Properties

Label 3.32
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 15.75323
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(15.7532336884908289702674270888 \pm 5 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.12044299 \pm 5.1 \cdot 10^{-5} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.98549349 \pm 9.3 \cdot 10^{-5} \) \(a_{5}= +0.47652764 \pm 7.1 \cdot 10^{-5} \) \(a_{6}= -0.06953779 \pm 5.1 \cdot 10^{-5} \)
\(a_{7}= +0.03761873 \pm 5.8 \cdot 10^{-5} \) \(a_{8}= +0.23913876 \pm 6.3 \cdot 10^{-5} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.05739441 \pm 4.0 \cdot 10^{-5} \) \(a_{11}= -1.18366316 \pm 6.4 \cdot 10^{-5} \) \(a_{12}= -0.56897493 \pm 9.3 \cdot 10^{-5} \)
\(a_{13}= +1.03533166 \pm 6.3 \cdot 10^{-5} \) \(a_{14}= -0.00453091 \pm 4.0 \cdot 10^{-5} \) \(a_{15}= +0.27512336 \pm 7.1 \cdot 10^{-5} \)
\(a_{16}= +0.95669090 \pm 7.5 \cdot 10^{-5} \) \(a_{17}= +1.33804212 \pm 4.7 \cdot 10^{-5} \) \(a_{18}= -0.04014766 \pm 5.1 \cdot 10^{-5} \)
\(a_{19}= +1.39631786 \pm 3.8 \cdot 10^{-5} \) \(a_{20}= -0.46961489 \pm 6.6 \cdot 10^{-5} \) \(a_{21}= +0.02171919 \pm 5.8 \cdot 10^{-5} \)
\(a_{22}= +0.14256392 \pm 3.2 \cdot 10^{-5} \) \(a_{23}= +1.28561551 \pm 1.4 \cdot 10^{-4} \) \(a_{24}= +0.13806683 \pm 6.3 \cdot 10^{-5} \)
\(a_{25}= -0.77292141 \pm 5.8 \cdot 10^{-5} \) \(a_{26}= -0.12469844 \pm 2.2 \cdot 10^{-5} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.03707302 \pm 3.8 \cdot 10^{-5} \) \(a_{29}= +0.13659671 \pm 1.3 \cdot 10^{-4} \) \(a_{30}= -0.03313668 \pm 1.2 \cdot 10^{-4} \)
\(a_{31}= +0.98573108 \pm 6.0 \cdot 10^{-5} \) \(a_{32}= -0.35436547 \pm 8.4 \cdot 10^{-5} \) \(a_{33}= -0.68338824 \pm 6.4 \cdot 10^{-5} \)
\(a_{34}= -0.16115779 \pm 5.7 \cdot 10^{-5} \) \(a_{35}= +0.01792637 \pm 2.5 \cdot 10^{-5} \) \(a_{36}= -0.32849783 \pm 9.3 \cdot 10^{-5} \)
\(a_{37}= +0.86623114 \pm 7.2 \cdot 10^{-5} \) \(a_{38}= -0.16817669 \pm 1.7 \cdot 10^{-5} \) \(a_{39}= +0.59774901 \pm 6.3 \cdot 10^{-5} \)
\(a_{40}= +0.11395623 \pm 3.9 \cdot 10^{-5} \) \(a_{41}= -0.47592056 \pm 1.3 \cdot 10^{-4} \) \(a_{42}= -0.00261592 \pm 1.1 \cdot 10^{-4} \)
\(a_{43}= -1.74460158 \pm 9.1 \cdot 10^{-5} \) \(a_{44}= +1.16649233 \pm 5.7 \cdot 10^{-5} \) \(a_{45}= +0.15884255 \pm 7.1 \cdot 10^{-5} \)
\(a_{46}= -0.15484337 \pm 4.1 \cdot 10^{-5} \) \(a_{47}= +0.71850691 \pm 1.1 \cdot 10^{-4} \) \(a_{48}= +0.55234575 \pm 7.6 \cdot 10^{-5} \)
\(a_{49}= -0.99858483 \pm 9.8 \cdot 10^{-5} \) \(a_{50}= +0.09309296 \pm 2.8 \cdot 10^{-5} \) \(a_{51}= +0.77251898 \pm 4.7 \cdot 10^{-5} \)
\(a_{52}= -1.02031261 \pm 5.7 \cdot 10^{-5} \) \(a_{53}= -0.07034417 \pm 5.6 \cdot 10^{-5} \) \(a_{54}= -0.02317926 \pm 5.1 \cdot 10^{-5} \)
\(a_{55}= -0.56404821 \pm 4.5 \cdot 10^{-5} \) \(a_{56}= +0.00899610 \pm 5.6 \cdot 10^{-5} \) \(a_{57}= +0.80616449 \pm 3.8 \cdot 10^{-5} \)
\(a_{58}= -0.01645212 \pm 5.5 \cdot 10^{-5} \) \(a_{59}= +1.42692944 \pm 9.1 \cdot 10^{-5} \) \(a_{60}= -0.27113228 \pm 1.6 \cdot 10^{-4} \)

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