Properties

Label 21.14
Level $21$
Weight $0$
Character 21.1
Symmetry even
\(R\) 3.735148
Fricke sign $-1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(3.73514871953766890769382896102 \pm 8 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70241476 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.50661350 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.60398502 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.40553935 \pm 1.1 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -1.05826756 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.42424799 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.85229220 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.29249344 \pm 1.1 \cdot 10^{-8} \)
\(a_{13}= -1.23504708 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.26548782 \pm 1.1 \cdot 10^{-8} \) \(a_{15}= +0.34871091 \pm 1.1 \cdot 10^{-8} \)
\(a_{16}= -0.23672925 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.68385076 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.23413825 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= -0.17564830 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.30598697 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.21821789 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.59866262 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.38166420 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.61099106 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= -0.63520210 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.86751530 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.19148191 \pm 1.1 \cdot 10^{-8} \) \(a_{29}= -0.91238014 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.24493969 \pm 1.1 \cdot 10^{-8} \)
\(a_{31}= +0.29133925 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.89198544 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.49207113 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +1.18276163 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.22828488 \pm 1.1 \cdot 10^{-8} \) \(a_{36}= -0.16887117 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= -1.01325930 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.12337796 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.71305476 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +0.63917775 \pm 1 \cdot 10^{-8} \) \(a_{41}= +1.40091428 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.15327947 \pm 1.1 \cdot 10^{-8} \)
\(a_{43}= -1.81136975 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.43178274 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.20132834 \pm 1.1 \cdot 10^{-8} \)
\(a_{46}= -0.26808657 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.21106836 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.13667570 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.44617533 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.97217169 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= +0.62569153 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.28993577 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.13517978 \pm 1.1 \cdot 10^{-8} \)
\(a_{55}= +0.51477172 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.39998754 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.10141059 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= -0.64086927 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.96678592 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.17666166 \pm 1.1 \cdot 10^{-8} \)

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