Properties

Label 6.25
Level $6$
Weight $0$
Character 6.1
Symmetry even
\(R\) 12.35443
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: \(12.3544320764145925864501458165 \pm 7 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.15375910 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.63080242 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.10872411 \pm 1.1 \cdot 10^{-8} \) \(a_{11}= -1.39010958 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= -1.19311603 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.44604467 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.08877286 \pm 1.1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.59084470 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= +1.39361270 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.07687955 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= +0.36419395 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.98295591 \pm 1.1 \cdot 10^{-8} \) \(a_{23}= +1.17196879 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= -0.97635814 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.84366043 \pm 1.1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.31540121 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +0.77742728 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.06277189 \pm 1.1 \cdot 10^{-8} \)
\(a_{31}= +0.54113220 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.80258014 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= -0.41779030 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= -0.09699162 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= -0.94225178 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.98543299 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= +0.68884586 \pm 1.1 \cdot 10^{-8} \)
\(a_{40}= -0.05436205 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= +1.05991310 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.25752401 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +1.78298098 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.69505479 \pm 1.1 \cdot 10^{-8} \) \(a_{45}= +0.05125303 \pm 1.1 \cdot 10^{-8} \)
\(a_{46}= -0.82870708 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= -0.47895242 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= -0.60208830 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.69038946 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.34112435 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -0.59655801 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= +1.64402471 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= -0.21374200 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.22302234 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.80460267 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= -0.54972410 \pm 1.1 \cdot 10^{-8} \) \(a_{59}= +1.76826089 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.04438643 \pm 1.1 \cdot 10^{-8} \)

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