Properties

Label 3.56
Level $3$
Weight $0$
Character 3.1
Symmetry even
\(R\) 20.54395
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(20.543950241888073385223396372 \pm 7 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.56919335 \pm 2.1 \cdot 10^{-3} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.46236777 \pm 1.3 \cdot 10^{-3} \) \(a_{5}= +1.23489771 \pm 1.8 \cdot 10^{-4} \) \(a_{6}= -0.90597420 \pm 2.1 \cdot 10^{-3} \)
\(a_{7}= -1.26913803 \pm 1.2 \cdot 10^{-3} \) \(a_{8}= -0.72554443 \pm 4.9 \cdot 10^{-4} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -1.93779327 \pm 2.2 \cdot 10^{-4} \) \(a_{11}= -1.25416914 \pm 6.4 \cdot 10^{-4} \) \(a_{12}= +0.84429843 \pm 1.3 \cdot 10^{-3} \)
\(a_{13}= +0.52326480 \pm 8.8 \cdot 10^{-4} \) \(a_{14}= +1.99152295 \pm 1.6 \cdot 10^{-3} \) \(a_{15}= +0.71296852 \pm 1.8 \cdot 10^{-4} \)
\(a_{16}= -0.32384828 \pm 1.8 \cdot 10^{-3} \) \(a_{17}= +1.05276855 \pm 1.5 \cdot 10^{-3} \) \(a_{18}= -0.52306445 \pm 2.1 \cdot 10^{-3} \)
\(a_{19}= +0.39428931 \pm 2.4 \cdot 10^{-3} \) \(a_{20}= +1.80587461 \pm 2.3 \cdot 10^{-4} \) \(a_{21}= -0.73273718 \pm 1.2 \cdot 10^{-3} \)
\(a_{22}= +1.96803388 \pm 8.6 \cdot 10^{-4} \) \(a_{23}= -1.31480939 \pm 5.5 \cdot 10^{-4} \) \(a_{24}= -0.41889327 \pm 4.9 \cdot 10^{-4} \)
\(a_{25}= +0.52497235 \pm 1.5 \cdot 10^{-3} \) \(a_{26}= -0.82110365 \pm 1.2 \cdot 10^{-3} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -1.85594655 \pm 9.9 \cdot 10^{-4} \) \(a_{29}= -1.02112348 \pm 4.0 \cdot 10^{-4} \) \(a_{30}= -1.11878547 \pm 2.3 \cdot 10^{-3} \)
\(a_{31}= +0.16601259 \pm 1.8 \cdot 10^{-3} \) \(a_{32}= +1.23372499 \pm 2.0 \cdot 10^{-3} \) \(a_{33}= -0.72409489 \pm 6.4 \cdot 10^{-4} \)
\(a_{34}= -1.65199741 \pm 2.0 \cdot 10^{-3} \) \(a_{35}= -1.56725564 \pm 1.6 \cdot 10^{-4} \) \(a_{36}= +0.48745592 \pm 1.3 \cdot 10^{-3} \)
\(a_{37}= +1.45877349 \pm 4.1 \cdot 10^{-4} \) \(a_{38}= -0.61871616 \pm 3.3 \cdot 10^{-3} \) \(a_{39}= +0.30210707 \pm 8.8 \cdot 10^{-4} \)
\(a_{40}= -0.89597315 \pm 1.4 \cdot 10^{-4} \) \(a_{41}= -0.51572974 \pm 1.7 \cdot 10^{-3} \) \(a_{42}= +1.14980631 \pm 3.3 \cdot 10^{-3} \)
\(a_{43}= -0.05664547 \pm 3.1 \cdot 10^{-4} \) \(a_{44}= -1.83405653 \pm 5.2 \cdot 10^{-4} \) \(a_{45}= +0.41163257 \pm 1.8 \cdot 10^{-4} \)
\(a_{46}= +2.06319014 \pm 7.9 \cdot 10^{-4} \) \(a_{47}= -1.30848433 \pm 1.6 \cdot 10^{-3} \) \(a_{48}= -0.18697389 \pm 1.8 \cdot 10^{-3} \)
\(a_{49}= +0.61071134 \pm 6.8 \cdot 10^{-4} \) \(a_{50}= -0.82378312 \pm 2.1 \cdot 10^{-3} \) \(a_{51}= +0.60781621 \pm 1.5 \cdot 10^{-3} \)
\(a_{52}= +0.76520558 \pm 8.3 \cdot 10^{-4} \) \(a_{53}= -0.71442960 \pm 4.7 \cdot 10^{-4} \) \(a_{54}= -0.30199140 \pm 2.1 \cdot 10^{-3} \)
\(a_{55}= -1.54877060 \pm 6.6 \cdot 10^{-5} \) \(a_{56}= +0.92081603 \pm 3.6 \cdot 10^{-4} \) \(a_{57}= +0.22764304 \pm 2.4 \cdot 10^{-3} \)
\(a_{58}= +1.60234017 \pm 5.8 \cdot 10^{-4} \) \(a_{59}= -0.90676890 \pm 1.4 \cdot 10^{-4} \) \(a_{60}= +1.04262219 \pm 1.5 \cdot 10^{-3} \)

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