Properties

Label 31.118
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 7.297037
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(7.2970372655741980323043556914 \pm 3 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.71492497 \pm 4.3 \cdot 10^{-7} \) \(a_{3}= -1.24455213 \pm 3.9 \cdot 10^{-7} \)
\(a_{4}= +1.94096765 \pm 4.3 \cdot 10^{-7} \) \(a_{5}= -1.33333549 \pm 3.7 \cdot 10^{-7} \) \(a_{6}= -2.13431353 \pm 4.4 \cdot 10^{-7} \)
\(a_{7}= -0.17678692 \pm 3.8 \cdot 10^{-7} \) \(a_{8}= +1.61368893 \pm 4.2 \cdot 10^{-7} \) \(a_{9}= +0.54891001 \pm 3.7 \cdot 10^{-7} \)
\(a_{10}= -2.28657032 \pm 3.6 \cdot 10^{-7} \) \(a_{11}= +0.63068862 \pm 3.7 \cdot 10^{-7} \) \(a_{12}= -2.41563543 \pm 4.1 \cdot 10^{-7} \)
\(a_{13}= +1.47036065 \pm 3.0 \cdot 10^{-7} \) \(a_{14}= -0.30317630 \pm 5.1 \cdot 10^{-7} \) \(a_{15}= +1.65940552 \pm 4.0 \cdot 10^{-7} \)
\(a_{16}= +0.82638778 \pm 4.5 \cdot 10^{-7} \) \(a_{17}= -0.23887252 \pm 3.5 \cdot 10^{-7} \) \(a_{18}= +0.94133948 \pm 3.3 \cdot 10^{-7} \)
\(a_{19}= +1.53279369 \pm 3.4 \cdot 10^{-7} \) \(a_{20}= -2.58796105 \pm 3.8 \cdot 10^{-7} \) \(a_{21}= +0.22002053 \pm 3.8 \cdot 10^{-7} \)
\(a_{22}= +1.08158366 \pm 4.4 \cdot 10^{-7} \) \(a_{23}= -0.32521159 \pm 3.0 \cdot 10^{-7} \) \(a_{24}= -2.00831999 \pm 4.5 \cdot 10^{-7} \)
\(a_{25}= +0.77778352 \pm 4.0 \cdot 10^{-7} \) \(a_{26}= +2.52155820 \pm 3.4 \cdot 10^{-7} \) \(a_{27}= +0.56140501 \pm 3.8 \cdot 10^{-7} \)
\(a_{28}= -0.34313769 \pm 5.5 \cdot 10^{-7} \) \(a_{29}= +0.51746345 \pm 3.6 \cdot 10^{-7} \) \(a_{30}= +2.84575597 \pm 4.1 \cdot 10^{-7} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.19649589 \pm 4.3 \cdot 10^{-7} \) \(a_{33}= -0.78492487 \pm 4.2 \cdot 10^{-7} \)
\(a_{34}= -0.40964845 \pm 3.7 \cdot 10^{-7} \) \(a_{35}= +0.23571627 \pm 3.9 \cdot 10^{-7} \) \(a_{36}= +1.06541657 \pm 3.3 \cdot 10^{-7} \)
\(a_{37}= +1.75166345 \pm 3.7 \cdot 10^{-7} \) \(a_{38}= +2.62862617 \pm 4.4 \cdot 10^{-7} \) \(a_{39}= -1.82994048 \pm 3.8 \cdot 10^{-7} \)
\(a_{40}= -2.15158871 \pm 3.5 \cdot 10^{-7} \) \(a_{41}= +1.51657109 \pm 2.9 \cdot 10^{-7} \) \(a_{42}= +0.37731871 \pm 5.0 \cdot 10^{-7} \)
\(a_{43}= -0.09524524 \pm 3.8 \cdot 10^{-7} \) \(a_{44}= +1.22414621 \pm 4.7 \cdot 10^{-7} \) \(a_{45}= -0.73188119 \pm 3.8 \cdot 10^{-7} \)
\(a_{46}= -0.55771347 \pm 3.8 \cdot 10^{-7} \) \(a_{47}= +0.05755514 \pm 3.3 \cdot 10^{-7} \) \(a_{48}= -1.02848267 \pm 4.1 \cdot 10^{-7} \)
\(a_{49}= -0.96874639 \pm 3.3 \cdot 10^{-7} \) \(a_{50}= +1.33384039 \pm 3.7 \cdot 10^{-7} \) \(a_{51}= +0.29728930 \pm 3.3 \cdot 10^{-7} \)
\(a_{52}= +2.85392246 \pm 3.3 \cdot 10^{-7} \) \(a_{53}= -1.61621993 \pm 3.7 \cdot 10^{-7} \) \(a_{54}= +0.96276747 \pm 4.1 \cdot 10^{-7} \)
\(a_{55}= -0.84091952 \pm 3.9 \cdot 10^{-7} \) \(a_{56}= -0.28527909 \pm 5.6 \cdot 10^{-7} \) \(a_{57}= -1.90764165 \pm 3.1 \cdot 10^{-7} \)
\(a_{58}= +0.88741100 \pm 4.4 \cdot 10^{-7} \) \(a_{59}= +1.59129741 \pm 3.0 \cdot 10^{-7} \) \(a_{60}= +3.22085244 \pm 3.8 \cdot 10^{-7} \)

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