Properties

Label 3.64
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 21.61265
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(21.6126500168040455946989560285 \pm 2 \cdot 10^{-3}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.90379959 \pm 2.0 \cdot 10^{-1} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.62445287 \pm 3.7 \cdot 10^{-1} \) \(a_{5}= +0.23860218 \pm 2.8 \cdot 10^{-1} \) \(a_{6}= +1.09915920 \pm 2.0 \cdot 10^{-1} \)
\(a_{7}= -1.31532827 \pm 2.3 \cdot 10^{-1} \) \(a_{8}= -3.09263270 \pm 2.5 \cdot 10^{-1} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.45425074 \pm 1.6 \cdot 10^{-1} \) \(a_{11}= +0.41870906 \pm 2.5 \cdot 10^{-1} \) \(a_{12}= -1.51522857 \pm 3.7 \cdot 10^{-1} \)
\(a_{13}= -0.68605132 \pm 2.5 \cdot 10^{-1} \) \(a_{14}= +2.50412141 \pm 1.5 \cdot 10^{-1} \) \(a_{15}= -0.13775704 \pm 2.8 \cdot 10^{-1} \)
\(a_{16}= +3.26329999 \pm 3.0 \cdot 10^{-1} \) \(a_{17}= +0.53331817 \pm 1.8 \cdot 10^{-1} \) \(a_{18}= -0.63459986 \pm 2.0 \cdot 10^{-1} \)
\(a_{19}= +0.68801104 \pm 1.5 \cdot 10^{-1} \) \(a_{20}= +0.62620019 \pm 2.6 \cdot 10^{-1} \) \(a_{21}= +0.75940513 \pm 2.3 \cdot 10^{-1} \)
\(a_{22}= -0.79713814 \pm 1.3 \cdot 10^{-1} \) \(a_{23}= +0.89149049 \pm 5.6 \cdot 10^{-1} \) \(a_{24}= +1.78553232 \pm 2.5 \cdot 10^{-1} \)
\(a_{25}= -0.94306900 \pm 2.3 \cdot 10^{-1} \) \(a_{26}= +1.30610422 \pm 8.8 \cdot 10^{-2} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -3.45201704 \pm 1.5 \cdot 10^{-1} \) \(a_{29}= +1.26885256 \pm 5.3 \cdot 10^{-1} \) \(a_{30}= +0.26226179 \pm 4.8 \cdot 10^{-1} \)
\(a_{31}= +0.37871522 \pm 2.3 \cdot 10^{-1} \) \(a_{32}= -3.12003648 \pm 3.3 \cdot 10^{-1} \) \(a_{33}= -0.24174179 \pm 2.5 \cdot 10^{-1} \)
\(a_{34}= -1.01533091 \pm 2.2 \cdot 10^{-1} \) \(a_{35}= -0.31384020 \pm 1.0 \cdot 10^{-1} \) \(a_{36}= +0.87481762 \pm 3.7 \cdot 10^{-1} \)
\(a_{37}= -0.43297660 \pm 2.8 \cdot 10^{-1} \) \(a_{38}= -1.30983513 \pm 6.9 \cdot 10^{-2} \) \(a_{39}= +0.39609191 \pm 2.5 \cdot 10^{-1} \)
\(a_{40}= -0.73790892 \pm 1.5 \cdot 10^{-1} \) \(a_{41}= +0.53662619 \pm 5.4 \cdot 10^{-1} \) \(a_{42}= -1.44575517 \pm 4.3 \cdot 10^{-1} \)
\(a_{43}= +0.32046125 \pm 3.6 \cdot 10^{-1} \) \(a_{44}= +1.09888220 \pm 2.2 \cdot 10^{-1} \) \(a_{45}= +0.07953406 \pm 2.8 \cdot 10^{-1} \)
\(a_{46}= -1.69721923 \pm 1.6 \cdot 10^{-1} \) \(a_{47}= +1.62309674 \pm 4.5 \cdot 10^{-1} \) \(a_{48}= -1.88406713 \pm 3.0 \cdot 10^{-1} \)
\(a_{49}= +0.73008845 \pm 3.9 \cdot 10^{-1} \) \(a_{50}= +1.79541437 \pm 1.1 \cdot 10^{-1} \) \(a_{51}= -0.30791139 \pm 1.8 \cdot 10^{-1} \)
\(a_{52}= -1.80050935 \pm 2.2 \cdot 10^{-1} \) \(a_{53}= -1.17850484 \pm 2.2 \cdot 10^{-1} \) \(a_{54}= +0.36638640 \pm 2.0 \cdot 10^{-1} \)
\(a_{55}= +0.09990490 \pm 1.8 \cdot 10^{-1} \) \(a_{56}= +4.06782721 \pm 2.2 \cdot 10^{-1} \) \(a_{57}= -0.39722336 \pm 1.5 \cdot 10^{-1} \)
\(a_{58}= -2.41564097 \pm 2.2 \cdot 10^{-1} \) \(a_{59}= -0.18564958 \pm 3.6 \cdot 10^{-1} \) \(a_{60}= -0.36153685 \pm 6.5 \cdot 10^{-1} \)

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