Properties

Label 21.33
Level $21$
Weight $0$
Character 21.1
Symmetry odd
\(R\) 5.712346
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(5.71234657180871979307804174412 \pm 10 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.71084109 \pm 1.7 \cdot 10^{-7} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.92697722 \pm 2.0 \cdot 10^{-7} \) \(a_{5}= -1.77860173 \pm 1.3 \cdot 10^{-7} \) \(a_{6}= -0.98775456 \pm 1.8 \cdot 10^{-7} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +1.58591072 \pm 2.0 \cdot 10^{-7} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -3.04290492 \pm 1.6 \cdot 10^{-7} \) \(a_{11}= -0.80584133 \pm 1.3 \cdot 10^{-7} \) \(a_{12}= -1.11254082 \pm 2.1 \cdot 10^{-7} \)
\(a_{13}= -1.13552203 \pm 1.5 \cdot 10^{-7} \) \(a_{14}= -0.64663715 \pm 1.8 \cdot 10^{-7} \) \(a_{15}= +1.02687619 \pm 1.4 \cdot 10^{-7} \)
\(a_{16}= +0.78626400 \pm 1.6 \cdot 10^{-7} \) \(a_{17}= +0.41665562 \pm 1.5 \cdot 10^{-7} \) \(a_{18}= +0.57028036 \pm 1.8 \cdot 10^{-7} \)
\(a_{19}= -0.29013871 \pm 1.4 \cdot 10^{-7} \) \(a_{20}= -3.42732503 \pm 1.9 \cdot 10^{-7} \) \(a_{21}= +0.21821789 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -1.37866646 \pm 1.7 \cdot 10^{-7} \) \(a_{23}= +1.48468768 \pm 1.4 \cdot 10^{-7} \) \(a_{24}= -0.91562598 \pm 2.1 \cdot 10^{-7} \)
\(a_{25}= +2.16342412 \pm 1.3 \cdot 10^{-7} \) \(a_{26}= -1.94269775 \pm 1.6 \cdot 10^{-7} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.72832893 \pm 2.1 \cdot 10^{-7} \) \(a_{29}= -0.34538544 \pm 1.5 \cdot 10^{-7} \) \(a_{30}= +1.75682198 \pm 3.2 \cdot 10^{-7} \)
\(a_{31}= -0.23212634 \pm 1.6 \cdot 10^{-7} \) \(a_{32}= -0.24073797 \pm 1.5 \cdot 10^{-7} \) \(a_{33}= +0.46525271 \pm 1.4 \cdot 10^{-7} \)
\(a_{34}= +0.71283156 \pm 1.4 \cdot 10^{-7} \) \(a_{35}= +0.67224827 \pm 1.4 \cdot 10^{-7} \) \(a_{36}= +0.64232574 \pm 2.1 \cdot 10^{-7} \)
\(a_{37}= -0.50402306 \pm 1.3 \cdot 10^{-7} \) \(a_{38}= -0.49638122 \pm 1.7 \cdot 10^{-7} \) \(a_{39}= +0.65559395 \pm 1.6 \cdot 10^{-7} \)
\(a_{40}= -2.82070356 \pm 1.8 \cdot 10^{-7} \) \(a_{41}= +1.11855956 \pm 1.1 \cdot 10^{-7} \) \(a_{42}= +0.37333613 \pm 1.8 \cdot 10^{-7} \)
\(a_{43}= -1.50555094 \pm 1.5 \cdot 10^{-7} \) \(a_{44}= -1.55283790 \pm 2.0 \cdot 10^{-7} \) \(a_{45}= -0.59286724 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +2.54006468 \pm 1.7 \cdot 10^{-7} \) \(a_{47}= -0.27375732 \pm 1.4 \cdot 10^{-7} \) \(a_{48}= -0.45394973 \pm 1.7 \cdot 10^{-7} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +3.70127488 \pm 1.3 \cdot 10^{-7} \) \(a_{51}= -0.24055624 \pm 1.6 \cdot 10^{-7} \)
\(a_{52}= -2.18812509 \pm 1.9 \cdot 10^{-7} \) \(a_{53}= -0.51957259 \pm 1.5 \cdot 10^{-7} \) \(a_{54}= -0.32925152 \pm 1.8 \cdot 10^{-7} \)
\(a_{55}= +1.43327079 \pm 1.2 \cdot 10^{-7} \) \(a_{56}= -0.59941791 \pm 2.1 \cdot 10^{-7} \) \(a_{57}= +0.16751166 \pm 1.5 \cdot 10^{-7} \)
\(a_{58}= -0.59089960 \pm 1.4 \cdot 10^{-7} \) \(a_{59}= -1.78362849 \pm 1.0 \cdot 10^{-7} \) \(a_{60}= +1.97876703 \pm 3.5 \cdot 10^{-7} \)

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