Properties

Label 31.2
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 1.062840
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(1.06284037123837548152868977754 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.59084640 \pm 2.6 \cdot 10^{-7} \) \(a_{3}= +0.38840372 \pm 2.3 \cdot 10^{-7} \)
\(a_{4}= -0.65090053 \pm 2.8 \cdot 10^{-7} \) \(a_{5}= -0.87900136 \pm 2.1 \cdot 10^{-7} \) \(a_{6}= +0.22948694 \pm 2.9 \cdot 10^{-7} \)
\(a_{7}= +1.67973048 \pm 2.1 \cdot 10^{-7} \) \(a_{8}= -0.97542864 \pm 2.9 \cdot 10^{-7} \) \(a_{9}= -0.84914255 \pm 2.2 \cdot 10^{-7} \)
\(a_{10}= -0.51935479 \pm 2.6 \cdot 10^{-7} \) \(a_{11}= -0.08882498 \pm 2.1 \cdot 10^{-7} \) \(a_{12}= -0.25281219 \pm 3.4 \cdot 10^{-7} \)
\(a_{13}= +1.08207949 \pm 2.2 \cdot 10^{-7} \) \(a_{14}= +0.99246271 \pm 2.2 \cdot 10^{-7} \) \(a_{15}= -0.34140740 \pm 2.2 \cdot 10^{-7} \)
\(a_{16}= +0.07457203 \pm 2.6 \cdot 10^{-7} \) \(a_{17}= +0.79742751 \pm 2.0 \cdot 10^{-7} \) \(a_{18}= -0.50171282 \pm 2.8 \cdot 10^{-7} \)
\(a_{19}= -0.75784964 \pm 2.2 \cdot 10^{-7} \) \(a_{20}= +0.57214245 \pm 2.7 \cdot 10^{-7} \) \(a_{21}= +0.65241356 \pm 2.3 \cdot 10^{-7} \)
\(a_{22}= -0.05248192 \pm 2.3 \cdot 10^{-7} \) \(a_{23}= +0.49492738 \pm 2.0 \cdot 10^{-7} \) \(a_{24}= -0.37886011 \pm 3.5 \cdot 10^{-7} \)
\(a_{25}= -0.22735661 \pm 2.0 \cdot 10^{-7} \) \(a_{26}= +0.63934277 \pm 2.2 \cdot 10^{-7} \) \(a_{27}= -0.71821384 \pm 1.9 \cdot 10^{-7} \)
\(a_{28}= -1.09333746 \pm 2.2 \cdot 10^{-7} \) \(a_{29}= -0.94335057 \pm 2.0 \cdot 10^{-7} \) \(a_{30}= -0.20171933 \pm 3.0 \cdot 10^{-7} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +1.01948925 \pm 2.8 \cdot 10^{-7} \) \(a_{33}= -0.03449995 \pm 2.2 \cdot 10^{-7} \)
\(a_{34}= +0.47115718 \pm 2.7 \cdot 10^{-7} \) \(a_{35}= -1.47648537 \pm 1.9 \cdot 10^{-7} \) \(a_{36}= +0.55270734 \pm 3.0 \cdot 10^{-7} \)
\(a_{37}= -1.21565202 \pm 1.9 \cdot 10^{-7} \) \(a_{38}= -0.44777273 \pm 2.7 \cdot 10^{-7} \) \(a_{39}= +0.42028370 \pm 2.1 \cdot 10^{-7} \)
\(a_{40}= +0.85740310 \pm 2.8 \cdot 10^{-7} \) \(a_{41}= -0.26938096 \pm 1.9 \cdot 10^{-7} \) \(a_{42}= +0.38547620 \pm 2.6 \cdot 10^{-7} \)
\(a_{43}= +0.37786146 \pm 1.8 \cdot 10^{-7} \) \(a_{44}= +0.05781622 \pm 2.2 \cdot 10^{-7} \) \(a_{45}= +0.74639746 \pm 2.1 \cdot 10^{-7} \)
\(a_{46}= +0.29242606 \pm 1.9 \cdot 10^{-7} \) \(a_{47}= +0.11991544 \pm 1.9 \cdot 10^{-7} \) \(a_{48}= +0.02896405 \pm 3.3 \cdot 10^{-7} \)
\(a_{49}= +1.82149447 \pm 2.0 \cdot 10^{-7} \) \(a_{50}= -0.13433283 \pm 2.6 \cdot 10^{-7} \) \(a_{51}= +0.30972381 \pm 2.3 \cdot 10^{-7} \)
\(a_{52}= -0.70432611 \pm 2.3 \cdot 10^{-7} \) \(a_{53}= +0.80890806 \pm 2.0 \cdot 10^{-7} \) \(a_{54}= -0.42435406 \pm 2.5 \cdot 10^{-7} \)
\(a_{55}= +0.07807727 \pm 2.3 \cdot 10^{-7} \) \(a_{56}= -1.63845721 \pm 2.2 \cdot 10^{-7} \) \(a_{57}= -0.29435162 \pm 2.2 \cdot 10^{-7} \)
\(a_{58}= -0.55737529 \pm 2.3 \cdot 10^{-7} \) \(a_{59}= +1.23064715 \pm 2.3 \cdot 10^{-7} \) \(a_{60}= +0.22222226 \pm 3.4 \cdot 10^{-7} \)

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