Properties

Label 6.30
Level $6$
Weight $0$
Character 6.1
Symmetry even
\(R\) 13.25452
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: \(13.2545279009091376360016084446 \pm 3 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.25362063 \pm 2.6 \cdot 10^{-8} \) \(a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.92043812 \pm 1.2 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.17933687 \pm 3.6 \cdot 10^{-8} \) \(a_{11}= -0.60127167 \pm 2.3 \cdot 10^{-8} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= +1.21883607 \pm 2.2 \cdot 10^{-8} \) \(a_{14}= +0.65084804 \pm 2.2 \cdot 10^{-8} \) \(a_{15}= +0.14642794 \pm 3.6 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.62990649 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= -1.02056651 \pm 1.0 \cdot 10^{-8} \) \(a_{20}= +0.12681032 \pm 3.6 \cdot 10^{-8} \) \(a_{21}= -0.53141520 \pm 2.2 \cdot 10^{-8} \)
\(a_{22}= +0.42516328 \pm 3.4 \cdot 10^{-8} \) \(a_{23}= -1.90228214 \pm 1.2 \cdot 10^{-8} \) \(a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= -0.93567657 \pm 1.2 \cdot 10^{-8} \) \(a_{26}= -0.86184725 \pm 3.2 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.46021906 \pm 2.2 \cdot 10^{-8} \) \(a_{29}= +1.25185803 \pm 1.8 \cdot 10^{-8} \) \(a_{30}= -0.10354019 \pm 3.6 \cdot 10^{-8} \)
\(a_{31}= -1.33588283 \pm 1.1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.34714436 \pm 3.4 \cdot 10^{-8} \)
\(a_{34}= -0.44541115 \pm 2.0 \cdot 10^{-8} \) \(a_{35}= -0.23344210 \pm 1.4 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= -0.08472825 \pm 3.3 \cdot 10^{-8} \) \(a_{38}= +0.72164950 \pm 2.0 \cdot 10^{-8} \) \(a_{39}= +0.70369533 \pm 3.2 \cdot 10^{-8} \)
\(a_{40}= -0.08966843 \pm 3.6 \cdot 10^{-8} \) \(a_{41}= -0.23770994 \pm 2.1 \cdot 10^{-8} \) \(a_{42}= +0.37576729 \pm 2.2 \cdot 10^{-8} \)
\(a_{43}= -1.54088966 \pm 3.6 \cdot 10^{-8} \) \(a_{44}= -0.30063584 \pm 3.4 \cdot 10^{-8} \) \(a_{45}= +0.08454021 \pm 3.6 \cdot 10^{-8} \)
\(a_{46}= +1.34511660 \pm 2.2 \cdot 10^{-8} \) \(a_{47}= -1.39058236 \pm 1.1 \cdot 10^{-8} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= -0.15279366 \pm 1.6 \cdot 10^{-8} \) \(a_{50}= +0.66162325 \pm 2.3 \cdot 10^{-8} \) \(a_{51}= +0.36367668 \pm 2.0 \cdot 10^{-8} \)
\(a_{52}= +0.60941803 \pm 3.2 \cdot 10^{-8} \) \(a_{53}= -0.24768209 \pm 1.3 \cdot 10^{-8} \) \(a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= -0.15249490 \pm 2.7 \cdot 10^{-8} \) \(a_{56}= +0.32542402 \pm 2.2 \cdot 10^{-8} \) \(a_{57}= -0.58922435 \pm 2.0 \cdot 10^{-8} \)
\(a_{58}= -0.88519730 \pm 2.8 \cdot 10^{-8} \) \(a_{59}= +0.91644587 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.07321397 \pm 3.6 \cdot 10^{-8} \)

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