Properties

Label 21.55
Level $21$
Weight $0$
Character 21.1
Symmetry odd
\(R\) 7.478486
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: \(7.47848697390734287270005683799 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.88377113 \pm 2.8 \cdot 10^{-5} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.54859368 \pm 3.3 \cdot 10^{-5} \) \(a_{5}= -0.68855838 \pm 2.2 \cdot 10^{-5} \) \(a_{6}= -1.08759577 \pm 2.8 \cdot 10^{-5} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +2.91719607 \pm 3.3 \cdot 10^{-5} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -1.29708641 \pm 2.7 \cdot 10^{-5} \) \(a_{11}= +1.81938821 \pm 2.2 \cdot 10^{-5} \) \(a_{12}= -1.47143125 \pm 3.3 \cdot 10^{-5} \)
\(a_{13}= +0.47983081 \pm 2.5 \cdot 10^{-5} \) \(a_{14}= +0.71199856 \pm 2.8 \cdot 10^{-5} \) \(a_{15}= +0.39753937 \pm 2.2 \cdot 10^{-5} \)
\(a_{16}= +2.94673606 \pm 2.7 \cdot 10^{-5} \) \(a_{17}= -0.79396107 \pm 2.4 \cdot 10^{-5} \) \(a_{18}= +0.62792371 \pm 2.8 \cdot 10^{-5} \)
\(a_{19}= +0.68941664 \pm 2.4 \cdot 10^{-5} \) \(a_{20}= -1.75485554 \pm 3.2 \cdot 10^{-5} \) \(a_{21}= -0.21821789 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +3.42731098 \pm 2.9 \cdot 10^{-5} \) \(a_{23}= +1.20351149 \pm 2.4 \cdot 10^{-5} \) \(a_{24}= -1.68424393 \pm 3.3 \cdot 10^{-5} \)
\(a_{25}= -0.52588735 \pm 2.2 \cdot 10^{-5} \) \(a_{26}= +0.90389143 \pm 2.7 \cdot 10^{-5} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.96327787 \pm 3.3 \cdot 10^{-5} \) \(a_{29}= -0.17375577 \pm 2.5 \cdot 10^{-5} \) \(a_{30}= +0.74887319 \pm 5.1 \cdot 10^{-5} \)
\(a_{31}= +1.37755508 \pm 2.6 \cdot 10^{-5} \) \(a_{32}= +2.63378025 \pm 2.5 \cdot 10^{-5} \) \(a_{33}= -1.05042427 \pm 2.2 \cdot 10^{-5} \)
\(a_{34}= -1.49564094 \pm 2.3 \cdot 10^{-5} \) \(a_{35}= -0.26025061 \pm 2.2 \cdot 10^{-5} \) \(a_{36}= +0.84953123 \pm 3.3 \cdot 10^{-5} \)
\(a_{37}= -0.33957869 \pm 2.2 \cdot 10^{-5} \) \(a_{38}= +1.29870317 \pm 2.8 \cdot 10^{-5} \) \(a_{39}= -0.27703045 \pm 2.5 \cdot 10^{-5} \)
\(a_{40}= -2.00865981 \pm 3.0 \cdot 10^{-5} \) \(a_{41}= -0.71199244 \pm 1.8 \cdot 10^{-5} \) \(a_{42}= -0.41107256 \pm 2.8 \cdot 10^{-5} \)
\(a_{43}= -1.21799357 \pm 2.5 \cdot 10^{-5} \) \(a_{44}= +4.63688128 \pm 3.3 \cdot 10^{-5} \) \(a_{45}= -0.22951946 \pm 2.2 \cdot 10^{-5} \)
\(a_{46}= +2.26714020 \pm 2.8 \cdot 10^{-5} \) \(a_{47}= -0.79505157 \pm 2.3 \cdot 10^{-5} \) \(a_{48}= -1.70129886 \pm 2.7 \cdot 10^{-5} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.99065141 \pm 2.2 \cdot 10^{-5} \) \(a_{51}= +0.45839364 \pm 2.4 \cdot 10^{-5} \)
\(a_{52}= +1.22289378 \pm 3.1 \cdot 10^{-5} \) \(a_{53}= -1.36342505 \pm 2.5 \cdot 10^{-5} \) \(a_{54}= -0.36253192 \pm 2.8 \cdot 10^{-5} \)
\(a_{55}= -1.25275500 \pm 1.9 \cdot 10^{-5} \) \(a_{56}= +1.10259647 \pm 3.3 \cdot 10^{-5} \) \(a_{57}= -0.39803488 \pm 2.4 \cdot 10^{-5} \)
\(a_{58}= -0.32731611 \pm 2.4 \cdot 10^{-5} \) \(a_{59}= +0.73815466 \pm 1.7 \cdot 10^{-5} \) \(a_{60}= +1.01316632 \pm 5.5 \cdot 10^{-5} \)

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