Properties

Label 2.12
Level $2$
Weight $0$
Character 2.1
Symmetry even
\(R\) 14.68501
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(14.6850159506009195638314416208 \pm 4 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.77757400 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.07814467 \pm 1 \cdot 10^{-8} \) \(a_{6}= -1.25693463 \pm 1.1 \cdot 10^{-8} \)
\(a_{7}= +0.16824328 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +2.15976934 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.05525663 \pm 1.1 \cdot 10^{-8} \) \(a_{11}= +0.60191406 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.88878700 \pm 1.1 \cdot 10^{-8} \)
\(a_{13}= +0.11544121 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.11896596 \pm 1.1 \cdot 10^{-8} \) \(a_{15}= -0.13890794 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.01121590 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.52718755 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= +0.56820884 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.03907234 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= +0.29906488 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.42561751 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.97561607 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.62846732 \pm 1.1 \cdot 10^{-8} \)
\(a_{25}= -0.99389341 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.08162927 \pm 1.1 \cdot 10^{-8} \) \(a_{27}= +2.06157583 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.08412164 \pm 1.1 \cdot 10^{-8} \) \(a_{29}= -1.77380799 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.09822275 \pm 1.2 \cdot 10^{-8} \)
\(a_{31}= +0.26027214 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +1.06994678 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.71503762 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= -0.01314732 \pm 1 \cdot 10^{-8} \) \(a_{36}= +1.07988467 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -1.27796089 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.40178432 \pm 1.1 \cdot 10^{-8} \) \(a_{39}= +0.20520530 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.02762831 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= +1.10714113 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.21147080 \pm 1.2 \cdot 10^{-8} \)
\(a_{43}= -0.41289358 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.30095703 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.16877447 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.68986474 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +0.03493710 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.44439350 \pm 1.1 \cdot 10^{-8} \)
\(a_{49}= -0.97169420 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.70278877 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= +1.79751110 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.05772061 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= -1.12774417 \pm 1 \cdot 10^{-8} \) \(a_{54}= -1.45775425 \pm 1.1 \cdot 10^{-8} \)
\(a_{55}= -0.04703638 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.05948298 \pm 1.1 \cdot 10^{-8} \) \(a_{57}= +1.01003326 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +1.25427166 \pm 1.1 \cdot 10^{-8} \) \(a_{59}= -0.88080145 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.06945397 \pm 1.2 \cdot 10^{-8} \)

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