Properties

Label 6.5
Level $6$
Weight $0$
Character 6.1
Symmetry odd
\(R\) 5.871682
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(5.8716820924994175763649865141 \pm 3 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.71064027 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +1.37696096 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.50249856 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.69909898 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= +1.62942973 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.97365843 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.41028835 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.96385680 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= -0.59958056 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.35532014 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= +0.79498878 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.49433763 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.53799956 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= -0.49499040 \pm 1 \cdot 10^{-8} \) \(a_{26}= -1.15218081 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.68848048 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -0.21613339 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.29011768 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.17063755 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.40362498 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.68154968 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= +0.97852391 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= -1.14826931 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.42396748 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= +0.94075169 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= -0.25124928 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -1.23544533 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.56214196 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -0.02105707 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.34954949 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= +0.23688009 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -0.38042314 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +1.09954718 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= +0.89602149 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.35001107 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.55648298 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= +0.81471487 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= -0.57370499 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= -0.49680789 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.48682922 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.34616800 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.15282939 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= -0.29864134 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.20514418 \pm 1.0 \cdot 10^{-8} \)

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