Properties

Label 31.73
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 5.799097
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(5.79909724296422976906434682561 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.03887710 \pm 1.1 \cdot 10^{-5} \) \(a_{3}= -1.85366179 \pm 1.0 \cdot 10^{-5} \)
\(a_{4}= -0.99848857 \pm 1.2 \cdot 10^{-5} \) \(a_{5}= +1.70542348 \pm 9.4 \cdot 10^{-6} \) \(a_{6}= -0.07206499 \pm 1.2 \cdot 10^{-5} \)
\(a_{7}= -0.15298275 \pm 9.2 \cdot 10^{-6} \) \(a_{8}= -0.07769544 \pm 1.2 \cdot 10^{-5} \) \(a_{9}= +2.43606202 \pm 9.6 \cdot 10^{-6} \)
\(a_{10}= +0.06630192 \pm 1.1 \cdot 10^{-5} \) \(a_{11}= +0.53142972 \pm 9.2 \cdot 10^{-6} \) \(a_{12}= +1.85086011 \pm 1.5 \cdot 10^{-5} \)
\(a_{13}= -0.94972871 \pm 9.6 \cdot 10^{-6} \) \(a_{14}= -0.00594753 \pm 9.5 \cdot 10^{-6} \) \(a_{15}= -3.16127834 \pm 9.8 \cdot 10^{-6} \)
\(a_{16}= +0.99546800 \pm 1.1 \cdot 10^{-5} \) \(a_{17}= +0.84886182 \pm 8.7 \cdot 10^{-6} \) \(a_{18}= +0.09470702 \pm 1.2 \cdot 10^{-5} \)
\(a_{19}= -1.37329722 \pm 9.8 \cdot 10^{-6} \) \(a_{20}= -1.70284586 \pm 1.1 \cdot 10^{-5} \) \(a_{21}= +0.28357828 \pm 9.9 \cdot 10^{-6} \)
\(a_{22}= +0.02066045 \pm 1.0 \cdot 10^{-5} \) \(a_{23}= -0.14553271 \pm 8.8 \cdot 10^{-6} \) \(a_{24}= +0.14402106 \pm 1.5 \cdot 10^{-5} \)
\(a_{25}= +1.90846925 \pm 9.0 \cdot 10^{-6} \) \(a_{26}= -0.03692270 \pm 9.8 \cdot 10^{-6} \) \(a_{27}= -2.66197330 \pm 8.5 \cdot 10^{-6} \)
\(a_{28}= +0.15275153 \pm 9.9 \cdot 10^{-6} \) \(a_{29}= +0.46473901 \pm 8.7 \cdot 10^{-6} \) \(a_{30}= -0.12290133 \pm 1.3 \cdot 10^{-5} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.11639634 \pm 1.2 \cdot 10^{-5} \) \(a_{33}= -0.98509097 \pm 9.9 \cdot 10^{-6} \)
\(a_{34}= +0.03300128 \pm 1.2 \cdot 10^{-5} \) \(a_{35}= -0.26090038 \pm 8.5 \cdot 10^{-6} \) \(a_{36}= -2.43238009 \pm 1.3 \cdot 10^{-5} \)
\(a_{37}= +0.39928628 \pm 8.5 \cdot 10^{-6} \) \(a_{38}= -0.05338981 \pm 1.1 \cdot 10^{-5} \) \(a_{39}= +1.76047581 \pm 9.4 \cdot 10^{-6} \)
\(a_{40}= -0.13250362 \pm 1.2 \cdot 10^{-5} \) \(a_{41}= -1.43845317 \pm 8.4 \cdot 10^{-6} \) \(a_{42}= +0.01102470 \pm 1.1 \cdot 10^{-5} \)
\(a_{43}= +0.80566865 \pm 8.0 \cdot 10^{-6} \) \(a_{44}= -0.53062651 \pm 9.8 \cdot 10^{-6} \) \(a_{45}= +4.15451738 \pm 9.3 \cdot 10^{-6} \)
\(a_{46}= -0.00565789 \pm 8.5 \cdot 10^{-6} \) \(a_{47}= -1.22980971 \pm 8.2 \cdot 10^{-6} \) \(a_{48}= -1.84526099 \pm 1.4 \cdot 10^{-5} \)
\(a_{49}= -0.97659628 \pm 8.8 \cdot 10^{-6} \) \(a_{50}= +0.07419575 \pm 1.1 \cdot 10^{-5} \) \(a_{51}= -1.57350272 \pm 1.0 \cdot 10^{-5} \)
\(a_{52}= +0.94829326 \pm 9.9 \cdot 10^{-6} \) \(a_{53}= -0.10259958 \pm 8.8 \cdot 10^{-6} \) \(a_{54}= -0.10348980 \pm 1.1 \cdot 10^{-5} \)
\(a_{55}= +0.90631273 \pm 1.0 \cdot 10^{-5} \) \(a_{56}= +0.01188606 \pm 9.5 \cdot 10^{-6} \) \(a_{57}= +2.54562859 \pm 9.6 \cdot 10^{-6} \)
\(a_{58}= +0.01806770 \pm 1.0 \cdot 10^{-5} \) \(a_{59}= -1.61367545 \pm 9.9 \cdot 10^{-6} \) \(a_{60}= +3.15650029 \pm 1.4 \cdot 10^{-5} \)

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