Properties

Label 6.6
Level $6$
Weight $0$
Character 6.1
Symmetry even
\(R\) 6.000335
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: \(6.00033540887598789021624611965 \pm 4 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +1.47084202 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.82328806 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +1.04004237 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.89776907 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= -0.41129702 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.58215257 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.84919104 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.91050557 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.23570226 \pm 7.3 \cdot 10^{-8} \)
\(a_{19}= +0.82911532 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.73542101 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.47532558 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.63481860 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= -1.44777894 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8} \)
\(a_{25}= +1.16337625 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.29083091 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.41164403 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +1.15365904 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.60046874 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -0.56882740 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.51832722 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -0.64382466 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= -1.21092667 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= +0.64792352 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.58627307 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -0.23746244 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +0.52002118 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +0.14829216 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.33610594 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +1.24886798 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.44888454 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= +0.49028067 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -1.02373430 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= -0.86283616 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7} \)
\(a_{49}= -0.32219678 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.82263123 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.52568064 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -0.20564851 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +0.93720373 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7} \)
\(a_{55}= -1.32047647 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.29107628 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.47868996 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.81576013 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= +0.26506928 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.42459552 \pm 1.0 \cdot 10^{-8} \)

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