Properties

Label 31.95
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 6.554378
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(6.55437864992990317601903463798 \pm 9 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.94285053 \pm 2.1 \cdot 10^{-7} \) \(a_{3}= +1.68415553 \pm 1.9 \cdot 10^{-7} \)
\(a_{4}= +2.77466820 \pm 2.1 \cdot 10^{-7} \) \(a_{5}= -0.95995530 \pm 1.8 \cdot 10^{-7} \) \(a_{6}= +3.27206246 \pm 2.1 \cdot 10^{-7} \)
\(a_{7}= -0.19651903 \pm 1.8 \cdot 10^{-7} \) \(a_{8}= +3.44791505 \pm 2.1 \cdot 10^{-7} \) \(a_{9}= +1.83637984 \pm 1.8 \cdot 10^{-7} \)
\(a_{10}= -1.86504966 \pm 1.7 \cdot 10^{-7} \) \(a_{11}= -0.87971284 \pm 1.8 \cdot 10^{-7} \) \(a_{12}= +4.67297278 \pm 2.0 \cdot 10^{-7} \)
\(a_{13}= +1.25398220 \pm 1.5 \cdot 10^{-7} \) \(a_{14}= -0.38180711 \pm 2.5 \cdot 10^{-7} \) \(a_{15}= -1.61671402 \pm 1.9 \cdot 10^{-7} \)
\(a_{16}= +3.92411541 \pm 2.2 \cdot 10^{-7} \) \(a_{17}= -0.06388626 \pm 1.7 \cdot 10^{-7} \) \(a_{18}= +3.56781154 \pm 1.6 \cdot 10^{-7} \)
\(a_{19}= -1.25652836 \pm 1.6 \cdot 10^{-7} \) \(a_{20}= -2.66355743 \pm 1.8 \cdot 10^{-7} \) \(a_{21}= -0.33096861 \pm 1.8 \cdot 10^{-7} \)
\(a_{22}= -1.70915056 \pm 2.2 \cdot 10^{-7} \) \(a_{23}= -0.44479040 \pm 1.4 \cdot 10^{-7} \) \(a_{24}= +5.80682519 \pm 2.2 \cdot 10^{-7} \)
\(a_{25}= -0.07848583 \pm 1.9 \cdot 10^{-7} \) \(a_{26}= +2.43629998 \pm 1.6 \cdot 10^{-7} \) \(a_{27}= +1.40859372 \pm 1.9 \cdot 10^{-7} \)
\(a_{28}= -0.54527511 \pm 2.7 \cdot 10^{-7} \) \(a_{29}= -0.05693357 \pm 1.7 \cdot 10^{-7} \) \(a_{30}= -3.14103369 \pm 2.0 \cdot 10^{-7} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +4.17605466 \pm 2.1 \cdot 10^{-7} \) \(a_{33}= -1.48157324 \pm 2.0 \cdot 10^{-7} \)
\(a_{34}= -0.12412146 \pm 1.8 \cdot 10^{-7} \) \(a_{35}= +0.18864949 \pm 1.9 \cdot 10^{-7} \) \(a_{36}= +5.09534473 \pm 1.6 \cdot 10^{-7} \)
\(a_{37}= -1.41848545 \pm 1.8 \cdot 10^{-7} \) \(a_{38}= -2.44124680 \pm 2.1 \cdot 10^{-7} \) \(a_{39}= +2.11190104 \pm 1.8 \cdot 10^{-7} \)
\(a_{40}= -3.30984432 \pm 1.7 \cdot 10^{-7} \) \(a_{41}= +1.15971531 \pm 1.4 \cdot 10^{-7} \) \(a_{42}= -0.64302255 \pm 2.4 \cdot 10^{-7} \)
\(a_{43}= +0.89329206 \pm 1.8 \cdot 10^{-7} \) \(a_{44}= -2.44091124 \pm 2.3 \cdot 10^{-7} \) \(a_{45}= -1.76284255 \pm 1.9 \cdot 10^{-7} \)
\(a_{46}= -0.86416127 \pm 1.8 \cdot 10^{-7} \) \(a_{47}= -0.53946255 \pm 1.6 \cdot 10^{-7} \) \(a_{48}= +6.60882064 \pm 2.0 \cdot 10^{-7} \)
\(a_{49}= -0.96138027 \pm 1.6 \cdot 10^{-7} \) \(a_{50}= -0.15248623 \pm 1.8 \cdot 10^{-7} \) \(a_{51}= -0.10759440 \pm 1.6 \cdot 10^{-7} \)
\(a_{52}= +3.47938452 \pm 1.6 \cdot 10^{-7} \) \(a_{53}= -0.14581953 \pm 1.8 \cdot 10^{-7} \) \(a_{54}= +2.73668706 \pm 2.0 \cdot 10^{-7} \)
\(a_{55}= +0.84448500 \pm 1.9 \cdot 10^{-7} \) \(a_{56}= -0.67758093 \pm 2.7 \cdot 10^{-7} \) \(a_{57}= -2.11618918 \pm 1.5 \cdot 10^{-7} \)
\(a_{58}= -0.11061342 \pm 2.1 \cdot 10^{-7} \) \(a_{59}= -1.03838333 \pm 1.4 \cdot 10^{-7} \) \(a_{60}= -4.48584497 \pm 1.8 \cdot 10^{-7} \)

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