Properties

Label 31.25
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 3.570957
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(3.57095767325986195615224710797 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.19993029 \pm 3.1 \cdot 10^{-8} \) \(a_{3}= -0.77641260 \pm 2.8 \cdot 10^{-8} \)
\(a_{4}= +0.43983269 \pm 3.2 \cdot 10^{-8} \) \(a_{5}= -1.26391731 \pm 2.7 \cdot 10^{-8} \) \(a_{6}= -0.93164099 \pm 3.2 \cdot 10^{-8} \)
\(a_{7}= +0.58807463 \pm 2.7 \cdot 10^{-8} \) \(a_{8}= -0.67216172 \pm 3.1 \cdot 10^{-8} \) \(a_{9}= -0.39718348 \pm 2.7 \cdot 10^{-8} \)
\(a_{10}= -1.51661267 \pm 2.6 \cdot 10^{-8} \) \(a_{11}= +1.11715185 \pm 2.7 \cdot 10^{-8} \) \(a_{12}= -0.34149165 \pm 3.0 \cdot 10^{-8} \)
\(a_{13}= -0.53594345 \pm 2.2 \cdot 10^{-8} \) \(a_{14}= +0.70564856 \pm 3.7 \cdot 10^{-8} \) \(a_{15}= +0.98132133 \pm 2.9 \cdot 10^{-8} \)
\(a_{16}= -1.24637990 \pm 3.3 \cdot 10^{-8} \) \(a_{17}= -1.38855599 \pm 2.5 \cdot 10^{-8} \) \(a_{18}= -0.47659248 \pm 2.4 \cdot 10^{-8} \)
\(a_{19}= -0.67650317 \pm 2.5 \cdot 10^{-8} \) \(a_{20}= -0.55591216 \pm 2.8 \cdot 10^{-8} \) \(a_{21}= -0.45658855 \pm 2.7 \cdot 10^{-8} \)
\(a_{22}= +1.34050434 \pm 3.2 \cdot 10^{-8} \) \(a_{23}= +1.32245778 \pm 2.2 \cdot 10^{-8} \) \(a_{24}= +0.52187482 \pm 3.3 \cdot 10^{-8} \)
\(a_{25}= +0.59748698 \pm 2.9 \cdot 10^{-8} \) \(a_{26}= -0.64309478 \pm 2.4 \cdot 10^{-8} \) \(a_{27}= +1.08479085 \pm 2.8 \cdot 10^{-8} \)
\(a_{28}= +0.25865445 \pm 4.0 \cdot 10^{-8} \) \(a_{29}= -0.54316425 \pm 2.6 \cdot 10^{-8} \) \(a_{30}= +1.17751718 \pm 2.9 \cdot 10^{-8} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.82340727 \pm 3.2 \cdot 10^{-8} \) \(a_{33}= -0.86737077 \pm 3.1 \cdot 10^{-8} \)
\(a_{34}= -1.66617039 \pm 2.7 \cdot 10^{-8} \) \(a_{35}= -0.74327770 \pm 2.8 \cdot 10^{-8} \) \(a_{36}= -0.17469428 \pm 2.4 \cdot 10^{-8} \)
\(a_{37}= +0.93843530 \pm 2.7 \cdot 10^{-8} \) \(a_{38}= -0.81175664 \pm 3.2 \cdot 10^{-8} \) \(a_{39}= +0.41611325 \pm 2.7 \cdot 10^{-8} \)
\(a_{40}= +0.84955683 \pm 2.6 \cdot 10^{-8} \) \(a_{41}= -0.75545971 \pm 2.1 \cdot 10^{-8} \) \(a_{42}= -0.54787443 \pm 3.6 \cdot 10^{-8} \)
\(a_{43}= -1.61669622 \pm 2.7 \cdot 10^{-8} \) \(a_{44}= +0.49135991 \pm 3.4 \cdot 10^{-8} \) \(a_{45}= +0.50200707 \pm 2.8 \cdot 10^{-8} \)
\(a_{46}= +1.58685715 \pm 2.7 \cdot 10^{-8} \) \(a_{47}= -0.49815457 \pm 2.4 \cdot 10^{-8} \) \(a_{48}= +0.96770505 \pm 3.0 \cdot 10^{-8} \)
\(a_{49}= -0.65416823 \pm 2.4 \cdot 10^{-8} \) \(a_{50}= +0.71694272 \pm 2.7 \cdot 10^{-8} \) \(a_{51}= +1.07809237 \pm 2.4 \cdot 10^{-8} \)
\(a_{52}= -0.23572545 \pm 2.4 \cdot 10^{-8} \) \(a_{53}= -0.46919937 \pm 2.7 \cdot 10^{-8} \) \(a_{54}= +1.30167340 \pm 3.0 \cdot 10^{-8} \)
\(a_{55}= -1.41198757 \pm 2.8 \cdot 10^{-8} \) \(a_{56}= -0.39528125 \pm 4.1 \cdot 10^{-8} \) \(a_{57}= +0.52524558 \pm 2.3 \cdot 10^{-8} \)
\(a_{58}= -0.65175923 \pm 3.2 \cdot 10^{-8} \) \(a_{59}= +1.84103460 \pm 2.2 \cdot 10^{-8} \) \(a_{60}= +0.43161720 \pm 2.7 \cdot 10^{-8} \)

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