Properties

Label 6.42
Level $6$
Weight $0$
Character 6.1
Symmetry odd
\(R\) 16.04269
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: \(16.0426930590212746595448890985 \pm 3 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +1.36060894 \pm 3.4 \cdot 10^{-4} \) \(a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -1.80473738 \pm 3.4 \cdot 10^{-4} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.96209580 \pm 3.4 \cdot 10^{-4} \) \(a_{11}= +0.17474705 \pm 2.7 \cdot 10^{-4} \) \(a_{12}= -0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= +0.44448836 \pm 4.5 \cdot 10^{-4} \) \(a_{14}= +1.27614204 \pm 3.4 \cdot 10^{-4} \) \(a_{15}= -0.78554793 \pm 3.4 \cdot 10^{-4} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.44230049 \pm 2.7 \cdot 10^{-4} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= -1.21873231 \pm 6.1 \cdot 10^{-4} \) \(a_{20}= +0.68030447 \pm 3.4 \cdot 10^{-4} \) \(a_{21}= +1.04196561 \pm 3.4 \cdot 10^{-4} \)
\(a_{22}= -0.12356483 \pm 2.7 \cdot 10^{-4} \) \(a_{23}= +1.28038308 \pm 4.3 \cdot 10^{-4} \) \(a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= +0.85125667 \pm 3.3 \cdot 10^{-4} \) \(a_{26}= -0.31430073 \pm 4.5 \cdot 10^{-4} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.90236869 \pm 3.4 \cdot 10^{-4} \) \(a_{29}= -0.53200567 \pm 3.2 \cdot 10^{-4} \) \(a_{30}= +0.55546627 \pm 3.4 \cdot 10^{-4} \)
\(a_{31}= -0.18049367 \pm 5.6 \cdot 10^{-4} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.10089026 \pm 2.7 \cdot 10^{-4} \)
\(a_{34}= -1.01986045 \pm 2.7 \cdot 10^{-4} \) \(a_{35}= -2.45554180 \pm 2.7 \cdot 10^{-4} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= -0.96606237 \pm 4.8 \cdot 10^{-4} \) \(a_{38}= +0.86177388 \pm 6.1 \cdot 10^{-4} \) \(a_{39}= -0.25662547 \pm 4.5 \cdot 10^{-4} \)
\(a_{40}= -0.48104790 \pm 3.4 \cdot 10^{-4} \) \(a_{41}= +0.14736262 \pm 2.6 \cdot 10^{-4} \) \(a_{42}= -0.73678095 \pm 3.4 \cdot 10^{-4} \)
\(a_{43}= -0.22838398 \pm 2.6 \cdot 10^{-4} \) \(a_{44}= +0.08737353 \pm 2.7 \cdot 10^{-4} \) \(a_{45}= +0.45353631 \pm 3.4 \cdot 10^{-4} \)
\(a_{46}= -0.90536756 \pm 4.3 \cdot 10^{-4} \) \(a_{47}= -1.53413251 \pm 3.9 \cdot 10^{-4} \) \(a_{48}= -0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= +2.25707700 \pm 3.8 \cdot 10^{-4} \) \(a_{50}= -0.60192937 \pm 3.3 \cdot 10^{-4} \) \(a_{51}= -0.83271257 \pm 2.7 \cdot 10^{-4} \)
\(a_{52}= +0.22224418 \pm 4.5 \cdot 10^{-4} \) \(a_{53}= -0.55238004 \pm 6.0 \cdot 10^{-4} \) \(a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= +0.23776240 \pm 2.9 \cdot 10^{-4} \) \(a_{56}= +0.63807102 \pm 3.4 \cdot 10^{-4} \) \(a_{57}= +0.70363543 \pm 6.1 \cdot 10^{-4} \)
\(a_{58}= +0.37618481 \pm 3.2 \cdot 10^{-4} \) \(a_{59}= -1.42346803 \pm 4.8 \cdot 10^{-4} \) \(a_{60}= -0.39277397 \pm 3.4 \cdot 10^{-4} \)

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