Properties

Label 3.50
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 19.17596
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(19.1759646544262442089015364564 \pm 2 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.79105220 \pm 2.8 \cdot 10^{-2} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.37423642 \pm 5.1 \cdot 10^{-2} \) \(a_{5}= -1.37664488 \pm 3.9 \cdot 10^{-2} \) \(a_{6}= -0.45671420 \pm 2.8 \cdot 10^{-2} \)
\(a_{7}= -1.12032810 \pm 3.2 \cdot 10^{-2} \) \(a_{8}= +1.08709274 \pm 3.4 \cdot 10^{-2} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +1.08899796 \pm 2.2 \cdot 10^{-2} \) \(a_{11}= -1.71520147 \pm 3.5 \cdot 10^{-2} \) \(a_{12}= -0.21606550 \pm 5.1 \cdot 10^{-2} \)
\(a_{13}= -0.44729529 \pm 3.4 \cdot 10^{-2} \) \(a_{14}= +0.88623801 \pm 2.2 \cdot 10^{-2} \) \(a_{15}= -0.79480629 \pm 3.9 \cdot 10^{-2} \)
\(a_{16}= -0.48571068 \pm 4.1 \cdot 10^{-2} \) \(a_{17}= -0.42943391 \pm 2.6 \cdot 10^{-2} \) \(a_{18}= -0.26368407 \pm 2.8 \cdot 10^{-2} \)
\(a_{19}= -0.85596626 \pm 2.1 \cdot 10^{-2} \) \(a_{20}= +0.51519065 \pm 3.6 \cdot 10^{-2} \) \(a_{21}= -0.64682173 \pm 3.2 \cdot 10^{-2} \)
\(a_{22}= +1.35681389 \pm 1.8 \cdot 10^{-2} \) \(a_{23}= +0.71058831 \pm 7.8 \cdot 10^{-2} \) \(a_{24}= +0.62763329 \pm 3.4 \cdot 10^{-2} \)
\(a_{25}= +0.89515114 \pm 3.2 \cdot 10^{-2} \) \(a_{26}= +0.35383392 \pm 1.2 \cdot 10^{-2} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.41926758 \pm 2.1 \cdot 10^{-2} \) \(a_{29}= +1.04035634 \pm 7.4 \cdot 10^{-2} \) \(a_{30}= +0.62873327 \pm 6.7 \cdot 10^{-2} \)
\(a_{31}= +0.62799514 \pm 3.3 \cdot 10^{-2} \) \(a_{32}= -0.70287024 \pm 4.6 \cdot 10^{-2} \) \(a_{33}= -0.99027203 \pm 3.5 \cdot 10^{-2} \)
\(a_{34}= +0.33970463 \pm 3.1 \cdot 10^{-2} \) \(a_{35}= +1.54229395 \pm 1.4 \cdot 10^{-2} \) \(a_{36}= -0.12474547 \pm 5.1 \cdot 10^{-2} \)
\(a_{37}= -0.22485173 \pm 3.9 \cdot 10^{-2} \) \(a_{38}= +0.67711399 \pm 9.6 \cdot 10^{-3} \) \(a_{39}= -0.25824606 \pm 3.4 \cdot 10^{-2} \)
\(a_{40}= -1.49654066 \pm 2.1 \cdot 10^{-2} \) \(a_{41}= +0.31215390 \pm 7.5 \cdot 10^{-2} \) \(a_{42}= +0.51166975 \pm 6.0 \cdot 10^{-2} \)
\(a_{43}= +0.28122374 \pm 5.0 \cdot 10^{-2} \) \(a_{44}= +0.64189086 \pm 3.1 \cdot 10^{-2} \) \(a_{45}= -0.45888163 \pm 3.9 \cdot 10^{-2} \)
\(a_{46}= -0.56211244 \pm 2.2 \cdot 10^{-2} \) \(a_{47}= +0.73891609 \pm 6.2 \cdot 10^{-2} \) \(a_{48}= -0.28042519 \pm 4.1 \cdot 10^{-2} \)
\(a_{49}= +0.25513506 \pm 5.4 \cdot 10^{-2} \) \(a_{50}= -0.70811128 \pm 1.5 \cdot 10^{-2} \) \(a_{51}= -0.24793378 \pm 2.6 \cdot 10^{-2} \)
\(a_{52}= +0.16739419 \pm 3.1 \cdot 10^{-2} \) \(a_{53}= -0.04890870 \pm 3.1 \cdot 10^{-2} \) \(a_{54}= -0.15223807 \pm 2.8 \cdot 10^{-2} \)
\(a_{55}= +2.36122332 \pm 2.4 \cdot 10^{-2} \) \(a_{56}= -1.21790055 \pm 3.0 \cdot 10^{-2} \) \(a_{57}= -0.49419235 \pm 2.1 \cdot 10^{-2} \)
\(a_{58}= -0.82297617 \pm 3.0 \cdot 10^{-2} \) \(a_{59}= +1.43856395 \pm 5.0 \cdot 10^{-2} \) \(a_{60}= +0.29744546 \pm 9.0 \cdot 10^{-2} \)

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