Properties

Label 31.122
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 7.450927
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(7.4509277931272663460605070073 \pm 4 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.19287803 \pm 4.8 \cdot 10^{-7} \) \(a_{3}= +1.01773665 \pm 4.3 \cdot 10^{-7} \)
\(a_{4}= +0.42295799 \pm 4.8 \cdot 10^{-7} \) \(a_{5}= -1.70793059 \pm 4.1 \cdot 10^{-7} \) \(a_{6}= +1.21403569 \pm 4.8 \cdot 10^{-7} \)
\(a_{7}= +1.39494518 \pm 4.2 \cdot 10^{-7} \) \(a_{8}= -0.68834074 \pm 4.7 \cdot 10^{-7} \) \(a_{9}= +0.03578789 \pm 4.1 \cdot 10^{-7} \)
\(a_{10}= -2.03735287 \pm 4.0 \cdot 10^{-7} \) \(a_{11}= +0.79992520 \pm 4.1 \cdot 10^{-7} \) \(a_{12}= +0.43045984 \pm 4.6 \cdot 10^{-7} \)
\(a_{13}= -1.24341253 \pm 3.3 \cdot 10^{-7} \) \(a_{14}= +1.66399945 \pm 5.6 \cdot 10^{-7} \) \(a_{15}= -1.73822355 \pm 4.4 \cdot 10^{-7} \)
\(a_{16}= -1.24406453 \pm 4.9 \cdot 10^{-7} \) \(a_{17}= -0.29787576 \pm 3.9 \cdot 10^{-7} \) \(a_{18}= +0.04269058 \pm 3.6 \cdot 10^{-7} \)
\(a_{19}= -1.29979405 \pm 3.8 \cdot 10^{-7} \) \(a_{20}= -0.72238288 \pm 4.2 \cdot 10^{-7} \) \(a_{21}= +1.41968683 \pm 4.2 \cdot 10^{-7} \)
\(a_{22}= +0.95421319 \pm 4.9 \cdot 10^{-7} \) \(a_{23}= -1.57159284 \pm 3.3 \cdot 10^{-7} \) \(a_{24}= -0.70054960 \pm 5.0 \cdot 10^{-7} \)
\(a_{25}= +1.91702690 \pm 4.4 \cdot 10^{-7} \) \(a_{26}= -1.48323948 \pm 3.7 \cdot 10^{-7} \) \(a_{27}= -0.98131400 \pm 4.2 \cdot 10^{-7} \)
\(a_{28}= +0.59000320 \pm 6.0 \cdot 10^{-7} \) \(a_{29}= +0.65962923 \pm 3.9 \cdot 10^{-7} \) \(a_{30}= -2.07348868 \pm 4.5 \cdot 10^{-7} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.79567650 \pm 4.8 \cdot 10^{-7} \) \(a_{33}= +0.81411319 \pm 4.7 \cdot 10^{-7} \)
\(a_{34}= -0.35532945 \pm 4.1 \cdot 10^{-7} \) \(a_{35}= -2.38246954 \pm 4.3 \cdot 10^{-7} \) \(a_{36}= +0.01513677 \pm 3.6 \cdot 10^{-7} \)
\(a_{37}= -1.40042360 \pm 4.1 \cdot 10^{-7} \) \(a_{38}= -1.55049576 \pm 4.9 \cdot 10^{-7} \) \(a_{39}= -1.26546650 \pm 4.1 \cdot 10^{-7} \)
\(a_{40}= +1.17563820 \pm 3.9 \cdot 10^{-7} \) \(a_{41}= +0.79912583 \pm 3.2 \cdot 10^{-7} \) \(a_{42}= +1.69351323 \pm 5.5 \cdot 10^{-7} \)
\(a_{43}= +0.82574191 \pm 4.2 \cdot 10^{-7} \) \(a_{44}= +0.33833475 \pm 5.2 \cdot 10^{-7} \) \(a_{45}= -0.06112323 \pm 4.2 \cdot 10^{-7} \)
\(a_{46}= -1.87471856 \pm 4.2 \cdot 10^{-7} \) \(a_{47}= -0.67472131 \pm 3.6 \cdot 10^{-7} \) \(a_{48}= -1.26613006 \pm 4.5 \cdot 10^{-7} \)
\(a_{49}= +0.94587205 \pm 3.7 \cdot 10^{-7} \) \(a_{50}= +2.28677926 \pm 4.1 \cdot 10^{-7} \) \(a_{51}= -0.30315908 \pm 3.7 \cdot 10^{-7} \)
\(a_{52}= -0.52591126 \pm 3.7 \cdot 10^{-7} \) \(a_{53}= -0.29917709 \pm 4.1 \cdot 10^{-7} \) \(a_{54}= -1.17058791 \pm 4.6 \cdot 10^{-7} \)
\(a_{55}= -1.36621671 \pm 4.3 \cdot 10^{-7} \) \(a_{56}= -0.96019760 \pm 6.2 \cdot 10^{-7} \) \(a_{57}= -1.32284804 \pm 3.4 \cdot 10^{-7} \)
\(a_{58}= +0.78685721 \pm 4.9 \cdot 10^{-7} \) \(a_{59}= +1.04858122 \pm 3.3 \cdot 10^{-7} \) \(a_{60}= -0.73519553 \pm 4.2 \cdot 10^{-7} \)

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