Properties

Label 31.86
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 6.345067
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(6.34506747083856200340834485636 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.65456836 \pm 3.9 \cdot 10^{-5} \) \(a_{3}= +1.15923229 \pm 3.5 \cdot 10^{-5} \)
\(a_{4}= +1.73759647 \pm 4.3 \cdot 10^{-5} \) \(a_{5}= -0.14865430 \pm 3.3 \cdot 10^{-5} \) \(a_{6}= -1.91802907 \pm 4.5 \cdot 10^{-5} \)
\(a_{7}= -0.35369458 \pm 3.2 \cdot 10^{-5} \) \(a_{8}= -1.22040379 \pm 4.5 \cdot 10^{-5} \) \(a_{9}= +0.34381949 \pm 3.3 \cdot 10^{-5} \)
\(a_{10}= +0.24595871 \pm 4.0 \cdot 10^{-5} \) \(a_{11}= +0.10671019 \pm 3.2 \cdot 10^{-5} \) \(a_{12}= +2.01427793 \pm 5.2 \cdot 10^{-5} \)
\(a_{13}= -0.21029073 \pm 3.4 \cdot 10^{-5} \) \(a_{14}= +0.58521186 \pm 3.3 \cdot 10^{-5} \) \(a_{15}= -0.17232487 \pm 3.4 \cdot 10^{-5} \)
\(a_{16}= +0.28164503 \pm 4.0 \cdot 10^{-5} \) \(a_{17}= -0.30638537 \pm 3.0 \cdot 10^{-5} \) \(a_{18}= -0.56887286 \pm 4.3 \cdot 10^{-5} \)
\(a_{19}= +1.26009377 \pm 3.4 \cdot 10^{-5} \) \(a_{20}= -0.25830120 \pm 4.2 \cdot 10^{-5} \) \(a_{21}= -0.41001417 \pm 3.5 \cdot 10^{-5} \)
\(a_{22}= -0.17655930 \pm 3.5 \cdot 10^{-5} \) \(a_{23}= +1.12101026 \pm 3.1 \cdot 10^{-5} \) \(a_{24}= -1.41473148 \pm 5.4 \cdot 10^{-5} \)
\(a_{25}= -0.97790190 \pm 3.1 \cdot 10^{-5} \) \(a_{26}= +0.34794039 \pm 3.4 \cdot 10^{-5} \) \(a_{27}= -0.76066563 \pm 3.0 \cdot 10^{-5} \)
\(a_{28}= -0.61457845 \pm 3.5 \cdot 10^{-5} \) \(a_{29}= -0.84374798 \pm 3.0 \cdot 10^{-5} \) \(a_{30}= +0.28512328 \pm 4.5 \cdot 10^{-5} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.75440283 \pm 4.3 \cdot 10^{-5} \) \(a_{33}= +0.12370190 \pm 3.4 \cdot 10^{-5} \)
\(a_{34}= +0.50693553 \pm 4.2 \cdot 10^{-5} \) \(a_{35}= +0.05257822 \pm 3.0 \cdot 10^{-5} \) \(a_{36}= +0.59741954 \pm 4.6 \cdot 10^{-5} \)
\(a_{37}= -0.38429428 \pm 3.0 \cdot 10^{-5} \) \(a_{38}= -2.08491129 \pm 4.1 \cdot 10^{-5} \) \(a_{39}= -0.24377581 \pm 3.3 \cdot 10^{-5} \)
\(a_{40}= +0.18141828 \pm 4.3 \cdot 10^{-5} \) \(a_{41}= -0.58651905 \pm 2.9 \cdot 10^{-5} \) \(a_{42}= +0.67839648 \pm 4.0 \cdot 10^{-5} \)
\(a_{43}= -0.17409869 \pm 2.8 \cdot 10^{-5} \) \(a_{44}= +0.18541925 \pm 3.4 \cdot 10^{-5} \) \(a_{45}= -0.05111025 \pm 3.3 \cdot 10^{-5} \)
\(a_{46}= -1.85478811 \pm 2.9 \cdot 10^{-5} \) \(a_{47}= -1.16566093 \pm 2.9 \cdot 10^{-5} \) \(a_{48}= +0.32649201 \pm 5.0 \cdot 10^{-5} \)
\(a_{49}= -0.87490015 \pm 3.1 \cdot 10^{-5} \) \(a_{50}= +1.61800554 \pm 3.9 \cdot 10^{-5} \) \(a_{51}= -0.35517181 \pm 3.5 \cdot 10^{-5} \)
\(a_{52}= -0.36540044 \pm 3.5 \cdot 10^{-5} \) \(a_{53}= +0.48159942 \pm 3.1 \cdot 10^{-5} \) \(a_{54}= +1.25857328 \pm 3.9 \cdot 10^{-5} \)
\(a_{55}= -0.01586293 \pm 3.5 \cdot 10^{-5} \) \(a_{56}= +0.43165020 \pm 3.3 \cdot 10^{-5} \) \(a_{57}= +1.46074139 \pm 3.3 \cdot 10^{-5} \)
\(a_{58}= +1.39603872 \pm 3.6 \cdot 10^{-5} \) \(a_{59}= +0.83732833 \pm 3.5 \cdot 10^{-5} \) \(a_{60}= -0.29943109 \pm 5.1 \cdot 10^{-5} \)

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