Properties

Label 3.77
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 23.53696
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: \(23.5369697072833267647159243432 \pm 7 \cdot 10^{-3}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.78195708 \pm 4.6 \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.17537102 \pm 8.3 \) \(a_{5}= +0.49755211 \pm 6.3 \) \(a_{6}= \pm1.02881340 \pm 2.6 \)
\(a_{7}= -1.18166936 \pm 5.2 \) \(a_{8}= +2.09446070 \pm 5.6 \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= +0.88661651 \pm 3.6 \) \(a_{11}= +1.76544377 \pm 5.7 \) \(a_{12}= \pm1.25595104 \pm 4.8 \)
\(a_{13}= +0.47906640 \pm 5.6 \) \(a_{14}= -2.10568407 \pm 3.5 \) \(a_{15}= \pm0.28726185 \pm 3.6 \)
\(a_{16}= +1.55686805 \pm 6.7 \) \(a_{17}= +0.13502687 \pm 4.2 \) \(a_{18}= \pm0.59398569 \pm 1.5 \)
\(a_{19}= +1.53145319 \pm 3.4 \) \(a_{20}= +1.08236045 \pm 5.9 \) \(a_{21}= \pm0.68223712 \pm 3.0 \)
\(a_{22}= +3.14594502 \pm 2.9 \) \(a_{23}= -0.47912024 \pm 12. \) \(a_{24}= \pm1.20923745 \pm 3.2 \)
\(a_{25}= -0.75244189 \pm 5.2 \) \(a_{26}= +0.85367577 \pm 1.9 \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= -2.57056927 \pm 3.4 \) \(a_{29}= +0.36387615 \pm 12. \) \(a_{30}= \pm0.51188828 \pm 2.1 \)
\(a_{31}= -1.15441263 \pm 5.3 \) \(a_{32}= +0.67981133 \pm 7.5 \) \(a_{33}= \pm1.01927944 \pm 3.3 \)
\(a_{34}= +0.24061208 \pm 5.1 \) \(a_{35}= -0.58794209 \pm 2.3 \) \(a_{36}= \pm0.72512367 \pm 2.7 \)
\(a_{37}= +0.37769440 \pm 6.4 \) \(a_{38}= +2.72898385 \pm 1.5 \) \(a_{39}= \pm0.27658912 \pm 3.2 \)
\(a_{40}= +1.04210335 \pm 3.4 \) \(a_{41}= -0.76651427 \pm 12. \) \(a_{42}= \pm1.21571726 \pm 2.0 \)
\(a_{43}= +0.12248149 \pm 8.1 \) \(a_{44}= +3.84049522 \pm 5.1 \) \(a_{45}= \pm0.16585070 \pm 2.1 \)
\(a_{46}= -0.85377170 \pm 3.6 \) \(a_{47}= -0.60210873 \pm 10. \) \(a_{48}= \pm0.89885819 \pm 3.9 \)
\(a_{49}= +0.39634247 \pm 8.8 \) \(a_{50}= -1.34081916 \pm 2.5 \) \(a_{51}= \pm0.07795780 \pm 2.4 \)
\(a_{52}= +1.04214717 \pm 5.1 \) \(a_{53}= +0.21564081 \pm 5.0 \) \(a_{54}= \pm0.34293780 \pm 8.8 \cdot 10^{-1} \)
\(a_{55}= +0.87840028 \pm 4.0 \) \(a_{56}= -2.47496003 \pm 5.0 \) \(a_{57}= \pm0.88418491 \pm 1.9 \)
\(a_{58}= +0.64841167 \pm 4.9 \) \(a_{59}= -1.02015336 \pm 8.1 \) \(a_{60}= \pm0.62490110 \pm 3.4 \)

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