Properties

Label 3.68
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 22.31326
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(22.3132655923334099233402763826 \pm 5 \cdot 10^{-3}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.97517230 \pm 1.4 \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.04903898 \pm 2.5 \) \(a_{5}= +0.79147542 \pm 1.9 \) \(a_{6}= \pm0.56301599 \pm 8.1 \cdot 10^{-1} \)
\(a_{7}= +1.68344869 \pm 1.5 \) \(a_{8}= -1.02299376 \pm 1.7 \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= +0.77182491 \pm 1.1 \) \(a_{11}= +0.21954090 \pm 1.7 \) \(a_{12}= \pm0.02831267 \pm 1.4 \)
\(a_{13}= -1.01551975 \pm 1.7 \) \(a_{14}= +1.64165254 \pm 1.0 \) \(a_{15}= \pm0.45695855 \pm 1.1 \)
\(a_{16}= -0.94855620 \pm 2.0 \) \(a_{17}= +1.33740961 \pm 1.2 \) \(a_{18}= \pm0.32505743 \pm 4.6 \cdot 10^{-1} \)
\(a_{19}= +1.24606861 \pm 1.0 \) \(a_{20}= -0.03881315 \pm 1.8 \) \(a_{21}= \pm0.97193955 \pm 9.1 \cdot 10^{-1} \)
\(a_{22}= +0.21409020 \pm 8.9 \cdot 10^{-1} \) \(a_{23}= -0.18461287 \pm 3.8 \) \(a_{24}= \pm0.59062572 \pm 9.9 \cdot 10^{-1} \)
\(a_{25}= -0.37356666 \pm 1.5 \) \(a_{26}= -0.99030673 \pm 6.0 \cdot 10^{-1} \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= -0.08255460 \pm 1.0 \) \(a_{29}= +0.51611436 \pm 3.6 \) \(a_{30}= \pm0.44561332 \pm 6.4 \cdot 10^{-1} \)
\(a_{31}= +0.81971856 \pm 1.6 \) \(a_{32}= +0.09798802 \pm 2.2 \) \(a_{33}= \pm0.12675200 \pm 1.0 \)
\(a_{34}= +1.30420481 \pm 1.5 \) \(a_{35}= +1.33240826 \pm 7.0 \cdot 10^{-1} \) \(a_{36}= \pm0.01634633 \pm 8.4 \cdot 10^{-1} \)
\(a_{37}= +0.69345325 \pm 1.9 \) \(a_{38}= +1.21513160 \pm 4.7 \cdot 10^{-1} \) \(a_{39}= \pm0.58631060 \pm 9.9 \cdot 10^{-1} \)
\(a_{40}= -0.80967441 \pm 1.0 \) \(a_{41}= +0.76755204 \pm 3.7 \) \(a_{42}= \pm0.94780853 \pm 6.2 \cdot 10^{-1} \)
\(a_{43}= +0.80698243 \pm 2.4 \) \(a_{44}= -0.01076606 \pm 1.5 \) \(a_{45}= \pm0.26382514 \pm 6.4 \cdot 10^{-1} \)
\(a_{46}= -0.18002936 \pm 1.1 \) \(a_{47}= -1.34516381 \pm 3.0 \) \(a_{48}= \pm0.54764918 \pm 1.1 \)
\(a_{49}= +1.83399949 \pm 2.6 \) \(a_{50}= -0.36429186 \pm 7.8 \cdot 10^{-1} \) \(a_{51}= \pm0.77215380 \pm 7.4 \cdot 10^{-1} \)
\(a_{52}= +0.04980005 \pm 1.5 \) \(a_{53}= -0.48172689 \pm 1.5 \) \(a_{54}= \pm0.18767200 \pm 2.7 \cdot 10^{-1} \)
\(a_{55}= +0.17376123 \pm 1.2 \) \(a_{56}= -1.72215750 \pm 1.5 \) \(a_{57}= \pm0.71941805 \pm 6.0 \cdot 10^{-1} \)
\(a_{58}= +0.50330043 \pm 1.5 \) \(a_{59}= +0.57783514 \pm 2.4 \) \(a_{60}= \pm0.02240878 \pm 1.0 \)

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