \pm 1 \cdot 10^{-8} \) \(a_{24}= +2.02998807 \pm 2.2 \cdot 10^{-8} \)
\(a_{25}= -0.92712758 \pm 1 \cdot 10^{-8} \) \(a_{26}= +1.79545347 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -1.29570165 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -0.19895701 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.30393674 \pm 2.7 \cdot 10^{-8} \)
\(a_{31}= +0.09443249 \pm 1 \cdot 10^{-8} \) \(a_{32}= -4.38924413 \pm 1.2 \cdot 10^{-8} \) \(a_{33}= -0.17407766 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.58305574 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.12478603 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.93432799 \pm 2.1 \cdot 10^{-8} \)
\(a_{37}= +0.05122555 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.82790145 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.53155876 \pm 1.8 \cdot 10^{-8} \)
\(a_{40}= +0.94915185 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.85831532 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.52045840 \pm 2.7 \cdot 10^{-8} \)
\(a_{43}= +1.71153798 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.84513147 \pm 2.1 \cdot 10^{-8} \) \(a_{45}= -0.08998297 \pm 1.8 \cdot 10^{-8} \)
\(a_{46}= -0.75564869 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.00195613 \pm 1 \cdot 10^{-8} \) \(a_{48}= -2.34042509 \pm 2.2 \cdot 10^{-8} \)
\(a_{49}= -0.78631758 \pm 1 \cdot 10^{-8} \) \(a_{50}= +1.80801384 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.17261844 \pm 1.8 \cdot 10^{-8} \)
\(a_{52}= -2.58067029 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= -0.75712650 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.37530156 \pm 1.9 \cdot 10^{-8} \)
\(a_{55}= -0.08139266 \pm 1.8 \cdot 10^{-8} \) \(a_{56}= +1.62531862 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.54116525 \pm 1.8 \cdot 10^{-8} \)
\(a_{58}= +0.38799086 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.49014077 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.43685929 \pm 2.9 \cdot 10^{-8} \)

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