Properties

Label 3.18
Level $3$
Weight $0$
Character 3.1
Symmetry even
\(R\) 12.58046
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(12.5804630570261302059900701126 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.81992642 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.32772066 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.55378752 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.47338474 \pm 1.1 \cdot 10^{-8} \)
\(a_{7}= +0.32162885 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.08863325 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -1.27399144 \pm 1 \cdot 10^{-8} \) \(a_{11}= -1.25679502 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.18920961 \pm 1.1 \cdot 10^{-8} \)
\(a_{13}= -0.29739046 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.26371199 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.89707964 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.56487851 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.70455719 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.27330881 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= -0.71743121 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.50920828 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.18569250 \pm 1.1 \cdot 10^{-8} \)
\(a_{22}= -1.03047944 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.43930859 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.62852270 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +1.41425566 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.24383830 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.10540442 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.37724240 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.73553930 \pm 1.1 \cdot 10^{-8} \)
\(a_{31}= +1.83715693 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.62547444 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.72561094 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.57768505 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.49974289 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.10924022 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= -0.34327806 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.58824081 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.17169846 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +1.69150476 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.50604504 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.15225419 \pm 1.2 \cdot 10^{-8} \)
\(a_{43}= -0.19390637 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.41187770 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.51792917 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +0.36020072 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.45467588 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.32613276 \pm 1.1 \cdot 10^{-8} \)
\(a_{49}= -0.89655488 \pm 1 \cdot 10^{-8} \) \(a_{50}= +1.15958558 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.40677628 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= +0.09746100 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.89731312 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.15779491 \pm 1.1 \cdot 10^{-8} \)
\(a_{55}= +1.95279242 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.35013586 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.41420910 \pm 1.1 \cdot 10^{-8} \)
\(a_{58}= -1.12923743 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.89738720 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.29399153 \pm 1.1 \cdot 10^{-8} \)

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