Properties

Label 31.85
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 6.257490
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(6.25749028728913051104672423251 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.43091504 \pm 1.2 \cdot 10^{-5} \) \(a_{3}= +0.83893686 \pm 1.1 \cdot 10^{-5} \)
\(a_{4}= -0.81431223 \pm 1.3 \cdot 10^{-5} \) \(a_{5}= +1.70819464 \pm 1.0 \cdot 10^{-5} \) \(a_{6}= -0.36151051 \pm 1.4 \cdot 10^{-5} \)
\(a_{7}= +1.36181413 \pm 1.0 \cdot 10^{-5} \) \(a_{8}= +0.78181443 \pm 1.4 \cdot 10^{-5} \) \(a_{9}= -0.29618494 \pm 1.0 \cdot 10^{-5} \)
\(a_{10}= -0.73608677 \pm 1.3 \cdot 10^{-5} \) \(a_{11}= -0.65082371 \pm 1.0 \cdot 10^{-5} \) \(a_{12}= -0.68315654 \pm 1.6 \cdot 10^{-5} \)
\(a_{13}= +0.37815664 \pm 1.0 \cdot 10^{-5} \) \(a_{14}= -0.58682619 \pm 1.0 \cdot 10^{-5} \) \(a_{15}= +1.43306745 \pm 1.1 \cdot 10^{-5} \)
\(a_{16}= +0.47741663 \pm 1.2 \cdot 10^{-5} \) \(a_{17}= -1.10907001 \pm 9.8 \cdot 10^{-6} \) \(a_{18}= +0.12763055 \pm 1.3 \cdot 10^{-5} \)
\(a_{19}= +0.59071319 \pm 1.1 \cdot 10^{-5} \) \(a_{20}= -1.39100378 \pm 1.3 \cdot 10^{-5} \) \(a_{21}= +1.14247608 \pm 1.1 \cdot 10^{-5} \)
\(a_{22}= +0.28044973 \pm 1.1 \cdot 10^{-5} \) \(a_{23}= +1.38842067 \pm 9.9 \cdot 10^{-6} \) \(a_{24}= +0.65589294 \pm 1.7 \cdot 10^{-5} \)
\(a_{25}= +1.91792893 \pm 1.0 \cdot 10^{-5} \) \(a_{26}= -0.16295338 \pm 1.1 \cdot 10^{-5} \) \(a_{27}= -1.08741733 \pm 9.6 \cdot 10^{-6} \)
\(a_{28}= -1.10894190 \pm 1.1 \cdot 10^{-5} \) \(a_{29}= +1.08658086 \pm 9.8 \cdot 10^{-6} \) \(a_{30}= -0.61753032 \pm 1.4 \cdot 10^{-5} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.98754044 \pm 1.3 \cdot 10^{-5} \) \(a_{33}= -0.54600000 \pm 1.1 \cdot 10^{-5} \)
\(a_{34}= +0.47791495 \pm 1.3 \cdot 10^{-5} \) \(a_{35}= +2.32624360 \pm 9.6 \cdot 10^{-6} \) \(a_{36}= +0.24118702 \pm 1.4 \cdot 10^{-5} \)
\(a_{37}= +1.19280659 \pm 9.5 \cdot 10^{-6} \) \(a_{38}= -0.25454720 \pm 1.3 \cdot 10^{-5} \) \(a_{39}= +0.31724954 \pm 1.0 \cdot 10^{-5} \)
\(a_{40}= +1.33549122 \pm 1.3 \cdot 10^{-5} \) \(a_{41}= +0.26524516 \pm 9.4 \cdot 10^{-6} \) \(a_{42}= -0.49231013 \pm 1.2 \cdot 10^{-5} \)
\(a_{43}= -1.77223060 \pm 9.0 \cdot 10^{-6} \) \(a_{44}= +0.52997370 \pm 1.1 \cdot 10^{-5} \) \(a_{45}= -0.50594153 \pm 1.0 \cdot 10^{-5} \)
\(a_{46}= -0.59829135 \pm 9.5 \cdot 10^{-6} \) \(a_{47}= +1.28073654 \pm 9.2 \cdot 10^{-6} \) \(a_{48}= +0.40052241 \pm 1.6 \cdot 10^{-5} \)
\(a_{49}= +0.85453773 \pm 9.9 \cdot 10^{-6} \) \(a_{50}= -0.82646443 \pm 1.2 \cdot 10^{-5} \) \(a_{51}= -0.93043972 \pm 1.1 \cdot 10^{-5} \)
\(a_{52}= -0.30793757 \pm 1.1 \cdot 10^{-5} \) \(a_{53}= +0.57451711 \pm 9.9 \cdot 10^{-6} \) \(a_{54}= +0.46858448 \pm 1.2 \cdot 10^{-5} \)
\(a_{55}= -1.11173357 \pm 1.1 \cdot 10^{-5} \) \(a_{56}= +1.06468594 \pm 1.0 \cdot 10^{-5} \) \(a_{57}= +0.49557107 \pm 1.0 \cdot 10^{-5} \)
\(a_{58}= -0.46822404 \pm 1.1 \cdot 10^{-5} \) \(a_{59}= -0.36469499 \pm 1.1 \cdot 10^{-5} \) \(a_{60}= -1.16696435 \pm 1.6 \cdot 10^{-5} \)

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