Properties

Label 31.72
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 5.781640
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(5.78164008165489866226667977895 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.00749428 \pm 1.6 \cdot 10^{-5} \) \(a_{3}= +0.84506787 \pm 1.4 \cdot 10^{-5} \)
\(a_{4}= +0.01504473 \pm 1.8 \cdot 10^{-5} \) \(a_{5}= -1.01456724 \pm 1.3 \cdot 10^{-5} \) \(a_{6}= -0.85140105 \pm 1.8 \cdot 10^{-5} \)
\(a_{7}= +0.94068809 \pm 1.3 \cdot 10^{-5} \) \(a_{8}= +0.99233680 \pm 1.8 \cdot 10^{-5} \) \(a_{9}= -0.28586029 \pm 1.4 \cdot 10^{-5} \)
\(a_{10}= +1.02217070 \pm 1.6 \cdot 10^{-5} \) \(a_{11}= +0.05751728 \pm 1.3 \cdot 10^{-5} \) \(a_{12}= +0.01271382 \pm 2.1 \cdot 10^{-5} \)
\(a_{13}= +1.22739352 \pm 1.4 \cdot 10^{-5} \) \(a_{14}= -0.94773787 \pm 1.3 \cdot 10^{-5} \) \(a_{15}= -0.85737818 \pm 1.4 \cdot 10^{-5} \)
\(a_{16}= -1.01481839 \pm 1.6 \cdot 10^{-5} \) \(a_{17}= +1.40531957 \pm 1.2 \cdot 10^{-5} \) \(a_{18}= +0.28800261 \pm 1.8 \cdot 10^{-5} \)
\(a_{19}= -1.81007241 \pm 1.4 \cdot 10^{-5} \) \(a_{20}= -0.01526389 \pm 1.7 \cdot 10^{-5} \) \(a_{21}= +0.79494528 \pm 1.4 \cdot 10^{-5} \)
\(a_{22}= -0.05794833 \pm 1.4 \cdot 10^{-5} \) \(a_{23}= -1.81385296 \pm 1.2 \cdot 10^{-5} \) \(a_{24}= +0.83859195 \pm 2.2 \cdot 10^{-5} \)
\(a_{25}= +0.02934669 \pm 1.3 \cdot 10^{-5} \) \(a_{26}= -1.23659195 \pm 1.4 \cdot 10^{-5} \) \(a_{27}= -1.08663922 \pm 1.2 \cdot 10^{-5} \)
\(a_{28}= +0.01415240 \pm 1.4 \cdot 10^{-5} \) \(a_{29}= +1.18218709 \pm 1.2 \cdot 10^{-5} \) \(a_{30}= +0.86380362 \pm 1.9 \cdot 10^{-5} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.03008693 \pm 1.8 \cdot 10^{-5} \) \(a_{33}= +0.04860601 \pm 1.4 \cdot 10^{-5} \)
\(a_{34}= -1.41585143 \pm 1.7 \cdot 10^{-5} \) \(a_{35}= -0.95439132 \pm 1.2 \cdot 10^{-5} \) \(a_{36}= -0.00430069 \pm 1.9 \cdot 10^{-5} \)
\(a_{37}= -1.02303158 \pm 1.2 \cdot 10^{-5} \) \(a_{38}= +1.82363761 \pm 1.7 \cdot 10^{-5} \) \(a_{39}= +1.03723082 \pm 1.3 \cdot 10^{-5} \)
\(a_{40}= -1.00679241 \pm 1.8 \cdot 10^{-5} \) \(a_{41}= -0.92794681 \pm 1.2 \cdot 10^{-5} \) \(a_{42}= -0.80090283 \pm 1.6 \cdot 10^{-5} \)
\(a_{43}= -1.15956986 \pm 1.1 \cdot 10^{-5} \) \(a_{44}= +0.00086533 \pm 1.4 \cdot 10^{-5} \) \(a_{45}= +0.29002449 \pm 1.3 \cdot 10^{-5} \)
\(a_{46}= +1.82744649 \pm 1.2 \cdot 10^{-5} \) \(a_{47}= +0.09088627 \pm 1.2 \cdot 10^{-5} \) \(a_{48}= -0.85759041 \pm 2.1 \cdot 10^{-5} \)
\(a_{49}= -0.11510592 \pm 1.2 \cdot 10^{-5} \) \(a_{50}= -0.02956662 \pm 1.6 \cdot 10^{-5} \) \(a_{51}= +1.18759041 \pm 1.4 \cdot 10^{-5} \)
\(a_{52}= +0.01846581 \pm 1.4 \cdot 10^{-5} \) \(a_{53}= +0.69119593 \pm 1.2 \cdot 10^{-5} \) \(a_{54}= +1.09478280 \pm 1.6 \cdot 10^{-5} \)
\(a_{55}= -0.05835515 \pm 1.4 \cdot 10^{-5} \) \(a_{56}= +0.93347941 \pm 1.4 \cdot 10^{-5} \) \(a_{57}= -1.52963404 \pm 1.4 \cdot 10^{-5} \)
\(a_{58}= -1.19104673 \pm 1.5 \cdot 10^{-5} \) \(a_{59}= +0.03609466 \pm 1.4 \cdot 10^{-5} \) \(a_{60}= -0.01289903 \pm 2.1 \cdot 10^{-5} \)

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