Properties

Label 31.87
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 6.354463
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(6.35446322203935852302608799097 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.85781826 \pm 3.0 \cdot 10^{-5} \) \(a_{3}= +1.85250790 \pm 2.7 \cdot 10^{-5} \)
\(a_{4}= -0.26414783 \pm 3.3 \cdot 10^{-5} \) \(a_{5}= -0.90884515 \pm 2.5 \cdot 10^{-5} \) \(a_{6}= +1.58911510 \pm 3.4 \cdot 10^{-5} \)
\(a_{7}= +1.08675969 \pm 2.4 \cdot 10^{-5} \) \(a_{8}= -1.08440909 \pm 3.4 \cdot 10^{-5} \) \(a_{9}= +2.43178551 \pm 2.5 \cdot 10^{-5} \)
\(a_{10}= -0.77962397 \pm 3.0 \cdot 10^{-5} \) \(a_{11}= +0.73753156 \pm 2.4 \cdot 10^{-5} \) \(a_{12}= -0.48933595 \pm 3.9 \cdot 10^{-5} \)
\(a_{13}= +1.79985217 \pm 2.5 \cdot 10^{-5} \) \(a_{14}= +0.93224231 \pm 2.5 \cdot 10^{-5} \) \(a_{15}= -1.68364282 \pm 2.6 \cdot 10^{-5} \)
\(a_{16}= -0.66607809 \pm 3.0 \cdot 10^{-5} \) \(a_{17}= -0.15065676 \pm 2.3 \cdot 10^{-5} \) \(a_{18}= +2.08603001 \pm 3.3 \cdot 10^{-5} \)
\(a_{19}= +0.86796947 \pm 2.6 \cdot 10^{-5} \) \(a_{20}= +0.24006948 \pm 3.1 \cdot 10^{-5} \) \(a_{21}= +2.01323092 \pm 2.6 \cdot 10^{-5} \)
\(a_{22}= +0.63266804 \pm 2.6 \cdot 10^{-5} \) \(a_{23}= +0.01707141 \pm 2.3 \cdot 10^{-5} \) \(a_{24}= -2.00887641 \pm 4.1 \cdot 10^{-5} \)
\(a_{25}= -0.17400049 \pm 2.3 \cdot 10^{-5} \) \(a_{26}= +1.54394605 \pm 2.6 \cdot 10^{-5} \) \(a_{27}= +2.65239396 \pm 2.2 \cdot 10^{-5} \)
\(a_{28}= -0.28706522 \pm 2.6 \cdot 10^{-5} \) \(a_{29}= -1.31082382 \pm 2.3 \cdot 10^{-5} \) \(a_{30}= -1.44425956 \pm 3.4 \cdot 10^{-5} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.51303515 \pm 3.2 \cdot 10^{-5} \) \(a_{33}= +1.36628304 \pm 2.6 \cdot 10^{-5} \)
\(a_{34}= -0.12923612 \pm 3.2 \cdot 10^{-5} \) \(a_{35}= -0.98769628 \pm 2.2 \cdot 10^{-5} \) \(a_{36}= -0.64235087 \pm 3.5 \cdot 10^{-5} \)
\(a_{37}= +0.77606787 \pm 2.2 \cdot 10^{-5} \) \(a_{38}= +0.74456006 \pm 3.1 \cdot 10^{-5} \) \(a_{39}= +3.33424036 \pm 2.5 \cdot 10^{-5} \)
\(a_{40}= +0.98555995 \pm 3.2 \cdot 10^{-5} \) \(a_{41}= -1.56714723 \pm 2.2 \cdot 10^{-5} \) \(a_{42}= +1.72698624 \pm 3.0 \cdot 10^{-5} \)
\(a_{43}= +0.81302963 \pm 2.1 \cdot 10^{-5} \) \(a_{44}= -0.19481736 \pm 2.6 \cdot 10^{-5} \) \(a_{45}= -2.21011647 \pm 2.4 \cdot 10^{-5} \)
\(a_{46}= +0.01464417 \pm 2.2 \cdot 10^{-5} \) \(a_{47}= -0.18586115 \pm 2.1 \cdot 10^{-5} \) \(a_{48}= -1.23391492 \pm 3.8 \cdot 10^{-5} \)
\(a_{49}= +0.18104663 \pm 2.3 \cdot 10^{-5} \) \(a_{50}= -0.14926079 \pm 3.0 \cdot 10^{-5} \) \(a_{51}= -0.27909285 \pm 2.6 \cdot 10^{-5} \)
\(a_{52}= -0.47542705 \pm 2.6 \cdot 10^{-5} \) \(a_{53}= -0.97030756 \pm 2.3 \cdot 10^{-5} \) \(a_{54}= +2.27527197 \pm 2.9 \cdot 10^{-5} \)
\(a_{55}= -0.67030198 \pm 2.6 \cdot 10^{-5} \) \(a_{56}= -1.17849210 \pm 2.5 \cdot 10^{-5} \) \(a_{57}= +1.60792030 \pm 2.5 \cdot 10^{-5} \)
\(a_{58}= -1.12444861 \pm 2.7 \cdot 10^{-5} \) \(a_{59}= -0.83897638 \pm 2.6 \cdot 10^{-5} \) \(a_{60}= +0.44473061 \pm 3.9 \cdot 10^{-5} \)

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