Properties

Label 6.7
Level $6$
Weight $0$
Character 6.1
Symmetry even
\(R\) 6.306363
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: \(6.3063635862299167471318702404 \pm 4 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.97192954 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.44871333 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.68725797 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +1.97215658 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= -0.83800685 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.31728824 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.56114378 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +1.25531527 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= +0.09576926 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.48596477 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.25906476 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -1.39452529 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.13218023 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= -0.05535297 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.59256033 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.22435667 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -0.46591850 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.39678857 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +1.32762435 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.13862513 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -0.88764194 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= +0.43611774 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= -0.31323642 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.06771909 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= +0.48382348 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= -0.34362898 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -0.18335567 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.18318645 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.59489458 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.98607829 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= +0.32397651 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -0.09346554 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= -0.71146143 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= -0.79865635 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.03914046 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.72475661 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -0.41900343 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= -0.40990219 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= +1.91679723 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.15864412 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.05529241 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.32945413 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= +1.37683804 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.28057189 \pm 1.0 \cdot 10^{-8} \)

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