Properties

Label 21.28
Level $21$
Weight $0$
Character 21.1
Symmetry odd
\(R\) 5.324601
Fricke sign $-1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(5.32460189801827366376576396356 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.60913961 \pm 2.8 \cdot 10^{-7} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.62894894 \pm 3.3 \cdot 10^{-7} \) \(a_{5}= -1.05109118 \pm 2.2 \cdot 10^{-7} \) \(a_{6}= -0.35168692 \pm 2.9 \cdot 10^{-7} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.99225732 \pm 3.3 \cdot 10^{-7} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.64026127 \pm 2.8 \cdot 10^{-7} \) \(a_{11}= -0.13565069 \pm 2.2 \cdot 10^{-7} \) \(a_{12}= -0.36312384 \pm 3.4 \cdot 10^{-7} \)
\(a_{13}= +1.52101849 \pm 2.5 \cdot 10^{-7} \) \(a_{14}= +0.23023313 \pm 2.9 \cdot 10^{-7} \) \(a_{15}= -0.60684777 \pm 2.3 \cdot 10^{-7} \)
\(a_{16}= +0.02452570 \pm 2.7 \cdot 10^{-7} \) \(a_{17}= +1.11446775 \pm 2.5 \cdot 10^{-7} \) \(a_{18}= -0.20304654 \pm 2.9 \cdot 10^{-7} \)
\(a_{19}= -0.45705995 \pm 2.4 \cdot 10^{-7} \) \(a_{20}= +0.66108268 \pm 3.2 \cdot 10^{-7} \) \(a_{21}= -0.21821789 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.08263021 \pm 2.9 \cdot 10^{-7} \) \(a_{23}= +0.87935696 \pm 2.4 \cdot 10^{-7} \) \(a_{24}= +0.57288003 \pm 3.4 \cdot 10^{-7} \)
\(a_{25}= +0.10479266 \pm 2.3 \cdot 10^{-7} \) \(a_{26}= -0.92651261 \pm 2.8 \cdot 10^{-7} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.23772035 \pm 3.4 \cdot 10^{-7} \) \(a_{29}= +1.25621853 \pm 2.5 \cdot 10^{-7} \) \(a_{30}= +0.36965501 \pm 5.2 \cdot 10^{-7} \)
\(a_{31}= -1.61977743 \pm 2.6 \cdot 10^{-7} \) \(a_{32}= -1.00719690 \pm 2.5 \cdot 10^{-7} \) \(a_{33}= -0.07831796 \pm 2.3 \cdot 10^{-7} \)
\(a_{34}= -0.67886645 \pm 2.3 \cdot 10^{-7} \) \(a_{35}= +0.39727512 \pm 2.3 \cdot 10^{-7} \) \(a_{36}= -0.20964965 \pm 3.4 \cdot 10^{-7} \)
\(a_{37}= +0.36694118 \pm 2.2 \cdot 10^{-7} \) \(a_{38}= +0.27841332 \pm 2.8 \cdot 10^{-7} \) \(a_{39}= +0.87816043 \pm 2.6 \cdot 10^{-7} \)
\(a_{40}= -1.04295291 \pm 3.0 \cdot 10^{-7} \) \(a_{41}= +0.83374417 \pm 1.9 \cdot 10^{-7} \) \(a_{42}= +0.13292516 \pm 2.9 \cdot 10^{-7} \)
\(a_{43}= +0.11065944 \pm 2.5 \cdot 10^{-7} \) \(a_{44}= +0.08531736 \pm 3.3 \cdot 10^{-7} \) \(a_{45}= -0.35036373 \pm 2.3 \cdot 10^{-7} \)
\(a_{46}= -0.53565115 \pm 2.8 \cdot 10^{-7} \) \(a_{47}= +1.62775627 \pm 2.3 \cdot 10^{-7} \) \(a_{48}= +0.01415992 \pm 2.8 \cdot 10^{-7} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.06383336 \pm 2.2 \cdot 10^{-7} \) \(a_{51}= +0.64343826 \pm 2.6 \cdot 10^{-7} \)
\(a_{52}= -0.95664296 \pm 3.1 \cdot 10^{-7} \) \(a_{53}= +0.28852237 \pm 2.6 \cdot 10^{-7} \) \(a_{54}= -0.11722897 \pm 2.9 \cdot 10^{-7} \)
\(a_{55}= +0.14258124 \pm 2.0 \cdot 10^{-7} \) \(a_{56}= -0.37503801 \pm 3.4 \cdot 10^{-7} \) \(a_{57}= -0.26388369 \pm 2.5 \cdot 10^{-7} \)
\(a_{58}= -0.76521246 \pm 2.4 \cdot 10^{-7} \) \(a_{59}= -0.68132027 \pm 1.7 \cdot 10^{-7} \) \(a_{60}= +0.38167626 \pm 5.7 \cdot 10^{-7} \)

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