Properties

Label 6.23
Level $6$
Weight $0$
Character 6.1
Symmetry even
\(R\) 11.70574
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(11.7057493188922908818178031444 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.66850969 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.07206613 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.47270773 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +1.67985412 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= -0.94390003 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.05095845 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.38596425 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -1.25685865 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= -1.08123179 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.33425484 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.04160740 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -1.18783624 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.42557446 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= -0.55309480 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.66743811 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.03603307 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -1.15829044 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.27291794 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -1.10192872 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.96986423 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.88873327 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= +0.04817691 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= -0.81918702 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.76454633 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -0.54496094 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +0.23635387 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -1.72746323 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.02942088 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.24615773 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.83992706 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.22283656 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -0.30092659 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +1.81532756 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= -0.99480647 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.39109708 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.72564768 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -0.47195002 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +1.02315543 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= -1.12299875 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.02547923 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.62424946 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.81903502 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= +0.31930564 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.19298212 \pm 1.0 \cdot 10^{-8} \)

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