Properties

Label 6.43
Level $6$
Weight $0$
Character 6.1
Symmetry odd
\(R\) 16.13506
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: \(16.1350656626952838892792751054 \pm 4 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +1.11804145 \pm 4.3 \cdot 10^{-4} \) \(a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +1.57650130 \pm 4.3 \cdot 10^{-4} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.79057469 \pm 4.3 \cdot 10^{-4} \) \(a_{11}= -0.54859093 \pm 3.4 \cdot 10^{-4} \) \(a_{12}= -0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= -1.48076976 \pm 5.6 \cdot 10^{-4} \) \(a_{14}= +1.11475476 \pm 4.3 \cdot 10^{-4} \) \(a_{15}= -0.64550153 \pm 4.3 \cdot 10^{-4} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.83954495 \pm 3.4 \cdot 10^{-4} \) \(a_{18}= +0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= +1.46995620 \pm 7.6 \cdot 10^{-4} \) \(a_{20}= +0.55902072 \pm 4.3 \cdot 10^{-4} \) \(a_{21}= -0.91019345 \pm 4.3 \cdot 10^{-4} \)
\(a_{22}= -0.38791237 \pm 3.4 \cdot 10^{-4} \) \(a_{23}= -0.18937809 \pm 5.4 \cdot 10^{-4} \) \(a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= +0.25001667 \pm 4.2 \cdot 10^{-4} \) \(a_{26}= -1.04706234 \pm 5.6 \cdot 10^{-4} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.78825065 \pm 4.3 \cdot 10^{-4} \) \(a_{29}= +1.46575056 \pm 4.0 \cdot 10^{-4} \) \(a_{30}= -0.45643851 \pm 4.3 \cdot 10^{-4} \)
\(a_{31}= +0.03377559 \pm 7.0 \cdot 10^{-4} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.31672912 \pm 3.4 \cdot 10^{-4} \)
\(a_{34}= +0.59364793 \pm 3.4 \cdot 10^{-4} \) \(a_{35}= +1.76259379 \pm 3.4 \cdot 10^{-4} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= +0.00310624 \pm 6.0 \cdot 10^{-4} \) \(a_{38}= +1.03941600 \pm 7.6 \cdot 10^{-4} \) \(a_{39}= +0.85492282 \pm 5.6 \cdot 10^{-4} \)
\(a_{40}= +0.39528734 \pm 4.3 \cdot 10^{-4} \) \(a_{41}= -0.90020675 \pm 3.2 \cdot 10^{-4} \) \(a_{42}= -0.64360396 \pm 4.3 \cdot 10^{-4} \)
\(a_{43}= +1.41185778 \pm 3.2 \cdot 10^{-4} \) \(a_{44}= -0.27429547 \pm 3.4 \cdot 10^{-4} \) \(a_{45}= +0.37268048 \pm 4.3 \cdot 10^{-4} \)
\(a_{46}= -0.13391053 \pm 5.4 \cdot 10^{-4} \) \(a_{47}= +0.69758544 \pm 4.9 \cdot 10^{-4} \) \(a_{48}= -0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= +1.48535634 \pm 4.7 \cdot 10^{-4} \) \(a_{50}= +0.17678849 \pm 4.2 \cdot 10^{-4} \) \(a_{51}= -0.48471150 \pm 3.4 \cdot 10^{-4} \)
\(a_{52}= -0.74038488 \pm 5.6 \cdot 10^{-4} \) \(a_{53}= -0.03577334 \pm 7.5 \cdot 10^{-4} \) \(a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= -0.61334740 \pm 3.6 \cdot 10^{-4} \) \(a_{56}= +0.55737738 \pm 4.3 \cdot 10^{-4} \) \(a_{57}= -0.84867961 \pm 7.6 \cdot 10^{-4} \)
\(a_{58}= +1.03644216 \pm 4.0 \cdot 10^{-4} \) \(a_{59}= -0.23452108 \pm 6.0 \cdot 10^{-4} \) \(a_{60}= -0.32275076 \pm 4.3 \cdot 10^{-4} \)

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