Properties

Label 31.65
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 5.544313
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(5.54431301671152222035488153346 \pm 9 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.55060734 \pm 2.3 \cdot 10^{-6} \) \(a_{3}= +0.63920337 \pm 2.0 \cdot 10^{-6} \)
\(a_{4}= +1.40438312 \pm 2.5 \cdot 10^{-6} \) \(a_{5}= -1.78809775 \pm 1.9 \cdot 10^{-6} \) \(a_{6}= +0.99115343 \pm 2.6 \cdot 10^{-6} \)
\(a_{7}= -1.77818165 \pm 1.8 \cdot 10^{-6} \) \(a_{8}= +0.62703943 \pm 2.6 \cdot 10^{-6} \) \(a_{9}= -0.59141905 \pm 1.9 \cdot 10^{-6} \)
\(a_{10}= -2.77263750 \pm 2.3 \cdot 10^{-6} \) \(a_{11}= +1.34264544 \pm 1.8 \cdot 10^{-6} \) \(a_{12}= +0.89768642 \pm 3.0 \cdot 10^{-6} \)
\(a_{13}= +0.50457257 \pm 1.9 \cdot 10^{-6} \) \(a_{14}= -2.75726151 \pm 1.9 \cdot 10^{-6} \) \(a_{15}= -1.14295811 \pm 2.0 \cdot 10^{-6} \)
\(a_{16}= -0.43209117 \pm 2.3 \cdot 10^{-6} \) \(a_{17}= -0.37495656 \pm 1.7 \cdot 10^{-6} \) \(a_{18}= -0.91705873 \pm 2.5 \cdot 10^{-6} \)
\(a_{19}= +0.22475320 \pm 2.0 \cdot 10^{-6} \) \(a_{20}= -2.51117430 \pm 2.4 \cdot 10^{-6} \) \(a_{21}= -1.13661970 \pm 2.0 \cdot 10^{-6} \)
\(a_{22}= +2.08191587 \pm 2.0 \cdot 10^{-6} \) \(a_{23}= +0.31423375 \pm 1.8 \cdot 10^{-6} \) \(a_{24}= +0.40080572 \pm 3.1 \cdot 10^{-6} \)
\(a_{25}= +2.19729358 \pm 1.8 \cdot 10^{-6} \) \(a_{26}= +0.78239393 \pm 2.0 \cdot 10^{-6} \) \(a_{27}= -1.01724042 \pm 1.7 \cdot 10^{-6} \)
\(a_{28}= -2.49724829 \pm 2.0 \cdot 10^{-6} \) \(a_{29}= -0.18403074 \pm 1.7 \cdot 10^{-6} \) \(a_{30}= -1.77227923 \pm 2.6 \cdot 10^{-6} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -1.29704318 \pm 2.5 \cdot 10^{-6} \) \(a_{33}= +0.85822349 \pm 2.0 \cdot 10^{-6} \)
\(a_{34}= -0.58141039 \pm 2.4 \cdot 10^{-6} \) \(a_{35}= +3.17956261 \pm 1.7 \cdot 10^{-6} \) \(a_{36}= -0.83057894 \pm 2.7 \cdot 10^{-6} \)
\(a_{37}= -1.16333125 \pm 1.7 \cdot 10^{-6} \) \(a_{38}= +0.34850396 \pm 2.4 \cdot 10^{-6} \) \(a_{39}= +0.32252449 \pm 1.9 \cdot 10^{-6} \)
\(a_{40}= -1.12120780 \pm 2.5 \cdot 10^{-6} \) \(a_{41}= -1.15736139 \pm 1.7 \cdot 10^{-6} \) \(a_{42}= -1.76245084 \pm 2.3 \cdot 10^{-6} \)
\(a_{43}= +0.27803102 \pm 1.6 \cdot 10^{-6} \) \(a_{44}= +1.88558859 \pm 2.0 \cdot 10^{-6} \) \(a_{45}= +1.05751508 \pm 1.9 \cdot 10^{-6} \)
\(a_{46}= +0.48725316 \pm 1.7 \cdot 10^{-6} \) \(a_{47}= -1.29142664 \pm 1.6 \cdot 10^{-6} \) \(a_{48}= -0.27619413 \pm 2.9 \cdot 10^{-6} \)
\(a_{49}= +2.16192996 \pm 1.8 \cdot 10^{-6} \) \(a_{50}= +3.40713955 \pm 2.3 \cdot 10^{-6} \) \(a_{51}= -0.23967349 \pm 2.0 \cdot 10^{-6} \)
\(a_{52}= +0.70861320 \pm 2.0 \cdot 10^{-6} \) \(a_{53}= -0.05683027 \pm 1.8 \cdot 10^{-6} \) \(a_{54}= -1.57734046 \pm 2.2 \cdot 10^{-6} \)
\(a_{55}= -2.40078129 \pm 2.0 \cdot 10^{-6} \) \(a_{56}= -1.11499001 \pm 1.9 \cdot 10^{-6} \) \(a_{57}= +0.14366300 \pm 1.9 \cdot 10^{-6} \)
\(a_{58}= -0.28535942 \pm 2.0 \cdot 10^{-6} \) \(a_{59}= +0.85326547 \pm 2.0 \cdot 10^{-6} \) \(a_{60}= -1.60515107 \pm 3.0 \cdot 10^{-6} \)

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