Properties

Label 6.21
Level $6$
Weight $0$
Character 6.1
Symmetry even
\(R\) 11.31308
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: \(11.3130895988813168021058701142 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.14054347 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +1.15074894 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.09937924 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.99003837 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= +1.12273858 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.81370238 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.08114281 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.58801406 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= +1.90355331 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.07027174 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= +0.66438521 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.70006284 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.35455201 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= -0.98024753 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.79389607 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.57537447 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +0.81829811 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.05737663 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -1.19963417 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.57159892 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.41578873 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= -0.16173025 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= -0.83256764 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.34601545 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= +0.64821342 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= -0.04968962 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -1.52261685 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.46979129 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.97696308 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.49501918 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.04684782 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +0.25070613 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= -1.22991819 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= +0.32422313 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.69313968 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= +0.33949007 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= +0.56136929 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= -0.15975122 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= +0.13914343 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.40685119 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +1.09901701 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.57862414 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= -1.47834962 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.04057141 \pm 1.0 \cdot 10^{-8} \)

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